Engr. FRANCIS M. MULIMBAYAN BSAE / MSMSE INSTRUCTOR 4 ENSC 14a Engineering Thermodynamics and Heat Transfer Department of Engineering Science University of the Philippines –Los Banos College, Los Banos, Philippines Basics of Heat Transfer ENSC 14A LECTURE NOTES PREPARED BY ENGR. FMMULIMBAYAN
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Engr. FRANCIS M. MULIMBAYAN
BSAE / MSMSE
INSTRUCTOR 4
ENSC 14a
Engineering Thermodynamics and Heat Transfer
Department of Engineering Science University of the Philippines –Los Banos
College, Los Banos, Philippines
Basics of
Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Thermodynamics Deals with the amount of heat
transfer as a system undergoes a process from one equilibrium state to another
First Law requires that the rate of energy transfer into a system should be equal to the rate of increase of energy of the system
Second Law requires that heat is transferred in the direction of decreasing temperature.
Makes no reference to how long the process will take
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Heat Transfer
Deals with the determination of the rates of energy transfer in the form of heat
Deals with systems that lack thermal equilibrium
Engineering Heat Transfer
Rating Problems – deal with the determination of heat transfer for an existing system at a specified temperature difference
Sizing Problems – deal with the determination of the size of a system in order to transfer heat at a specified rate for a specified temperature difference.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Heat
Form of energy that can be transferred from one system to another as a result of temperature difference.
Sensible Heat
Heat absorbed or given off by a substance that is not in the process of changing its phase.
Latent Heat
Heat absorbed or given off by a substance while it is changing its phase.
Specific Heat (𝐶𝑝, 𝐶𝑣)
Represents energy required to raise the temperature of a unit mass of a substance by one degree in a specified way.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Total Energy
Sum of thermal, mechanical, kinetic, potential, electrical, magnetic, chemical, and nuclear energy.
Microscopic Energy
Forms of energy related to the molecular structure of a system and the degree of the molecular activity
Internal Energy (U)
Sum of all microscopic forms of energy of solids and stationary fluids
Enthalpy (H)
Represents the microscopic energy of flowing fluids.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Units of Energy
SI unit: kilojoules (kJ)
English: British Thermal Unit (BTU)
1 BTU = 1.055056 kJ
1 cal = 4.1868 J
British Thermal Unit
Energy needed to raise the temperature of 1 lbm of water at 60°F by 1°F.
Calories
Energy needed to raise the temperature of 1 gram of water at 14.5°F by 1°C.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Energy Balance for a Closed System
𝑄 = 𝑚 ∆𝑢 = 𝑚 𝐶𝑣𝛥𝑇
Energy Balance for a Steady-Flow Systems
𝑄 = 𝑚 ∆ℎ = 𝑚 𝐶𝑝𝛥𝑇
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Introduction
Amount of Heat Transfer (kJ or Btu) 𝐐 = 𝐦𝐂𝚫𝐓
Heat Transfer Rate (kW or Btu/hr)
𝐐 =𝐐
∆𝐭
Heat Transfer per unit length (kW/m or Btu/hr-ft)
𝐐 ′ =𝐐
𝐋
Heat Flux (kW/m² or Btu/hr-ft²)
𝐪 = 𝐐 ′′ =𝐐
𝐀𝐬
Heat Generation (kW/m³ or Btu/hr-ft³)
𝐠 = 𝐐 ′′′ =𝐐
𝐕
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Application Areas of Heat Transfer
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Modes of Heat Transfer
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Modes of Heat Transfer
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Conduction
Conduction
Transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles.
Transfer of thermal energy in solids or fluids at rest
In fluids, conduction is due to collisions and diffusion of the molecules during their random motion.
In solids, it is due to combination of vibrations of the molecules in a lattice and energy transport by free electrons.
Depends on the geometry, thickness and material composition of the medium and on the temperature difference across the medium.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Conduction
Physical Mechanism of Conduction
The thickness and area of a given large plane wall is ∆𝑥 = 𝐿 and 𝐴, respectively.
The temperature difference across the wall is,
ΔT = T2 − T1
Experiments revealed that,
Q ∝ AΔT
L
Incorporating the proportionality constant and letting Δx → 0, results to
𝐐 𝐜𝐨𝐧𝐝 = −𝐤𝐀𝐝𝐓
𝐝𝐱
→ 𝐅𝐨𝐮𝐫𝐢𝐞𝐫′𝐬 𝐋𝐚𝐰 𝐨𝐟 𝐇𝐞𝐚𝐭 𝐂𝐨𝐧𝐝𝐮𝐜𝐭𝐢𝐨𝐧
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Conduction
Fourier’s Law of Heat Conduction
The temperature gradient is the slope of the temperature curve on the T-x diagram
Thermal conductivity of a material is the measure of the ability of the material to conduct heat.
The negative sign indicates that the heat transfer in the positive x direction is a positive quantity.
𝐐 𝐜𝐨𝐧𝐝 = −𝐤𝐀𝐝𝐓
𝐝𝐱
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Conduction
Sample Problem 9.1 Calculate the rate of heat transfer through a pane of window glass (𝑘 = 0.81 W/m-K) 1 m high, 0.5 m wide, and 0.5 cm thick, if the outer surface temperature is 24°C and the inner-surface temperature is 24.5°C.
Chapter 9 Basics of Heat Transfer
𝑄 𝑐𝑜𝑛𝑑 = −𝑘𝐴𝑑𝑇
𝑑𝑥= 𝑘𝐴
𝑇1 − 𝑇2𝐿
=0.81
𝑊𝑚 − 𝐾
1 𝑚 𝑥 0.5 𝑚 24.5 − 24 𝐾
0.005 𝑚= 𝟒𝟎. 𝟓 𝑾
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Convection
Convection
Thermal energy is transferred to or from a fluid near a solid surface
Conduction with added complexity of thermal energy transfer by moving fluid molecules
Physical Mechanism
Energy is first transferred to the air layer adjacent to the block by conduction.
The energy is then carried away from the surface by convection
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Convection
Types of Convection
Forced Convection
Also known as assisted convection
Occurs when fluid motion is induced by an external mean such as pump or fan
Natural Convection
Also known as free convection
Brought by buoyancy forces due to density differences caused by temperature variations in the fluid
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Convection
Newton’s Law of Cooling
𝐐 𝐜𝐨𝒏𝒗 = 𝒉𝑨(𝑻𝒔 − 𝑻∞)
Convective Heat Transfer Coefficient (𝒉)
Depends on all the variables influencing convection such as surface geometry and orientation, flow regime, properties of fluids, bulk velocity, etc.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Conduction
Sample Problem 9.2 Calculate the rate of heat transfer by natural convection between a shed roof of area 20 m x 20 m and ambient air, if the roof surface temperature is 27°C, the air temperature is -3°C, and the average convection heat transfer coefficient is 10 W/m2-K.
Chapter 9 Basics of Heat Transfer
𝑄 𝑐𝑜𝑛𝑑 = ℎ𝐴𝑠 𝑇𝑠 − 𝑇∞
= 10𝑊
𝑚2 − 𝐾20 𝑚 𝑥 20 𝑚 (27
− (−3))𝐾
= 120,000 𝑊
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Radiation Heat Transfer
Thermal energy is transferred by electromagnetic waves
Does not require medium
Electromagnetic radiation
Emitted by all bodies with temperature greater than absolute zero
e.g. x-rays, gamma rays, microwave, television waves
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Thermal Radiation
Radiation emitted by bodies because of their temperature
Stefan-Boltzmann Law
Gives the blackbody emissive power or the maximum rate of radiation per unit surface area that can be emitted by a body at an absolute temperature 𝑇𝑠
𝐐 𝐞𝐦𝐢𝐭,𝐦𝐚𝐱 = 𝛔𝐀𝐬𝐓𝐬𝟒
σ = 5.67 × 108W
m2 ∙ K4= 0.1714 × 108
Btu
hr ∙ ft2 ∙ R4
As = Surface area in 𝑚2 𝑜𝑟 𝑓𝑡2
Blackbody
Idealized surface that emits radiation at its maximum rate
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Emissivity, 𝛆
Ratio of the radiation emitted by the surface at a given temperature to the radiation emitted by a blackbody at the same temperature.
Real Surfaces
Radiation emitted is always less than the radiation emitted by blackbody at the same temperature.
𝐐 𝐞𝐦𝐢𝐭 = 𝛆𝛔𝐀𝐬𝐓𝐬𝟒
Irradiation, G
Radiation flux incident on a surface from all directions
Radiosity, J
Radiation flux leaving a surface from all directions
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Absorptivity (𝜶)
The fraction of irradiation absorbed by the surface
Reflectivity 𝝆
The fraction of irradiation reflected by the surface
Transmissivity 𝝉
The fraction of irradiation transmitted by the surface
𝜶 + 𝝆 + 𝝉 = 𝟏
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Opaque material
It has 𝝉 = 𝟎
It allows thermal radiation to be emitted or absorbed within the first few microns of the surface, and thus radiation for this material are said to be a surface phenomenon.
Semi-transparent material
Allows certain type of radiation to penetrate while inhibits other type of radiation.
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Radiation
Net Radiation Heat Transfer
Difference between the rates of radiation emitted by the surface and the radiation absorbed
The emitted radiation is given by the Stefan-Boltzmann Law
The absorbed radiation is α𝐺
Simplifying Assumptions
Radiation exchange occurs between surfaces in which 𝜶 = 𝟏 and that 𝝆 = 𝟎
All surfaces involved are opaque, that is, 𝝉 = 𝟎
Each surface is isothermal and diffuse
𝑸 𝟏−𝟐 = 𝝈𝑨𝟏[𝜺𝟏𝑻𝟏𝟒 − 𝜺𝟐𝑻𝟐
𝟒]
Chapter 9 Basics of Heat Transfer
ENSC 14A LECTURE NOTES PREPARED BY
ENGR. FMMULIMBAYAN
Conduction
Sample Problem 9.3 A long, cylindrical electrically heated rod, 2 cm in diameter, is in a vacuum furnace. The surface of the heating rod has an emissivity of 0.9 and is maintained at 1000 K, while the interior walls of the furnace are black and are at 800 K. Calculate the net rate at which heat is lost from the rod per unit length.