Heat Transfer
26
It is that area of mechanical engineering that deals with the different principles and mechanisms involved in transferring heat from one point to another. Heat Transfer Heat Transfer
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Transcript of Heat Transfer
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
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
