11 Heat Transfer

HEAT TRANSFER

Content

• Modes of heat transfer?

• Fourier Law of heat conduction

• Convective heat coefficient

• Radiant heat coefficient

• Overall heat transfer coefficient

• Hands-on example

Temperature

• A measure of energy due to level of heat

– Freezing point of water is 0 ˚ C

– Boiling point of water is 100 ˚ C

Common Temperature Scales

What is Heat?

Heat is the total internal kinetic energy due to molecular motion in an object

Quantity of heat is BTU or Kilo Joule (kJ)

• One BTU is the amount of heat required to raise 1 lb of water by 1 ˚ F

• One calorie is required to raise 1 g of water by 1 ˚ C

1 cal = 4.187 J

• 1 BTU= 1.055 kJ= 1055 J

Heat Vs Temperature

• Heat energy depends on mass. Temperature is independent of mass.

– 2 litres of boiling water has more heat energy than 1 litre of boiling water

• Temperature is not energy, but a measure of it

• Heat is energy

Heat is Energy

When heat (ie energy) goes into a substance, one of two things can happen:

1. Temperature goes up

2. Change of state

Temperature Goes Up

• Heat that causes a rise in temperature e.g. heating water before boiling

• The heat energy is used to increase the kinetic energy of the molecules in the substance

• This is also known as the sensible heat

Change Of State

• Heat that brings about a change in potential energy of the molecules (temperature remains constant). Also called the latent heat.

Specific Heat

• It is the heat required to the temperature of 1 kg (lb) a substance by 1 ˚ K (F)

• Example:

water’s specific heat is 1 btu/ lb F (4.2 kJ/kg K)

air’s specific heat is 0.24 btu/ lb F (1.0 kJ/kg K)

Sizing Heating Capacity

Theat x specific x mass requiredheat ofQuantity

Example:

What is the heat required to raise air

temperature from 15 ˚C to 25 ˚C at a

flow rate of 2000 l/s?

Heat Transfer

• If there is a temperature difference in a system, heat will always move from higher to lower temperatures

What is actually flowing?

Heat Transfer Modes

There are 3 modes of heat transfer.

1. Conduction

2. Convection

3. Radiation

Conduction

• Heat transfer through a solid medium via direct contact

• Expressed by Fourier’s Law

Fourier’s Law

Q

X

T2 T1

dx

dTkq "

k = thermal conductivity (W/ m K)T = temperature (K)q” = heat flux (W/m2)

Heat flow rate = q” x area (W)

Fourier’s law at steady state

kAL

TT

q

kL

TTq

L

TTkq

dx

dTkq

inout

inout

inout

/

flowheat of Area x "Q

ratefer Heat trans

/

"

State)(Steady "

Law)(Fourier "

T1

T2

q

R=L/k Unit thermal resistance

Example 1

• Temperature of 35 C and 22 C are maintained on opposite sides of a steel floor of 6mm thick. Compute the heat flux through the floor.

• Thermal conductivity for steel = 50 W/m K

Thermal Conductivity, k (W/m K)

LiquidsWater: 0.556Ammonia: 0.54GasesAir : 0.024Water vapor: 0.021

Common Metals Copper: 385 Aluminum: 221Steel: 50 Non-metalsCommon brick: 0.6 Mineral wool: 0.04Ceiling board: 0.06

Quiz

• Suppose a human could live for 2 h unclothed in air at 45 ˚F. How long could she live in water at 45 ˚F?

Electrical- Thermal Analogy

cesis

cesis

tanRe

difference eTemperaturq flux,Heat

Thermal

tanRe

Potential VoltageI Current,

Law) s(Ohm' Electrical

T1T2

q

R=L/kA

Composite Wall

Using the resistance concept,

T1

T2R1 R2

Q

2

22

1

11

21

12"

k

xR

k

xR

RR

TTq

Example 2A wall of a Switchgear room consists the

following:

QQ

q2

k2

35 C 22 C

6mm 25mm100mm

TNF panelk = 0.02 W/m K

Firebattk = 0.04 W/m K

Steel platek = 50 W/m K

Q

Determine Q, if the wall is 3m x 4m ?

Convection

• Energy transfer by fluid motion

• Two kinds of convection

– Forced convection: Fluid is forced

– Natural or free convection: fluid is induced by temperature difference

where:

h c is convection coefficient (W/m2C),

Ts is surface temperature (C),

T a is surrounding air temperature (C)

Rc= unit convective resistance.

Convective Heat Transfer

air flow

Ta

Ts

y

q

c

c

C

as

asc

hR

h

TTq

TThq

1

1

("

)("

cooling of Law sNewton'

)

Magnitude of Convection Coefficients

Arrangement h, W/m2 K Btu/(h.ft2.F)

Air, free (indoor) 10-30 1-5

Air, forced (outdoor)

30-300 5-50

Oil, forced 60-1800 10-300

Water, forced 300-6000 50-1000

Steam, condensing 6000-120000 1000-20000

Example 3

The same as Example 2. Consider convection of the exposed surfaces, calculate Q.

QQ

q2

k2

35 C 22 C

6mm 25mm100mm

TNF panelk = 0.02 W/m K

Firebattk = 0.04 W/m K

Steel platek = 50 W/m K

Q

Radiation

• Energy emitted by object that is at any temperature above absolute zero

• Energy is in the form electromagnetic waves

• No medium needed and travel at speed of light

Hot Body

Radiator

radiationolar

:Example

S

Radiation

• Important mode of heat at high temperatures, e.g. combustion furnace

• At room temperature it may just be measurable.

• Intensity depends on body temperature and surface characteristics

• Solar radiation is the radiation emitted by the sun due to nuclear fusion reaction

• Solar Constant: The amount of solar energy arriving at the top of the atmosphere perpendicular to the sun’s rays.

• = 1375 W m-2

Solar Radiation

Solar Radiation Spectrum

99% of solar radiation is between 0.3 to 3 µm.

Wien’s Law

mT

2900 m

Wien’s Law

The Black Body

E = AT4

• E =The amount of energy (W ) emitted by an object

• = Stefan-Boltzmann constant =5.67 x 10-8 W m-2 K-4

• T = Temperature (K)

• A= area (m2)

The Grey Body

metals polishedfor 0.07-0.02

materialscommon for 0.9-0.8

tyemissitivi

where)(E E

body, actualan For 4

b

TA

Net Radiant Heat

• If a hot object is radiating to a cold surrounding, the radiation loss is

)( q 44ch TTA

Quiz

How much energy does human body radiate?

• Body temperature is 37 C

• Body area is 1.5 m2

• ε= 0.7

Radiant Heat Transfer

• Unit thermal resistance for radiation is written as

r

c

r

h

1 R

T)(h q"

Radiation coefficient is a function of temperature, radiation properties and geometrical arrangement of the enclosure and the body in question.

Combined convection and radiant Coefficient

• The heat transfer is combination of convection and radiation

rc hh

1R

,resistance thermalCombined

))(("

"

Thhq

qqq

rc

rc

Combined Surface Coefficients

Air velocity Emissivity, ε=0.9

3.5 m/s h = 22.7 W/m2 K

7 m/s h = 35 W/m2 K

Still air h = 8.5 W/ m2 K

• Some practical values of surface coefficients:(source: ASHRAE Fundamentals 1989)

k2

Combined modes

T

k1

Outside

Inside

Thot

Tcold

T1

T3

R2=L1/k1 + L2/K2

R3=1/hhot

R1=1/hcold

T2

T1

Tcold

Thot

Resistance in parallel, R= R1 + R2 +R3

T3

Compute

2211

2

1

2211

2

2

1

1

321

///1"

/1"

///1/1"

1/

1

kLkLh

TTq

h

TTq

kLkLhh

TTq

hk

L

k

L

hR

RRRR

cold

cold

cold

cold

coldhot

coldhot

hotcold

Thot

Tcold

T1

T2R2=L1/k1 + L2/k2

R3=1/hhot

R1=1/hcold

Overall Heat Transfer Coefficient

• Heat transfer processes includes conduction, convection and radiation simultaneously

• The total conduction heat transfer for a wall or roof is expressed asQ = A x U x ∆T whereU is the overall heat transfer coefficient (or U-value)

RU

RRRR

1

.......321

Example

• Find the overall heat transfer coefficient of a flat roof having the construction shown in the figure.

Solution

T2

T1

R3

R1

R2

R4

R5

R6

SolutionResistance Construction Unit resistance (m2 K/ W)

R1 Outside air

R2 steel

R3 Mineral wool

R4 Air space

R5 Ceiling board

R6 Inside air

Total R

Solution

K W/m40.048.2

1

R

1U

tcoefficienfer heat trans Overall

2

Heat Transfer Loop in a DX System

Heat Exchanger Coil

Heat is exchanged between 2 fluids.Q= UA ∆TFor cross flow,Q= UA (LMTD)

Heat Exchanger- Mean Temperature Difference

LTD

GTDLn

LTD-GTD x Areax U Q

LMTD x Area x U Q Transfer,Heat

Heat transfer optimization

• We have the following relations for heat transfer:– Conduction: Q = k A ∆T /d – Convection: Q = A h c ∆T– Radiation: Q = A h r ∆T

• As a result, when equipment designers want to improve heat transfer rates, they focus on:– Increasing the area A, e.g. by using profiled tubes and ribbed

surfaces.– Increasing T (which is not always controllable).– For conduction, increasing k /d.– Increase h c by not relying on natural convection, but

introducing forced convection.– Increase hr, by using “black” surfaces.