It is that area of mechanical engineering that dealswith the different principles and mechanisms involvedin transferring heat from one point to another.

Heat Transfer

Heat Transfer

Modes of Heat Transfer1. Conduction: Is the transfer of heat from one point to another point within

a body or from one body to another body when they are physical contact with each other.

2. Convection: Is the transfer of heat from one point to another within a fluid.a. Natural or Free convection – motion of the fluid is due to the

difference in density because of a difference in temperature.b. Force Convection – motion of fluid is accomplished by

mechanical means, such as a fan or a blower.3. Radiation: It the flow of heat from one body to another body separated by

a distance due to electromagnetic waves.

fire

Metal rod

t1

Hotter body

t2

Colder body

Conduction

Fluid

Convection

2

t2

t1surface

1

Radiation

Hot body

Cold body

Conduction

L1

2k

A

Q

t1

t2

kAL

tt

kL

ttAQ

LttkA

LttkA

Q

Law sFourier' From

2121

2112

)()(

)()(

Where: L – thickness, meters A – surface area, m2

k – thermal conductivity, Q – conductive heat flow, Watts

K-mW

or Cm

W

Thermal Circuit Diagram

1 2R

Q

kAL

R

K or C potential, etemperaturtWK

orWC

,resistanceR

Rtt

RΔt

kAL

)t(tQ 2112

)(

Conduction through a Composite Plane Wall

L1L2 L3

k1 k2 k3

1A 2

3

4

Q

3

3

2

2

1

1

41

3

3

2

2

1

1

41

3

3

2

2

1

1

41

321

41

3

3

2

2

1

1

41

kL

kL

kL

ttAQ

kL

kL

kL

ttA

kL

kL

kL

A1

ttQ

RRRtt

AkL

AkL

AkL

ttQ

)(

)()(

)()(

Thermal Circuit Diagram

12

R1

Q

43

R2 R3

AkL

R

AkL

R

AkL

R

3

33

2

22

1

11

A furnace is constructed with 20 cm of firebrick, k = 1.36 W/m-K, 10 cm of insulating brick, k = 0.26 W/m-K, and 20 cm of building brick, k = 0.69 W/m-K. The inside surface temperature is 650C. The heat loss from the furnace wall is 56 W/m2. Determine a. the interface temperature and the outside wall temperature, C b. the total resistance Rt, for 1 m2

L1 L2 L31

2

3

4

Q

A

1 2

R1

Q

43

R2 R3

Given: L1 =0.20 m ; L2 = 0.10 m ; L3 = 0.20 m k1 = 1.46 ; k2 = 0.26 ; k3 = 0.69 t1 = 650C Q/A = 56 W/m2

At 1 to 2

C7641361200

56650t

kL

AQ

tt

kL

ttAQ

2

1

112

1

1

21

..

.

)(

C2620260100

361200

56650t

kL

kL

AQ

tt

kL

kL

ttAQ

3

2

2

1

113

2

2

1

1

31

..

.

.

.

)(

At 1 to 3

At 1 to 4

C604690200

260100

361200

56650t

kL

kL

kL

AQ

tt

kL

kL

kL

ttAQ

4

3

3

2

2

1

114

3

3

2

2

1

1

41

.

.

.

.

.

.

)(

Convection

FluidA

1

2

Q

t2

t1

h

Watts

hA1

ttQ

Watts tthAQdirection) opposite in flows (heat ttIf

Watts tthAQt t If

12

12

21

21

21

)(

)(

)(

Where:Q – convective heat flow, WattsA – surface area in contact with the fluid, m2

h – convective coefficient, W/m2-C or W/m2-Kt1, t2 – temperature, C

Conduction from Fluid to Fluid separated by a composite plane wall

L1L2 L3

k1 k2 k3

1A 2

3

4

Q

i hi ti

o ho, to

o3

3

2

2

1

1

i

oi

o3

3

2

2

1

1

i

oi

o3

3

2

2

1

1

i

oi

o321i

oi

o3

3

2

2

1

1

i

oi

h1

kL

kL

kL

h1

ttAQ

h1

kL

kL

kL

h1

ttA

h1

kL

kL

kL

h1

A1

ttQ

RRRRRtt

Ah1

AkL

AkL

AkL

Ah1

ttQ

)(

)()(

)()(

Thermal Circuit Diagram

1 2R1

Q

43R2 R3

i o

Ri Ro

AkL

R

AkL

R

AkL

R

3

33

2

22

1

11

Ah1

R

Ah1

R

oo

ii

Overall Coefficient of Heat Transfer

o3

3

2

2

1

1

i

o3

3

2

2

1

1

i

oi

o3

3

2

2

1

1

i

oi

h1

kL

kL

kL

h1

1U

tUAQ

h1

kL

kL

kL

h1

ttAQ

Ah1

AkL

AkL

AkL

Ah1

ttQ

)(

)(

)(

Where:U – overall coefficient of heat transfer, W/m2-C or W/m2-K

CONDUCTION THROUGH CYLINDRICAL COORDINATES

kL2r

r

R

tttR

tQ

kL2r

rtt

Q

1

2

21

1

2

21

ln

)()(

)(

ln

)(

Where: r1 – inside radius, m r2 – outside radius, m L – length of pipe, m k – thermal conductivity of material, W/m-Cr1

r2

1 2

t1

t2

Q

k

For composite cylindrical pipes (Insulated pipe)

r1

r2

1 2

t1

t2

Q

k1

3

r3t3

k2

Lk2r

r

R ; Lk2r

r

R

tttR Rt

Q

kr

r

kr

rttL2

Lk2r

r

Lk2r

rtt

Q

2

2

3

21

1

2

1

31

21

2

2

3

1

1

2

31

2

2

3

1

1

2

31

lnln

)()(

)(

lnln

)(

lnln

)(

Heat Flow from fluid to fluid separated by a composite cylindrical wall

r1

r2

1 2

t1

t2

Q

k1

3

r3t3

k2

ihi

ti

o

ho

to

Lr2A ; Lr2A

Ah1

R ; Lk2r

r

R ; Lk2r

r

R ; Ah1

R

tttRR RR

tQ

Ah1

Lk2r

r

Lk2r

r

Ah1

ttQ

3o1i

ooo

2

2

3

21

1

2

1ii

i

oi

o21i

oo2

2

3

1

1

2

ii

oi

lnln

)()(

)(

lnln

)(

Overall Coefficient of Heat Transfer

2

2

i

o

m surface, inside on based areaAi

m surface, outside on based area - Ao

area inside on based transfer heatof tcoefficien-Uarea outside on based transfer heatof nt-coefficieU

:where

oo2

2

3

1

1

2

ii

iioo

ii

oo

Ah1

Lk2rrln

Lk2r

rln

Ah1

1AUAU

)t(AUQ

)t(AUQ

Heat Exchangers

Types of Heat Exchangers1. Direct Contact Type: The same fluid at

different states are mixed.2. Shell and Tube Type: One fluid flows inside

the tubes and the other fluid on the outside.

Direct Contactm1, h1

m2, h2

m3, h3

3 Eq. hmhmhm

2 Eq. hmhmhmnegligible PE and KE balance, Energy

1 Eq. mm mBalance Mass

SYSTEM OPEN an for Law First Applying

312211

332211

321

)hh(m)hh(m

hm

232311

32

Shell and Tube Type

mc

mc

mh

mh

1

2A

B

twA

twB

h1

h2

By energy balanceHeat rejected by the hot fluid = Heat absorbed by the cold fluid

2.Eq)tt(CmQ

1.Eq)hh(mQ

QQ

wAwBpccc

21hh

ch

Where:mc – mass flow rate of cold fluid, kg/secmh – mass flow rate of hot fluid, kg/sech – enthalpy, kj/kgt – temperature,CCpc – specific heat of the cold fluid, KJ/kg-CQ – heat transfer, KWh, c – refers to hot and cold, respectively1, 2 – refers to entering and leaving conditions of hot fluidA, B – refers to entering and leaving conditions of cold fluid

Heat Transfer in terms of OVERALL COEFFICIENTOf HEAT TRANSFER U

difference etemperatur mean log m area, surface transfer heat total - A

K-m

W

or C-m

W transfer, heatof tcoefficien overall - U

:where

KW

2

2

2

LMTD

1000

)LMTD(UAQ

Log Mean Temperature Difference (LMTD)

1

2

12

lnLMTD

Where:1 – small terminal temperature difference, C2 – large terminal temperature diffrence,C