Development of an efficient solar drying system

QUEENSLAND UNIVERSITY OF TECHNOLOGY

Thesis final report Development of an efficient solar drying system

Erond Perez N7341113

Supervised by: Dr. Zakaria Amin and Dr. Azharul Karim

Development of an efficient solar drying system Erond Perez – n7341113

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Table of contents

1. Research topic ..................................................................................................................................... 3

2. Background ......................................................................................................................................... 3

3. Outline of the Project .......................................................................................................................... 6

4. Statement of work .............................................................................................................................. 6

5. Solar drying system components ........................................................................................................ 9

5.1 Solar air collector .......................................................................................................................... 9

5.2 Thermal storage tank .................................................................................................................. 10

5.3 Blower ......................................................................................................................................... 11

5.4 Auxiliary Heater........................................................................................................................... 11

5.5 Drying chamber ........................................................................................................................... 11

5.6 Dehumidifier ............................................................................................................................... 11

5.7 Ducts and mixing chamber ......................................................................................................... 12

6. Mathematical model formulation ..................................................................................................... 12

6.1 Mathematical modelling of the solar collector ........................................................................... 13

6.1.1 Thermal network .................................................................................................................. 14

6.1.2 Energy balance ..................................................................................................................... 15

6.1.3 Heat transfer coefficients .................................................................................................... 16

6.1.4 Matrix method solution for a double-pass counter flow v-groove ..................................... 21

6.2 Mathematical modelling of the thermal storage tank ................................................................ 22

6.2.1 Nodal element temperature ................................................................................................ 23

6.3. Mathematical modelling of mixing tank .................................................................................... 24

6.4 Mathematical modelling of the heater ....................................................................................... 26

6.5 Mathematical modelling of the drying chamber ........................................................................ 26

6.5.1 Material model ..................................................................................................................... 27

6.5.2 Equipment model ................................................................................................................. 28

6.6 Mathematical modelling of the dehumidifier ............................................................................. 29

6.7 Mathematical modelling of system pressure loss ...................................................................... 30

6.7.1 Pressure loss in the solar collector ...................................................................................... 30

6.7.2 Pressure loss in the storage tank ......................................................................................... 31

6.7.3 Pressure loss in the ducts ..................................................................................................... 31

6.8 MATLAB Simulation .................................................................................................................... 32


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7. Simulation results and discussion ..................................................................................................... 32

7.1 Solar air collector ........................................................................................................................ 33

7.2 Verifying simulation model of solar air collector ........................................................................ 38

7.3 Parametric study of the solar air collector ................................................................................. 41

7.3.1 Solar radiation ...................................................................................................................... 41

7.3.2 Mass flow rate ...................................................................................................................... 42

7.3.3 Inlet air temperature ........................................................................................................... 43

7.3.4 Length of solar collector ...................................................................................................... 45

7.3.5 V-groove height .................................................................................................................... 46

7.3.6 V-groove gap to glass cover ................................................................................................. 48

7.3 Parametric study of the solar air collector ................................................................................. 53

8. Problems encountered ..................................................................................................................... 59

9. Project plan ....................................................................................................................................... 61

10. Conclusion ....................................................................................................................................... 65

References ............................................................................................................................................ 66

Parametric values used for simulation ................................................................................................. 69

Nomenclature ....................................................................................................................................... 70


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Thesis Final Report

Development of an efficient solar drying system

By: Erond Perez

1. Research topic

One of the most potential applications of solar energy is the solar drying of

agricultural products. The drying of fruits and vegetables demands special attention, as

these are considered important sources of vitamins and minerals essential for mankind.

Most fruits and vegetables contain more than 80% water and are, therefore, highly

perishable. The post-harvest losses of agriculture products in the rural areas can be reduced

drastically by using well designed solar drying system.

A new solar drying system is developed in this project which has higher efficiency

and more reliable. By incorporating the high efficiency solar collector configuration found by

Dr Azharul Karim, a more efficient and high capacity thermal storage, an optimized air

condition at the inlet of the drying chamber for faster drying and higher quality product, and

a dehumidifier at the outlet of the drying chamber for air recirculation, a new solar drying

system is produced. Furthermore, this design is able to operate even at times of low

sunlight or night time thus enabling the system to be used for long hours.

2. Background

World population will continuously increase and around 80% of the world population

will be living in developing countries. In effect, population-food imbalance will also continue

to increase. To keep up with the demands of the fast growing population, agricultural


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production must also increase. However, extending agricultural lands might not be possible

in the next decades and will be difficult to maintain. Another solution to the world’s food

problems will be by greatly reducing the food losses which occurs throughout the food

production, harvest, post - harvest and marketing. Nearly 10 to 40% of production in

developing countries never reaches the consumer due to various reasons such as spoilage,

waste and pest [1]. Food losses can be reduced by using various preservation techniques

such as food drying.

Drying is a basic operation in various industries. Due to the latent heat of

vaporization that must be supplied, thermal drying could be the most energy intensive of

the major industrial processes [2]. It accounts for up to 15% of all industrial energy usage

[3]thus improving its efficiency even by a bit can lead to significant operational savings.

Drying is the process of moisture removal due to simultaneous heat and mass transfer [4].

One of the oldest applications of solar energy is drying by exposure to sun [5]. Food drying is

one of the oldest methods of preserving food for later use and even from prehistoric times,

solar energy is used to dry and preserve all necessary foodstuffs for winter time [5] [6]. Most

fruits and vegetables generally contains 25 to 80% water thus making them highly

perishable [5] [7]. Once the moisture content is reduced to a certain level, it restricts the

growth of enzymes, bacteria, yeasts and molds [4] which are causes of spoilage, thus

increasing its shelf life and enables it to be transported over long distances.

Small farmers in developing countries who produce more than 80% of the food only

have access to traditional sun drying techniques [1]. Traditional sun drying is a slow process

and reduces the quality of the product. This is due to insect infestation, enzymatic reactions,

microorganism growth and mycotoxin development. And since sun drying is done under the


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open sky, spoilage of product due to adverse climatic condition such as rain, wind, moist

and dust, deterioration of the material by decomposition, insect infestation and fungal

growth may occur. It is also labour extensive, time consuming and requires large area. On

the other hand, the use of mechanical drying using fossil fuel or electricity will solve quality

problem with traditional sun drying but is highly energy intensive and expensive.

Furthermore, most small farmers cannot afford this technology and fossil fuel [1] [4] [8] [9].

These drawbacks can be solved by the use of solar dryer except the initial cost, thus to get

successful investment returns, the solar dryer needs to be efficient [5] [8] [9].

As mentioned previously, solar drying offers almost no disadvantage except its high

initial cost for the dryer, the collector field and all necessary auxiliary equipment such as

ducts, pipes, blower, control and measurement instruments and perhaps a skilled operator

of the drying process [5].

To successfully develop an efficient solar drying system, it is important to design an

air collector of high efficiency since it is one of the main components and would lead to a

better performance of the system [10]. Flat plate air collectors are widely used however, out

of the three collector plates (namely flat plate, v-corrugated and finned air collectors)

studied in [7], v-corrugated collector has higher efficiency thus considered to be better for

the solar drying system. The efficiency is further increased in double pass operation and

optimal flow rate is determined to be 0.035 𝑘𝑔/𝑚2𝑠 [7].

A need arises to consider a new design approach and to enhance what was

previously done. This project will be based on the previous work of Dr Azharul Karim.


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3. Outline of the Project

The ever increasing demand for food calls for an increase in food production. One

way to meet up with this demand is to reduce the losses in production which are estimated

to be 10 to 40%. To reduce the losses, drying is a preservation technique which reduces the

moisture content of the material, consequently increasing its shelf life and allows it to be

transported over long distances.

This project aims to

Contribute on the existing knowledge in solar drying and provide new insights in

effective and efficient designs

Aid in the reduction of production losses due to lack of proper solar drying facilities

in developing countries

Successfully develop an efficient solar drying system that yield high quality product

Propose design approach and construction method of the developed solar dryer

Build and test the performance of the developed solar dryer

4. Statement of work

A background research and literature review was done on existing literature

regarding solar air collectors and their applications in food drying. Journal articles with

topics about mathematical modelling and performance simulation of solar dryer are looked

upon. References [9-16] are particularly useful at this stage because of their discussion of

mathematical equations needed for modelling the air collector. S. Janjai [11] examined

various solar dryers in terms of drying performance, product quality and economics in the


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rural areas of the tropics and subtropics while R. Tchinda [12] investigated the mathematical

models for predicting the performance of solar air heaters. Various mathematical models to

analyse the heat transfer process involved are reviewed and classified based on the air

collector characteristic. Papers by R. Smitabhindu et al [13] and K. E. J. Al-Juamily et al [14]

constructed a drying system and tested its drying performance. It is then compared to their

mathematical model. From their tests, the resulting dried materials were confirmed to be at

required standards.

The solar air collector being investigated is a double-pass counter flow v-grove air

collector in which the inlet air initially flows at the top part of the collector and changes

direction once it reaches the end of the collector and flows below the collector to the

outlet. This configuration of air collector is found by M. N. A. Hawlader M. A. Karim [10] to

be more efficient than a single pass however, the pressure drop was not considered during

the investigation but it is expected that a double-pass configuration will have a higher

pressure loss which would lead to requiring a larger air circulator compared to single pass

thus increasing electricity consumption.

In creating a mathematical model for a double-pass counter flow v-groove,

numerous literature were investigated and the analytical models of the most relevant

papers [13-16] are referred to and combined since there is no published paper that showed

the simulation model for double-pass counter flow v-groove. The configurations that were

found were about two-pass parallel flow flat plate [15], single pass v-groove [16], two-pass

parallel flow v-groove [17], and double-pass counter flow flat plate [18] [19].

The energy balance equation used for the simulation is obtained from [15] which

investigated a two-pass parallel flow flat plate. Energy balance for parallel flow is also valid


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for counter flow since the equations are independent of the air flow direction [18]. Then the

equation for calculating Nusselt number, heat transfer coefficients and other variables that

defines a v-groove collector is obtained from [16] [17], then the equation to calculate the

instantaneous temperature of the air along the length of the collector is found in [18].

Matrix method is used to solve for the temperature and heat transfer coefficient of the air

collector similar to what is used in [15]. Once the temperature and heat transfer coefficients

were determined, the performance of the air collector can be predicted.

The output air of the solar collector then goes to the branched section in which the

air flow is divided. The amount of air flow in each branch depends on the current setting of

the valves and condition of the air. If the output air of the solar collector exceeds the

current requirement at the drying chamber, higher percentage of the air will go through the

thermal storage tank. If the air condition is just enough for drying, then higher percentage of

the air flow will flow straight to the drying chamber. Otherwise, a 50-50 flow will be set and

some air flows to the thermal storage and some will flow straight to the drying chamber.

Varying the air flow leads to a more flexible system that is more reliable and operates at

optimum conditions. At times of low sunlight or when it is night time, the stored energy in

the thermal storage will be discharged thus allowing the air to be used for drying. The

auxiliary heater at the inlet of the drying chamber is used for back up heating or in keeping

the air temperature at the inlet of the drying chamber constant. At the outlet of the drying

chamber, the air is expected to have higher moisture content due to the drying process thus

for air recirculation purposes, a dehumidifier is added. Later in this report, a parametric

study will be presented and it was determined that increasing the inlet temperature at the

solar collector increases the outlet temperature but reduces the efficiency. Thus a trade-off

exists. If the temperature at the outlet of the solar collector is higher, the use of the


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auxiliary heater is minimized however the efficiency of the collector is lower and more solar

energy is left unutilized. To determine the optimized operation, a MATLAB simulation of all

the components and the whole system must be developed. Once a system simulation for

the solar dryer is achieved, the performance of the system can be predicted and optimized.

5. Solar drying system components

The principal components of solar drying systems are solar air collector which is used for

heating ambient air, a drying unit where the drying of material takes place and air extracts

moisture from the product and the air handling unit which circulates the air [20]. And

additionally a thermal storage tank is added to store energy for later use. Presented in this

section is each component of the solar drying system explained in detail. The description

and designs are taken from Dave Molde’s report.

Figure 1. Solar drying system components

5.1 Solar air collector

The solar collector is the main component of a solar drying system. It transforms the

radiant energy from the sun into usable heat [21]. The design of efficient and suitable air

collectors is one of the most important factors controlling the economics of solar drying [7].

The efficiency of the solar drying system is greatly affected by the efficiency of the solar

collector [9]. Therefore it is important that the collector to be used in the system has high

efficiency. In response to this requirement, a double-pass counter flow v-groove is selected

for the system in consideration since according to the studies done by [17] [10], this kind of

configuration will yield the highest efficiency.


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The main components of the air collector are the glass cover, the absorber plate, the

back plate and insulation. The air will pass on the top of the absorber plate first then once it

reaches the end of the collector, a bend directs the air to flow at the bottom and opposite

its initial direction. Through this process the air absorbs energy thus increasing its

temperature.

5.2 Thermal storage tank

Energy storage plays a very important role in conserving energy and improving the

performance and reliability of a wide range of energy systems especially if the energy source

is intermittent such as solar [22]. Thermal storage provides balance on the supply and

demand of heat over a certain period of time [23].

Both sensible (i.e rocks) and latent (phase change materials, PCM) heat storage

materials can be used for thermal storage units in solar systems [24]. The heat storage

medium used for our system is a rock bed thermal storage which uses rocks to store energy

from the air when passing through the system. To make the energy transfer more efficient,

a conical geometry for the storage tank is selected instead of the traditional cylindrical

shape. According to experiments done by Zanganeh G. et.al [25] this type of configuration

provides better efficiency and heat transfer thus it is adopted for our drying system. The

heated air flows from the solar collectors into the thermal storage tank from the top which

consequently transfers thermal energy and charges the rock bed. The stored energy is

recovered by reversing the air circulation flow in the storage tank [22].


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5.3 Blower

The blower is used for circulating air around the system. This component pulls air

through the collector, creating a slight negative pressure inside the collector. The flow rate

is controlled by controlling the fan speed and adjusting the dampers [9].

5.4 Auxiliary Heater

The purpose of the heater is to increase the temperature of the air to the desired

temperature before entering the drying chamber. It assists in maintaining the air condition

at the drying chamber to optimum condition thus keeping the air temperature ideal for

drying at all times.

5.5 Drying chamber

The materials to be dried are placed in the drying chamber. This is where the process

of drying takes place and where the heated air extracts moisture from the material [20]. The

purpose of a dryer is to supply the product with heat by conduction and convection from

the surrounding air more than that available under ambient conditions at temperatures

above that of the product, or conduction from heated surfaces in contact with the product

[26]. The chamber must be able to contain heat with minimum losses to maximize the

drying effect, thus insulation are added. Some rules of thumb in the design of drying

chambers is that there should be at least 50mm distance between trays and that each

square meter of tray area should contain 5 to 10kg of material to be dried [27].

5.6 Dehumidifier

The performance of the dehumidifier in terms of moisture removal will vary with the

condition of the incoming air [28]. The air that will leave the drying chamber has higher

moisture content compared to the condition of air beforehand. The dehumidifier removes


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the moisture absorbed by the air at the drying chamber for recirculation. Recirculating the

air at the chamber outlet increases the inlet air temperature of the solar collector which

affects it performance.

5.7 Ducts and mixing chamber

Ducts are used to transport air from one component to the next. A flexible circular

duct s used in the system. The mixing chamber is a simple device which evenly mixes the air

that enters through it. There are two inlets to the mixing tank. One is from the thermal

storage tank and one is directly from the solar air collector. The mixing chamber, although

simple, has an important role in ensuring efficient and reliable performance of the solar

drying system.

6. Mathematical model formulation

Defining the behaviours of real world processes are complicated and difficult. And to

describe them with sufficient accuracy, the difficulties arising from lack of knowledge about

parts of a process have to be overcome [29]. Therefore, a necessary step in understanding

and predicting the performance of the solar drying system is to formulate mathematical

models that will represent the performance and characteristics of each component.

Furthermore, with the help of mathematical models, it will be possible to determine how

the system performance will be if the operating parameter of a component is changed thus

allowing the opportunity for system optimization. Performing a mathematical model of the

system before construction of the solar dryer prototype is very important. It can assist in

minimizing or eliminating mistakes in the design that may inversely affect system

development.


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In this section, the mathematical formulation that defines the thermodynamic

performance of each component will be presented in detail.

6.1 Mathematical modelling of the solar collector

The following assumptions [16] are taken to simplify the modelling of the collector

The collector is at steady state

The temperature drop through the glass cover, absorbing plate and bottom plate is

negligible

The heat flow is one-dimensional at the back insulation and flows perpendicular to the

air flow

The sky is considered as a blackbody for long-wavelength radiation at an equivalent sky

temperature

Front and back surface are exposed to the same ambient temperature thus having equal

heat losses

Dust and dirt and shading has no effect on the collector

Thermal inertia of the collector components is negligible

Operating temperatures of collector components and mean air temperatures in air

channels are all assumed to be uniform

The collector is free of leaks

Thermal radiation of the insulation are assumed to be negligible

A straight-forward, analytic solution does not exist yet to solve for the temperatures

𝑇1,𝑇𝑓1,𝑇2,𝑇𝑓2 and 𝑇3 as can be seen later since to calculate the temperatures, the heat


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transfer coefficients must be determined which depends on temperature. Also, to define

the performance of the collector, the efficiency must be known which is also dependent of

temperature. Therefore, to calculate these parameters, numerical iteration is necessary.

The solution from [15] will be used to calculate the temperatures where iterative matrix

method is involved. First, a guess temperature is used to calculate the heat transfer

coefficients and losses. A matrix is set up and inverted to calculate new temperature. These

new temperatures are compared to the initial guess and if the difference is greater than

0.01 °𝐶, the matrix inversion is repeated using the new calculated temperature until the

difference is less than 0.01 °𝐶. Once the difference is at the acceptable level, the iteration

stops and the calculated temperature is considered to be each component’s temperature.

6.1.1 Thermal network

The thermal network for the v-corrugated collector is illustrated in Figure 1.


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Figure 2. Cross section and thermal network of a double-pass v-groove solar air collector

6.1.2 Energy balance

Energy balance equations based on the thermal network from Figure 1, for the glass cover,

first pass fluid, absorber plate, second pass fluid and back plate are given in equation (1) to

(5).

The energy balance in the top plate is given by

𝑆1 + 𝑕𝑟21 𝑇2 − 𝑇1 + 𝑕1 𝑇𝑓1 − 𝑇1 = 𝑈𝑇 𝑇1 − 𝑇𝑎 (1)

For the fluid’s first pass,

𝑕2 𝑇2 − 𝑇𝑓1 = 𝑕1 𝑇𝑓1 − 𝑇1 + 𝑄1 (2)


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Energy balance in the absorber plate is

𝑆2 = 𝑕3 𝑇2 − 𝑇𝑓2 + 𝑕2 𝑇2 − 𝑇𝑓1 + 𝑕𝑟23 𝑇2 − 𝑇3 + 𝑕𝑟21(𝑇2 − 𝑇1) (3)

For the fluid’s second pass,

𝑕3 𝑇2 − 𝑇𝑓2 = 𝑕4 𝑇𝑓2 − 𝑇3 + 𝑄2 (4)

For the bottom plate,

𝑕4 𝑇𝑓2 − 𝑇3 + 𝑕𝑟23 𝑇2 − 𝑇3 = 𝑈𝑏(𝑇3 − 𝑇𝑎) (5)

6.1.3 Heat transfer coefficients

The set of equations given in this section is laid out in the sequence as on how they

appeared in the energy balance equation presented in equations (1) to (5). It is important to

identify the values of the heat transfer coefficient to determine the performance of the air

collector.

Variables in 𝑇1

The incident solar radiation in the glass cover is calculated by [15]

𝑆1 = 𝛼1𝐼 (6)

The convection heat transfer due to wind is [15] [16]

𝑕𝑤 = 5.7 + 3.8𝑉 (7)

The radiation heat transfer coefficient between the glass cover and sky is [16]

𝑕𝑟𝑠 = 𝜎𝜀1 𝑇2 + 𝑇1 (𝑇22 + 𝑇1

2)(𝑇1 − 𝑇𝑆)

(𝑇1 − 𝑇𝑎) (8)


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The overall top heat loss coefficient is calculated using an empirical equation developed by

Klein [30]

𝑈𝑇 = 𝑁

𝐶𝑇3 𝑇3 − 𝑇𝑎𝑁 + 𝑓

𝑒 +

1

𝑕𝑤

−1

+𝜎 𝑇3 + 𝑇𝑎 (𝑇3

2 + 𝑇𝑎2)

𝜀𝑝 + 0.00591𝑁𝑕𝑤 −1

+ 2𝑁 + 𝑓 − 1 + 0.133𝜀𝑝

𝜀𝑔 − 𝑁

𝑓 = 1 + 0.089𝑕𝑤 − 0.1166𝑕𝑤𝜀𝑝 1 + 0.07866𝑁

𝐶 = 520 1 − 0.000051∅2 for 0° < ∅ < 70°. Use ∅ = 70° 𝑖𝑓 70° 𝑡𝑜 90°

𝑒 = 0.43 1 −100

𝑇3

(9)

The radiation heat transfer coefficient between the glass cover and absorbing plate can be

predicted by [16]

𝑕𝑟21 =𝜎 𝑇2

2 + 𝑇12 (𝑇2 + 𝑇1)

1𝜀2

+1𝜀1− 1

(10)

The conductive heat transfer coefficient between the glass cover and the first pass fluid is

determined by the equation developed by Hollands [31]

𝑕′1 = 𝑁𝑢12

𝑘

𝐷𝑕 (11)

However, the developed area of the plate is greater than the area of the bottom channels

by a factor of 1/sin(𝜃/2) thus the value of 𝑕′1 as calculated must be divided by sin(𝜃/2)

to account for this difference [32]. Therefore the actual value of the conductive heat ransfer

coefficient is


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𝑕1 = 𝑁𝑢12

𝑘

𝐷𝑕

1

sin 𝜃 2 (12)

Where 𝜃 is the included angle of the v-groove plate and 𝐷𝑕 is the hydraulic diameter of the

airflow channel and is calculated by 4*Area/Wetted perimeter. For the first pass, 𝐷𝑕 is

derived as

𝐷𝑕 =1.155(𝐻𝑔

2 + 2𝐻𝑔𝐻𝑐)

3𝐻𝑔 + 𝐻𝑐

(13)

The equation for the Nusselt number is dependent on the flow inside the channel. First is to

calculate the Reynolds number and determine which Nusselt number equation should be

used. The Reynolds number is calculated by 𝑅𝑒 = 𝜌 𝑈𝑓𝐷𝑕

𝜇 but 𝜌 𝑈𝑓 is equal to

𝑚𝐿

𝑏 where b is

𝐻𝑔

2. Therefore, the Reynolds number may be expressed as [32]

𝑅𝑒 = 𝑚𝐿

𝑏 𝐷𝑕𝜇

(14)

If 𝑅𝑒 < 2800 [32],

𝑁𝑢12 = 2.821 + 0.126 𝑅𝑒𝑏

𝐿 (15)

If 2800 < 𝑅𝑒 < 104 [32]

𝑁𝑢12 = 1.9 × 10−6𝑅𝑒1.79 + 225𝑏

𝐿 (16)

If 104 < 𝑅𝑒 < 105 [32]

𝑁𝑢12 = 0.0302𝑅𝑒0.74 + 0.242 𝑅𝑒0.74𝑏

𝐿 (17)

Variables in 𝑇𝑓1


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The conductive heat transfer coefficient between the first pass fluid and the absorber plate

is assumed to be equal to the conductive heat transfer coefficient between the glass cover

and first pass fluid [32] [13] thus,

𝑕2 = 𝑕1 (18)

The amount of heat transferred in the first pass fluid is calculated as [15]

𝑄1 = 2 𝑚 𝐶𝑝(𝑇𝑓1 − 𝑇𝑓𝑖) (19)

Variables in 𝑇2

The incident solar radiation absorbed by the absorbing plate is [15]

𝑆2 = 𝜏1 𝛼2 𝐼 (20)

The radiation heat transfer coefficient between the absorbing plate and the bottom plate

can be predicted by [16]

𝑕𝑟23 =𝜎 𝑇2

2 + 𝑇32 (𝑇2 + 𝑇3)

1𝜀2

+1𝜀3− 1

(21)

The conductive heat transfer coefficient between the absorbing plate and the second pass

fluid will be calculated similarly to the previous coefficient except that the hydraulic

diameter is 𝐷′𝑕 = 2/3𝐻𝑔 [16].

𝑕3 = 𝑁𝑢34

𝑘

𝐷′𝑕

1

sin 𝜃 2 (22)

Variables in 𝑇𝑓2


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The conductive heat transfer coefficient between the second pass fluid and the bottom

plate is assumed to be equal to the conductive heat transfer coefficient between the

absorber plate and second pass fluid [13] [32] thus,

𝑕4 = 𝑕3 (23)

The amount of heat transferred in the second pass fluid is calculated as [15]

𝑄2 = 2 𝑚 𝐶𝑝(𝑇𝑓2 − 𝑇𝑓1) (24)

Variables in 𝑇3

The heat loss coefficient at the bottom plate is given by [15]

𝑈𝑏 =1

𝑥𝑘𝑖

+1𝑕𝑤

(25)

The following empirical equations (26) to (28) can be used to estimate air density, thermal

conductivity, and dynamic viscosity for 𝑇 from 280K to 470K [16].

𝜌 = 3.9147 − 0.016082𝑇 + 2.9013 × 10−5𝑇2 − 1.9407 × 10−8𝑇3 (26)

𝑘 = 0.0015215 + 0.097459𝑇 − 3.3322 × 10−5𝑇2 × 10−3 (27)

𝜇 = (1.6157 + 0.06523𝑇 − 3.0297 × 10−5𝑇2) × 10−6 (28)

And finally, the output temperature and collector efficiency can be determined by

𝑇𝑜 = 𝑇𝑓𝑖 +(𝑄1 + 𝑄2)

𝑚 𝐶𝑝 (29)


21

𝑛𝑐 =𝑚 𝐶𝑝 (𝑇0 − 𝑇𝑓𝑖)

𝐼 (30)

6.1.4 Matrix method solution for a double-pass counter flow v-groove

Rather than performing complicated algebraic manipulations to solve the energy equations,

a matrix method solution is applied. It is significantly easier to perform with the help of

computers and provides a straight forward approach. To simplify the expression, equations

(19) and (24) can be expressed as [15]

𝑄1 = 𝛾1(𝑇𝑓1 − 𝑇𝑓𝑖) (31)

𝑄2 = 𝛾1(𝑇𝑓2 − 𝑇𝑓1) (32)

where

𝛾1 = 2 𝑚 𝐶𝑝 (33)

By rearranging the energy balance equations (1) to (5) in terms of temperature, the

following expressions can be obtained;

𝑕1 + 𝑕𝑟21 + 𝑈𝑡 𝑇1 − 𝑕1𝑇𝑓1 − 𝑕𝑟21𝑇2 = 𝑆1 + 𝑈𝑡𝑇𝑎 (34)

𝑕1𝑇1 − 𝑕1 + 𝑕2 + 𝛾1 𝑇𝑓1 + 𝑕2𝑇2 = −𝛾1𝑇𝑓𝑖 (35)

−𝑕𝑟21𝑇1 − 𝑕2𝑇𝑓1 + 𝑕2 + 𝑕3 + 𝑕𝑟21 + 𝑕𝑟23 𝑇2 − 𝑕3𝑇𝑓2 − 𝑕𝑟23𝑇3 = 𝑆2 (36)

𝛾1𝑇𝑓1 + 𝑕3𝑇2 − 𝑕3 + 𝑕4 + 𝛾1 𝑇𝑓2 + 𝑕4𝑇3 = 0 (37)

−𝑕𝑟23𝑇2 − 𝑕4𝑇𝑓2 + 𝑕𝑟23 + 𝑈𝑏 + 𝑕4 𝑇3 = 𝑈𝑏𝑇𝑎 (38)

Equations (35) to (39) can be arranged into a 5 x 5 matrix in the form

𝑨 𝑻 = [𝑩] (39)


22

(𝑕1 + 𝑕𝑟21 + 𝑈𝑡) −𝑕1 −𝑕𝑟21 0 0

𝑕1 − 𝑕1 + 𝑕2 + 𝛾1 𝑕2 0 0

−𝑕𝑟21 −𝑕2 𝑕2 + 𝑕3 + 𝑕𝑟21 + 𝑕𝑟23 −𝑕3 −𝑕𝑟23

0 𝛾1 𝑕3 − 𝑕3 + 𝑕4 + 𝛾1 𝑕4

0 0 −𝑕𝑟23 −𝑕4 𝑕𝑟23 + 𝑈𝑏 + 𝑕4

𝑇1

𝑇𝑓1

𝑇2

𝑇𝑓2

𝑇3

=

𝑆1 + 𝑈𝑡𝑇𝑎−𝛾1𝑇𝑓𝑖𝑆2

0𝑈𝑏𝑇𝑎

The mean temperature can be determined by using array division

𝑻 = 𝑨 −1 [𝑩] (40)

The newly calculated value of temperature will then be compared to the previous value of

temperature. The process repeats until all the temperature difference of the newly

calculated temperature and previous temperature is less than 0.01 °𝐶.

6.2 Mathematical modelling of the thermal storage tank

The thermal storage tank improves the performance of the solar drying system and

allows continuous operation even at period of low or no solar radiation. Energy is

transferred and stored on the rock element and used by reversing the air flow direction.

To model the storage tank mathematically, the length 𝐿 of the storage tank is

divided into several nodal elements 𝑑𝑥 as depicted in Figure 3. The value of 𝑑𝑥 is small and

only exaggerated in the figure. Schumann [33] derived a differential equation to describe

the temperature along the bed at any location. For a one dimensional transient analysis, it is

assumed that

Properties of both solid and fluid are constant

No heat loss to the surroundings


23

No mass transfer

Conduction from the fluid to the rocks is negligible.

Figure 3. Conical thermal storage tank (left) and element ‘m’ of the tank

6.2.1 Nodal element temperature

The following governing temperature are used to evaluate the temperature distribution for

air and solid in the thermal storage tank [34].

𝑇𝑎 ,𝑚+1 = 𝑇𝑏 ,𝑚 + 𝑇𝑎 ,𝑚 − 𝑇𝑏 ,𝑚 exp −𝜙1 (41)

𝜙1 =𝑕𝑣𝐴𝐿

𝑁 𝑚 𝑎𝐶𝑝𝑎 =𝑁𝑇𝑈

𝑁; 𝑁 =

𝐿

∆𝑥

𝑇𝑏 ,𝑚 𝑡+∆𝑡 = 𝑇𝑏 ,𝑚 𝑡 + 𝜙2 𝑇𝑎 ,𝑚 − 𝑇𝑎 ,𝑚+1 − 𝜙3 𝑇𝑏 ,𝑚 − 𝑇𝑎𝑚𝑏 ∆𝑡 (42)

𝜙2 =𝑚 𝑎𝐶𝑝𝑎𝑁

𝜌𝑟𝐶𝑝𝑟 𝐴𝐿 1 − 𝜖

𝜙3 = 𝜙2 𝑈∆𝐴𝑚𝑚 𝑎𝐶𝑝𝑎

Neglecting loss to the surroundings, 𝑇𝑏 ,𝑚 𝑡+∆𝑡 becomes


24

𝑇𝑏 ,𝑚 𝑡+∆𝑡 = 𝑇𝑏 ,𝑚 𝑡 + 𝜙2 𝑇𝑎 ,𝑚 − 𝑇𝑎 ,𝑚+1 ∆𝑡 (43)

6.3. Mathematical modelling of mixing tank

The section where the mixing of two stream of fluid takes place is commonly referred to as

mixing tank (Shown in Figure 4). The conservation of mass principle for a mixing chamber

requires that the sum of the incoming mass flow rates equal the mass flow rate of the

outgoing mixture. To model the mixing tank, the following are assumed [35]

No heat flow in or out

Any kind of work is not involved

Kinetic and potential energy is negligible

Figure 4. Mixing tank schematic [35]

Under the stated assumption, the equation at the mixing tank is


25

𝑚1 𝑕1 + 𝑚 2𝑕2 = 𝑚 3𝑕3 (44)

A psychrometric chart may be used to determine fluid enthalpy. However, to simulate it in

MATLAB, the following equations are used [36]

𝑃𝑤𝑠 = 𝐴 ∙10

𝑚𝑇𝑇+𝑇𝑛

0.01

(45)

Where the variables are determined by its temperature range as indicated. An if-else

statement is used to handle this dependence in temperature

𝑃𝑤 =𝑅𝐻 ∙ 𝑃𝑤𝑠

100 (46)

𝑃𝑤𝑠 is saturation vapour pressure and 𝑃𝑤 is water vapour pressure both in kPa. Then to

calculate humidity ratio with Pa = 101.325 kPa

𝑥 = 0.62198𝑃𝑤

𝑃𝑎 − 𝑃𝑤 (47)

Calculating enthalpy,

𝑕 = 𝑇 1.01 + 0.00189𝑥 + 2.5𝑥 (48)

Once enthalpy is known, equation 44 can be used to determine the enthalpy of the air

mixture. Then use equation 48 to determine its resulting temperature.


26

6.4 Mathematical modelling of the heater

Air flows through the heater with a known mass flow rate and inlet temperature. Assuming

a constant heat transfer and negligible heat loss to the environment, the performance of

the auxiliary heater is determined by the simple equation

𝑄 = 𝑚 𝐶𝑝 𝑇2 − 𝑇1 (49)

6.5 Mathematical modelling of the drying chamber

The drying kinetics and quality of the product is significantly influenced by drying

temperature, relative humidity and air velocity [37]. With apple as material to be dried,

Menges and Ertekin reported a reduction of 50% in drying time when air temperature is 60C

to 80C [38] with 75C being the most favourable temperature [37]. Karim suggested an air

flow rate of 0.035 kg/m2 s [7] and Sturm, Hofacker and Hensel suggested 3.4 m/s for air

velocity [37]. Keeping the air humidity at low levels can also reduce the drying time. All

these suggestions by different researchers are taken as the optimum air condition in the

drying chamber that will minimize drying time and yield high quality dried apple.

The mathematical modelling of the drying chamber section of this thesis is mainly taken

from Dr. Azharul Karim’s paper [9]. In the model, moisture transport occurs by diffusion in

only one direction. Shrinkage is also considered in the calculations since it may have a

significant effect on mass diffusivity and moisture removal rate. The assumptions to simplify

the equations are as follows

One-dimensional heat and mass transfer with material as an infinite slab with

uniform moisture content and temperature


27

The drying sample is a composite material consisting of solid material and moisture.

No chemical reaction takes place during drying

Moisture transport occurs by diffusion from the interior and evaporation at the

surface

The material shrinks as drying progresses.

6.5.1 Material model

The moisture balance equation is

𝜕𝑀

𝜕𝑡+ 𝑢

𝜕𝑀

𝜕𝑥= 𝐷𝑒𝑓𝑓

𝜕2𝑀

𝜕𝑥2 (50)

Temperature balance equation is

𝜕𝑇

𝜕𝑡+ 𝑢

𝜕𝑇

𝜕𝑥= 𝐷𝑒𝑓𝑓

𝜕2𝑇

𝜕𝑥2 (51)

With initial condition at t = 0,

𝑀 = 𝑀0 and 𝑇 = 𝑇0

Boundary condition at x = 0,

𝜕𝑀

𝜕𝑡= 0 and

𝜕𝑇

𝜕𝑡= 0

Effective diffusivity is

2

0

b

b

D

D

eff

ref (52)

Thickness ratio obtained by the following equation


28

sw

sww

M

Mbb

0

0 (53)

6.5.2 Equipment model

The next step in modelling the drying chamber is to determine the heat and mass balance of

the air passing through the chamber. The following assumptions are made in modelling the

equipment

Thermal properties of moisture and air are constant within the range of air

temperatures under consideration

Conduction heat transfer within the bed is negligible

Effect of condensation within the bed is negligible

One dimensional heat transfer

Uniform product size

Uniform distribution of drying product in the drying chamber

The energy balance at the drying chamber is

𝜕𝑇𝑎𝜕𝑧

=𝜌𝑆 𝐶𝑠 + 𝐶𝑚𝑀 (1 − 𝜖)

(𝐺0𝐶𝑝𝑎 )

𝜕𝑇

𝜕𝑡+𝜕𝑀

𝜕𝑡𝑕𝑓𝑔

𝜌𝑠(1 − 𝜖)

𝐺0𝐶𝑝𝑎 (54)

The moisture balance is

𝜕𝑌

𝜕𝑧=𝜌𝑠(1 − 𝑡)

𝐺0

𝜕𝑀

𝜕𝑡 (55)

Boundary and initial conditions are

At x=0 and t = 0,

𝑇𝑎 = 𝑇0 and 𝑌 = 𝑌0


29

𝑑𝑇𝑎𝑑𝑡

= 0 and𝑑𝑌

𝑑𝑡= 0

At x > 0 and t = 0,

𝑇𝑎 = 𝑇0 and 𝑌 = 𝑌0

The differential equations are discretized and written in finite difference form before

performing simulation.

6.6 Mathematical modelling of the dehumidifier

An energy saving of 29-31% was realized by recirculating the hot air and varying the degree

of venting [39]. Though this finding couldn’t be confirmed from simulations, it gives an

impression that air recirculation is beneficial. Air dehumidification is achieved by moisture

condensation by cooling the air exiting the drying chamber below its dew point

temperature. A schematic of this process is shown in Figure 5.

Figure 5. Schematic for dehumidification [40]

The mathematical equations governing dehumidification are [40]

𝑚 𝑤 = 𝑚 𝑑𝑎 (𝑊1 −𝑊2) (56)

𝑞2 = 𝑚 𝑑𝑎 [ 𝑕1 − 𝑕2 − 𝑊1 −𝑊2 𝑕𝑤2] (57)


30

6.7 Mathematical modelling of system pressure loss

This section discusses the equations used to calculate the pressure loss of the solar drying

system. It is assumed that pressure drop is negligible in other parts of the system except at

the solar collector, thermal storage tank and the ducts.

6.7.1 Pressure loss in the solar collector

Pressure drop for all types of internal flows (laminar or turbulent, circular of non-circular

tubes, smooth or rough surfaces) is calculated by [41]

∆𝑃 = 𝐹 2𝐿

𝐷𝑕 𝜌𝑉2 (58)

Where 𝑓 is the Darcy friction factor which is equal to 4𝐹 where 𝐹 is the Fanning friction

factor

To simplify the equation to be applied in the air collector taking out the velocity term,

𝑉2 = 𝑀

𝑘𝑔

𝑠

𝜌𝐴𝑓𝑙𝑜𝑤

2

= 𝑚 𝐿 𝑊

𝜌 𝑏+𝐻𝑐 𝑊

2

. The pressure drop can be alternatively expressed as

∆𝑃 = 𝐹 2𝐿

𝐷𝑕

𝑚2

𝜌

𝐿2

𝑏 + 𝐻𝑐 2 (59)

with 𝐻𝑐 equated to zero in the second pass. The total pressure drop in the air collector is the

sum of the pressure drop in the first pass and the second pass.

The value of 𝐹 changes with flow regime as follows [42]

𝐹 = 𝐹0 + 𝛾𝑏

𝐿𝑛 (60)

For laminar flow (𝑅𝑒 < 2,800)

𝐹0 =13.33

𝑅𝑒 and 𝛾 = 0.65


31

For transient flow 2,800 ≤ 𝑅𝑒 ≤ 10,000

𝐹0 = 3.2 × 10−4𝑅𝑒0.34 and 𝛾 = 2.94𝑅𝑒−0.19

For early turbulent flow (104 < 𝑅𝑒 < 105)

𝐹0 = 0.0733𝑅𝑒−0.25 and 𝛾 = 0.51

Since the solar collector is a double pass, the pressure drop at the second pass is calculated

in the same manner and added to the first pass pressure drop.

6.7.2 Pressure loss in the storage tank

The pressure drop in the packed bed is calculated by [25]

∆𝑃 =𝐿𝐺2

𝜌𝑑 𝐴 1 − 𝜀 2

𝜀3𝜓2

𝜇

𝐺𝑑+ 𝐵

1 − 𝜀

𝜀3𝜓 + 𝜌𝑔𝐿

Δ𝑇

𝑇 (61)

Where 𝐴 = 217,𝐵 = 1.83 and 𝜓 = 0.6. The equation above is solved for every layer after

every time step then summed in order to calculate the pressure drop across the packed bed.

6.7.3 Pressure loss in the ducts

The pressure loss in the duct is determined by

Δ𝑃 = 𝑓𝜌𝐿𝑣2

2𝐷 (62)

Where the friction coefficient 𝑓 is calculated by the Swamee-Jain equation as

𝑓 =0.25

log 𝜀

3.7𝐷 +5.74𝑅𝑒0.9

2 (63)

𝜀 is the surface roughness which is determined by the material and the Reynolds number is

𝑅𝑒 =𝜌𝑣𝐷

𝜇


32

6.8 MATLAB Simulation

The simulation codes for each component are prepared in MATLAB. The codes are written

so that the program runs in the sequence as shown in Figure 6. Each box represents

MATLAB codes. The codes are connected by “function” command to simulate the whole

system as a whole.

Figure 6. MATLAB simulation of the solar drying system

7. Simulation results and discussion

This section will discuss and demonstrate the capabilities of the simulation codes

produced in MATLAB. Particular focus will be given to the solar air collector since it is the

main component of the solar drying system and its efficiency greatly affects the efficiency of

the system. The simulation codes will be used;

To fully study and understand the solar air collector. It will also be used to optimize

different variables in the design of the collector.

To determine the effect of air recirculation and varying the degree of venting and

flow rate at different parts of the solar drying system.


33

To find the optimum operating condition of the solar drying system that will yield a

good balance between high efficiency and low operating cost.

7.1 Solar air collector

The mathematical solution presented in the earlier section is used to calculate the

temperatures and heat transfer coefficients in the v-groove air collector. These results are

then used to produce the graphs that will be used to assess the performance of the air

collector and assist in developing an efficient solar drying system. Values of absorptivity,

emissivity and transmissivity for the surfaces in the air collector are assumed values but are

identified to have a minimal impact on the result of the simulation. Small temperature

differences in the order of 1°𝐶 or less could be obtained from modifying these values [15]

[16]. By using the matrix method solution for a double-pass counter flow v-groove shown in

the previous section, the temperature of the components of the air collector as well as its

efficiency can be determined. And to verify the simulation, parameters such as outlet

temperature will be compared to other’s experimental result where the simulation will use

the same meteorological condition and collector characteristics.

Figure 7 shows the hourly variation of solar irradiation and ambient temperature. At

this stage, hourly data of Singapore is used since the meteorological data of Brisbane,

Australia is yet to be obtained from the Bureau of Meteorology. Currently, the temperature

ranges from 298 K to 302.4 K, reaching its maximum temperature at 2:00pm. The solar

radiation value ranges from 0 to 552 𝑊/𝑚2 with its peak radiation occurring at 12:00pm.


34

Figure 7. Solar radiation and ambient temperature vs Time

The simulation of temperature variation in the various elements of the solar air

collector using Singapore’s meteorological data (Figure 7) when 𝑚 = 0.035 𝑘𝑔/𝑚2𝑠 is

shown in Figure 8. The maximum values of mean temperature in the elements of the air

collector occurred at 1:00 pm where 𝑇1, 𝑇𝑓1, 𝑇2, 𝑇𝑓2 and 𝑇3 are found to be 308.30 K,

306.07 K, 316.53 K, 308.51 K and 310.43 K, respectively.


35

Figure 8. Mean temperature variation in the air collector with respect to time

In Figure 9, the output air temperature in the double-pass v-groove air collector is

plotted against time. It also shows the temperature of the input air. It can be seen from the

graph the change in temperature of the air once it passed through the air collector. The

maximum output temperature occurs at 1:00pm which is approximately 315 K. It might

raise a concern that the temperature in Figure 8 of second pass air at 1:00pm is

approximately 308 K, however it must be understood that this temperature is the average

temperature in the second pass air over the length of the collector at that time unlike in

Figure 9 which is the actual output temperature. Knowing the temperature output of the air

collector is important since this will assist in determining the design of the dryer that will

satisfy the required temperature in the drying cabinet.


36

Figure 9. Simulated input and output air temperature in the air collector during operation

The temperature of air as it passes through the air collector is presented in Figure

10. The first pass of air is shown in the bottom part of the graph and the second pass is

shown in the upper part. There is a relatively high rise in temperature in the first pass of air

as compared to the second pass. The approximate temperature rise in the first pass is about

80% of the total rise in temperature. This is where a double-pass configuration is

advantageous; it interacts with a section of air twice thus the temperature is significantly

increased compared to a single pass configuration.


37

Figure 10. Temperature of air as it flows through the air collector

In Figure 11 is the efficiency curve from the simulation. In the x-axis, the most

common term for plotting against efficiency is (𝑇𝑖 − 𝑇𝑎)/𝐼 but this is not possible for the

model since it assumed that inlet air temperature is equal to the ambient temperature

which would result in a straight vertical line at zero. This kind of plot would not have any

significance for investigation. An alternative is to use (𝑇𝑜 − 𝑇𝑓𝑖 )/𝐼 which will show the

relationship between change in fluid temperature and radiation to efficiency. As can be

seen, as the ratio of temperature difference and radiation increase the efficiency of the

collector also increase. Investigation of the efficiency curve is not part of this project but

from the study done by Karim [43], as the flow rate increase, the points in the graph will be

in a higher position which means that the efficiency is higher.


38

Figure 11. Efficiency curve

7.2 Verifying simulation model of solar air collector

The comparison of experimental results from references [9] and [18] to the

simulation model produced is shown in Figures 12 and 13. The solar radiation data, ambient

and inlet air temperature and the air collector’s characteristics used to perform the

experiment are all inserted into the MATLAB simulation model to reproduce the

experimental result as close as possible and verify if the simulation model generate reliable

outputs. However, results variations have been observed from the graph and these may be

attributed to dissimilarity of the experiment set-up and the simulation codes since not all

detail of the set-up and the air collector are given by the authors where the experimental

results are taken. From Figure 12, the simulated results closely follow the experimental

result but a problem was encountered during simulation since the author used kg/s for mass

flow rather than kg/m2s. This problem is fixed by combining the original simulation code and

the solution procedure of [18] to solve the temperature output. Note that difference is

calculated from Kelvins unit temperature. A maximum difference of 1.2% is observed from


39

the results therefore considering the uncertainties from the input, the simulation model can

predict the performance of the air collector. This is further proven from Figure 13. Figure 13

shows the simulated result seems to deviate quite a lot from the experimental result,

however by performing a percent difference analysis on the results obtained, it was

determined that the maximum deviation between the two results is just approximately

10.3%, which is still acceptable considering the uncertainties from the input. Therefore

there is no significant difference in value between the two results but rather the deviation is

only more obvious because it does not follow the same trend. The deviation in trend in

Figure 13 is likely due to the introduction of an imaginary number during the solution

procedure. This type of problem arises when the inlet air temperature is assumed to be

equal to the ambient temperature. It does not significantly affect the result but caution

must be taken in assuming that inlet air temperature is equal to ambient temperature since

it may promote error in the results if dealing with high temperatures.

Figure 12. Comparison of simulated to experimental result using data from Reference [18]


40

Figure 13. Comparison of simulated to experimental result using data from Reference [9]

Air temperature along the length of the collector is shown in Figure 14 where it is

compared with the result from reference [18]. Similar to the previous simulations, the solar

radiation data, ambient and inlet air temperature and the air collector’s characteristics used

to perform the experiment are all inserted into the MATLAB simulation model to reproduce

the experimental result. As can be seen from Figure 14, the two graphs very closely follow

each other for both first and second pass air. Thus, confirming that the simulation model

can predict accurately the temperature of air in the air collector at any instant.

Figure 14. Comparison of air temperature along the length of the collector from [18]


41

7.3 Parametric study of the solar air collector

An investigation of several parameters of the double pass v-groove air collector is

taken to see their effect on the output temperature and efficiency of the air collector. Also,

the absorber plate temperature is taken to allow comparison with the output temperature

and observe how it interacts within the system. The parameters considered are: solar

radiation, mass flow rate, inlet air temperature, air velocity in the collector, length, height of

the v-groove section and its gap from the tip of the vee to the glass cover, number of glass

cover and insulation thickness. A parametric study is also done by [16] where a single pass v-

groove air collector is investigated. Constant reference with the results from [16] will be

done to compare the difference in the effect of the parameters under investigation to both

single and double pass configuration. The approach used to analyse the effect of each

parameter is to keep all parameter values of the air collector constant and only varying the

parameter of interest.

7.3.1 Solar radiation

The first to be looked upon is the effect of solar radiation to the output temperature

and efficiency when 𝐼 value ranges from 0 𝑡𝑜 1000 𝑊/𝑚2. The result of the simulation is

presented in Figure 15. It can be observed from the graph that both absorber plate

temperature and output temperature linearly increases as the radiation increase. However,

the temperature becomes lower as the mass flow rate is increased. Thus the lower the mass

flow rate, the higher the output temperature. On the other hand, solar radiation does not

have a significant effect on the efficiency and only becomes apparent on low values of mass

flow rate. The effect of mass flow rate to efficiency is opposite to temperature since as the

mass flow rate is increased, the efficiency also increase. Compared to [16], the trend of the

result between the two configuration is similar.


42

Figure 15. Effect of solar radiation to the output temperature and efficiency when I ranges from 0 to 1000 W/m2

7.3.2 Mass flow rate

The effect of mass flow rate to the output temperature and efficiency when 𝑚 value

ranges from0 𝑡𝑜 0.1 𝑘𝑔/𝑚2𝑠 is shown in Figure 16. It can be observed that the effect of

mass flow rate at some point is becoming less and less significant for both output

temperature and efficiency. When the flow rate is less than 0.01 𝑘𝑔/𝑚2𝑠, its effect is very

large but as its value increases, the effect becomes insignificant. Considering the absorber

plate temperature and output temperature, when the mass flow rate is less than


43

0.015 𝑘𝑔/𝑚2𝑠, the output temperature is higher than the absorber plate temperature.

Once the mass flow rate exceeds this value, the trend switches. This is attributed to the high

radiation and convection heat transfer occurring at low mass flow rate. Compared to [16],

the trend of the result between the two configuration is similar.

Figure 16. Effect of mass flow rate to the output temperature and efficiency when m ranges from 0 to 0.1 kg/m2s

7.3.3 Inlet air temperature

The effect of inlet air temperature to the output temperature and efficiency when

𝑇𝑓𝑖value ranges from 280 𝑡𝑜 340 𝐾 is shown in Figure 17. It can be observed from the graph

that both absorber plate temperature and output temperature linearly increase as the inlet

air temperature is increased and it will be notice as well that the outlet temperature is

higher at low values of mass flow rate. On the other hand, as the inlet air temperature

increase, the efficiency linearly decreases. This indicates that the inlet air temperature has a

significant effect on the air collector. Therefore in choosing the optimal inlet air

temperature for the design, caution must be taken to ensure that a reasonable value for

inlet air temperature is selected. Compared to [16], the trend of the result is similar. Due to

this kind of effect of the inlet temperature, a further study about the possibility of air

recirculation is required. The increase in inlet temperature is provided by the recirculated


44

air. This air is processed by the dehumidifier to enable its use for drying. If the inlet

temperature is increased, the outlet temperature also increase which consequently lessens

the amount of heat required to be supplied by the auxiliary heater. However, this lowers the

efficiency of the solar collector. On the other hand, if the inlet temperature is low, the solar

collector will be more efficient but the auxiliary heater must provide more heat. A trade-off

exists and operational study is required to find an optimal condition where the efficiency of

the solar collector is maximized and the operational cost of the solar drying system is low.

Figure 17. Effect of inlet air temperature to the output temperature and efficiency when Tfi ranges from 280

to 340 Kelvins


45

7.3.4 Length of solar collector

The effect of length to the output temperature and efficiency when 𝐿 value ranges from

0 𝑡𝑜 5 𝑚 is shown in Figure 18. It can be observed from the graph that length has some

effect on the output temperature and efficiency of the air collector but it does not

significantly affect the performance of the collector. This is in agreement to the results from

[16] where it is found that the length of the collector has negligible effect.

Figure 18. Effect of length to the temperature and efficiency when L ranges from 0 to 5 m

The effect of length to the Reynolds number is observed in Figure 19. It is known that

turbulence increases heat transfer. As can be seen, the Reynolds number increase as length


46

increases. Thus increasing the length has benefits of improved thermal performance. With

reference to Figure 20, at the laminar regime, the heat transfer coefficient can be observed

to be constant. At the transition regime, the heat transfer coefficient goes down then after

reaching a minimum, goes up continuously until the turbulent regime is reached. At low

values of mass flow rate, the heat transfer coefficient does not increase as much relative to

higher values of mass flow rate.

Figure 19. Flow regime in the first and second pass as the length increase

Figure 20. Heat transfer coefficient in the first and second pass as the length increase

7.3.5 V-groove height

The effect of the height of the v-groove to the output temperature and efficiency when 𝐻𝑔

value ranges from 0 𝑡𝑜 0.1 𝑚 is shown in Figure 21. As the v-groove height increases, the


47

absorber plate temeprature is observed to increase but the output temperature decreases.

This phenomenon can be attributed to the decreasing heat transfer coefficient occuring as

the v-groove height increase. The efficiency is also affected by the v-groove height. As can

be seen in Figure 22, at low values of v-groove height, the flow is turbulent then approaches

laminar flow as the height increase. Consequently, the heat transfer coefficient is highest at

low v-groove height. However, the more turbulent the flow, the higher the pressure losses

which consequently means higher operational cost for the fan. Thus in selecting the v-

groove height, it must be as low as possible with an acceptable value of pressure loss.

Figure 21. Effect of v-groove height to temperature and efficiency


48

Figure 22. Flow regime in the first and second pass as the v-groove height increase

Figure 23. Heat transfer coefficient in the first and second pass as the v-groove height increase

7.3.6 V-groove gap to glass cover

The effect of the gap between the v-groove absorber and glass cover to the output

temperature and efficiency when 𝐻𝑐 value ranges from 0 𝑡𝑜 0.1 𝑚 is shown in Figure 24.

The gap has negligible effect on the output temperature and efficiency of the air collector.

The absorber plate temperature varied slightly as the gap increases. This is due to the

change in flow condition in the channel. However, this variation is in close agreement with

the result from [16] where their absorber plate temperature remained constant. The

reasoning behind their variation is due to difference in configuratio. Thus for a double pass

v-groove air collector, the the gap between the v-groove absorber and glass cover will not


49

have a significant effect on output temperature and efficiency. However, the gap should be

kept at a reasonable value to avoid high pressure loss.

Figure 24. Effect of v-groove gap to temperature and efficiency

Figure 25 shows the flow regime in the first and second pass as the v-groove gap increases.

In the first pass, the flow regime is affected by the v-groove gap but in the second pass,

Reynolds number remains constant. Then considering Figure 26 which shows the heat

transfer coefficient graph, it can be observed that when the flow is at the transition regime,

the heat transfer coefficient increase slightly. A decrease is observed when flow is turbulent.


50

Figure 25. Flow regime in the first and second pass as the v-groove gap increases

Figure 26. Heat transfer coefficient in the first and second pass as the v-groove gap increases


51


52


53

7.3 Parametric study of the solar air collector

An investigation of several parameters of the double pass v-groove air collector is

taken to see their effect on the output temperature and efficiency of the air collector. Also,

the absorber plate temperature is taken to allow comparison with the output temperature

and observe how it interacts within the system. The parameters considered are: solar

radiation, mass flow rate, inlet air temperature, air velocity in the collector, length, height of

the v-groove section and its gap from the tip of the vee to the glass cover. A parametric

study is also done by [16] where a single pass v-groove air collector is investigated. Constant

reference with the results from [16] will be done to compare the difference in the effect of

the parameters under investigation to both single and double pass configuration. The

approach used to analyse the effect of each parameter is to keep all parameter values of the


54

air collector constant and only varying the parameter of interest.

The first to be looked upon is the effect of solar radiation to the output temperature

and efficiency when 𝐼 value ranges from 0 𝑡𝑜 1000 𝑊/𝑚2. The result of the simulation is

presented in Figure 15. It can be observed from the graph that both absorber plate

temperature and output temperature linearly increases as the radiation increase. On the

other hand, it does not have a significant effect on the efficiency. Compared to [16], the

trend of the result between the two configuration is similar.

Figure 27. Effect of solar radiation to the output temperature and efficiency when I ranges from 0 to 1000 W/m2

The effect of mass flow rate to the output temperature and efficiency when 𝑚 value

ranges from0 𝑡𝑜 0.1 𝑘𝑔/𝑚2𝑠 is shown in Figure 16. It can be observed that the effect of

mass flow rate at some point is becoming less and less significant for both output

temperature and efficiency. When the flow rate is less than 0.01 𝑘𝑔/𝑚2𝑠, its effect is very

large but as its value increases, the effect becomes insignificant. Considering the absorber

plate temperature and output temperature, when the mass flow rate is less than

0.015 𝑘𝑔/𝑚2𝑠, the output temperature is higher than the absorber plate temperature.

Once the mass flow rate exceeds this value, the trend switches. This is attributed to the high


55

radiation and convection heat transfer occurring at low mass flow rate. Compared to [16],

the trend of the result between the two configuration is similar.

Figure 28. Effect of mass flow rate to the output temperature and efficiency when m ranges from 0 to 0.1 kg/m2s

The effect of inlet air temperature to the output temperature and efficiency when

𝑇𝑓𝑖value ranges from 280 𝑡𝑜 400 𝐾 is shown in Figure 17. It can be observed from the graph

that both absorber plate temperature and output temperature linearly increases as the inlet

air temperature increase and apparently, both temperature are increasing at the same rate.

On the other hand, as the inlet air temperature increase, the efficiency linearly decreases.

This indicates that the inlet air temperature has a significant effect on the air collector.

Therefore in choosing the optimal inlet air temperature for the design, caution must be

taken to ensure that a reasonable value for inlet air temperature is selected. Compared to

[16], the trend of the result between the two configuration is similar.


56

Figure 29. Effect of inlet air temperature to the output temperature and efficiency when Tfi ranges from 280 to 400 Kelvins

The effect of air velocity to the output temperature and efficiency when 𝑈𝑓 value

ranges from 0 𝑡𝑜 10 𝑚/𝑠 is shown in Figure 18. Air velocity does not affect the output

temperature and efficiency significantly. It can be observed that the effect of air velocity

becomes insignificant for both output temperature and efficiency once it exceeds

approximately 1 𝑚/𝑠. This has a positive effect on the air collector performance thus the air

velocity should always be kept at values greater than 1 𝑚/𝑠 to ensure higher output

temperature and efficiency. Considering the absorber plate temperature and output

temperature, when air velocity is approximately 2.9 𝑚/𝑠 the output temperature is higher

than the absorber plate temperature. However, this will not occur but rather, the

temperatures will just diverge to absorber plate temperature as the air velocity increase.

This is due to the turbulent flow occuring inside the channels which consequently increases

convective heat transfer.


57

Figure 30. Effect of air velocity to the output temperature and efficiency when Uf ranges from 0 to 10 m/s

The effect of length to the output temperature and efficiency when 𝐿 value ranges

from 0 𝑡𝑜 50 𝑚 is shown in Figure 19. It can be observed from the graph that has some

effect on the output temperature and efficiency of the air collector. Its effect on output

temperature is a decrease of about 3 Kelvins and its effect on efficiency leads to a non-linear

decrease of about 10% as the length increased. Considering the absorber plate temperature

and the output temperature, it can be seen that the temperature difference between the

two increases as the length increase. This is contradictory to the results from [16] where it is

found that the length of the collector has negligible effect. This variation of result may be

attributed to the change in configuration of the collector. A single pass air collector only

goes through the collector one without undergoing any directional changes or turns.

However, for a double pass, the air has to go through the same section twice with not only

the change in flow direction and turn but also the flow section. Therefore the absorber plate

interacts with the same section of air along its length twice which consequently causes

convective heat transfer between the two medium.


58

Figure 31. Effect of length to the output temperature and efficiency when L ranges from 0 to 50 m

The effect of the height of the v-groove to the output temperature and efficiency

when 𝐻𝑔 value ranges from 0 𝑡𝑜 0.2 𝑚 is shown in Figure 20. V-groove height has negligible

effect on the output temperature and efficiency of the air collector and the absorber

temperature generally decreases as the v-groove height increase which is in contrast with

the result from [16]. The reasoning behind their variation is due to difference in

configuration as stated previosly. Thus for a double pass v-groove air collector, the height of

the v-groove will not have a significant effect on output temperature and efficiency.

Figure 32. Effect of v-groove height to the output temperature and efficiency when Hg ranges from 0 to 0.2 m


59

The effect of the gap between the v-groove absorber and glass cover to the output

temeprature and efficiency when 𝐻𝑐 value ranges from 0 𝑡𝑜 0.2 𝑚 is shown in Figure 21.

The gap has negligible effect on the output temperature and efficiency of the air collector.

The absorber plate varies in temperature as the gap increases. This is due to the change in

flow condition in the channel. However, this variation is in contrast with the result from

[16]. The reasoning behind their variation is due to difference in configuration as stated

previosly. Thus for a double pass v-groove air collector, the the gap between the v-groove

absorber and glass cover will not have a significant effect on output temperature and

efficiency.

Figure 33. Effect of gap between absorber and glass cover to the output temperature and efficiency when Hc ranges from 0 to 0.2 m

8. Problems encountered

Developing an efficient solar dryer is not an easy task. There are a lot of problems

encountered along the way related to the development of the simulation model as well as

problems encountered within the group. Some setbacks experienced during the project are

listed;


60

There are numerous air collector configurations that currently exist throughout the

world and there is quite a lot of literature written for each. One problem

encountered during the early stage of the project is selecting which air collector

configuration should be employed. The solar air collector is one of the most

important part of the solar dryer thus care should be taken. To solve this problem, a

lot of research effort was done by the team and from this research and literature

review, it was decided to use a double pass v-groove solar air collector.

Researching the equations to use for the configuration chosen was difficult since no

journal was found that provides the equation needed to create a simulation model.

Therefore, various literatures from different author which discusses about modelling

and experimenting the performance of an air collector are used.

There have been a lot of changes and revisions done on the simulation model.

During the early stage of developing the simulation model, the codes would not

function with reason that is difficult to figure. It gets quite frustrating. Then as the

project moves on, the problem became the codes themselves where a number is

mistyped or an equation is wrong. These types of problem were solved by doing a

comparison of the experimental result from journals and comparing it with the

simulation model. All in all, the most difficult part of the project so far is to ensure

that the model can accurately predict the performance of the solar air collector. A lot

of revision and changes happen but with each change, the simulation model gets

more and more accurate.


61

9. Project plan

The first part of the project is completed according to the timeline set during the project

proposal (see Project Timeline in the proceeding page). A group of 3 students are working

on developing an efficient solar dryer and each are assigned a different task. Everyone

managed to meet the deadline set and satisfy the timeline of the project.

The project task is divided into different categories and Parts 1 to 4 is completed.

Theoretical performance is done by Erond, Optimization is done by Anthony and design is

done by Dave.


62


63

Project timeline: Part 1 to 4 is to be completed during semester 1 and Part 5 to 7 is to be completed during semester 2


64


65

10. Conclusion

Overall, the first phase of the project is successfully delivered. The project progress is

as planned and all the necessary task needed to be done is completed. The simulation codes

created in MATLAB was able to predict the mean temperature of any component of the air

collector, the instantaneous air temperature at any section of the collector, the output air

temperature, and efficiency.

The simulation results were verified and it was found that the simulation has the

ability to predict the performance of the air collector accurately as proven by the

comparison of experimental result and simulation. The percent difference between the

results is, at maximum, approximately 7% only which is within the acceptable limit

considering some uncertainties in the input parameter values to allow comparison.

A parametric study was done and it was determined that inlet air temperature and

mass flow rate has a significant effect on the efficiency of the air collector. Other

parameters that were studied are the solar radiation, air velocity, length, v-groove height

and gap between the absorber and glass cover. These parameters have relatively less

significant effect on the output temperature and efficiency with the exception of solar

radiation. Along with the parametric study, a comparison is also made with the investigation

done by Tao Liu, et al., for a single pass v-groove. It was found that solar radiation, mass

flow rate and inlet air temperature has similar effect on the performance of a single and

double pass configuration. On the other hand, the effect of other remaining parameters

deviates significantly compared to the single pass configuration. This deviation is attributed

to the change in flow condition in the channel.


66

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69

Parametric values used for simulation

𝐼 600 W/m2 𝜀1 0.94

∅ 30 degrees

𝜀2 0.9

𝑊 1 m

𝜀3 0.94

𝐿 2 m

𝛼1 0.06

𝐻𝑔 0.05 m

𝛼2 0.95

𝐻𝑐 0.025 m

𝜏1 0.84

𝑚 0.035 kg/m2s 𝑉 1 m/s


70

𝑇𝑎 300 Kelvins

𝜎 5.67E-08 W/m2K4

𝑇𝑓𝑖 300 Kelvins

𝑔 9.81 m/s2

𝑥 0.06 m 𝑈𝑓 1 m/s

𝑘𝑖 0.025 W/mK

Nomenclature

𝐶𝑝 - specific heat of air (𝐽/𝑘𝑔𝐾)

𝐷𝑕 ,𝐷𝑕′ - hydraulic diameter of first and second pass (𝑚)

𝑔 - gravitational constant (9.81 𝑚2/𝑠)

𝑕1,2,3,4 - convection heat transfer coefficients (𝑊/𝑚2𝐾)

𝑕𝑟𝑠 - glass cover to sky radiative heat transfer coefficient (𝑊/𝑚2𝐾)

𝑕𝑟21 ,𝑟23 – radiative heat transfer coefficient (𝑊/𝑚2𝐾)

𝑕𝑤 - wind convection heat transfer coefficieny (𝑊/𝑚2𝐾)

𝐻𝑐 – gap between v-groove absorber and glass cover (𝑚)

𝐻𝑔 - height of v-groove (𝑚)

𝐼 – solar radiation (𝑊/𝑚2)

𝑘 - thermal conductivity of air (𝑊/𝑚𝐾)

𝑘𝑖 - insulation thermal conductivity (𝑊/𝑚𝐾)

𝐿 - length of the collector (𝑚)

𝑚 – air mass flow rate (𝑘𝑔/𝑚2𝑠)

𝑛𝑐 – efficiency of the collector

N – number of glass cover

𝑄1,2 - heat transferred to the air in first and second pass (𝑊/𝑚2)

𝑆1,2 - solar radiation absorbed by glass cover and absorber plate (𝑊/𝑚2)

𝑇1,2,3,4 – mean temperatures of surfaces (𝐾)


71

𝑇𝑎 - ambient temperature (𝐾)

𝑇𝑓1 ,𝑓2 – mean fluid temperature (𝐾)

𝑇𝑠 - sky temperature (𝐾)

𝑇𝑓𝑖 - initial air temperature (𝐾)

𝑇𝑜 - output air temperature (𝐾)

𝑈𝑏 – bottom heat loss coefficient (𝑊/𝑚2𝐾)

𝑈𝑡 - top heat loss coefficient (𝑊/𝑚2𝐾)

𝑈𝑓 - air velocity in the collector (𝑚/𝑠)

𝑉 - wind velocity (𝑚/𝑠)

𝑊 - width of the collector (𝑚)

𝑥 - insulation thickness (𝑚)

𝛼1- absorptivity of glass cover

𝛼2 - absoptivity of absorber

𝜀1 - emissivity of glass cover

𝜀2 - emissivity of absorber

𝜀3 - emissivity of bottom plate

𝜏1 - transmittance of glass cover

𝜎 – Boltzmann constant (5.67 × 10−8 𝑊/𝑚2𝐾4)

𝜌 - air density (𝑘𝑔/𝑚3)

∅ - tilt angle of the collector (degrees)

𝜇 - dynamic viscosity (𝑘𝑔/𝑚𝑠)

Drying chamber nomenclature

𝐴 −Area, m

𝐶𝑝𝑎 −Specific heat of air, J/kg°C

𝑕𝑣 −Volumetric heat loss coefficient, W/m3 °C

𝐿 −Length, m

𝑚 −Mass flow rate, kg/s

𝑁 −Number of bed elements

𝑇𝑎𝑚𝑏 −Ambient air temperature, °C


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𝑇𝑎 ,𝑚 −Inlet air temperature to bed elemen, °C

𝑇𝑏 ,𝑚 −Mean temperature of bed element, °C

𝑇𝑎 ,𝑚+1 −Outlet air temperature of bed element, °C

∆𝑡 −Time increment, s

Development of an efficient solar drying system

Documents

solar collector

solar drying system

drying chamber

solar air collector

thermal storage tank

mathematical model formulation

thermal network

mixing chamber