TITLE.PM5

HEAT TRANSFER 801

dharm
\M-therm\Th15-2.pm5

kA = Thermal conductivity of the inside layer A,

kB = Thermal conductivity of the outside layer B,

t 1 , t 2 , t 3 = Temperature at the points 1, 2 and 3 (see Fig. 15.18),

L = Length of the composite cylinder, and

hhf, hcf = Inside and outside heat transfer coefficients.

Q hcf

tcf

thf hhf

Hot

fluid

r 2

r 1

t 1 t 2 t 3

Cold fluid (air)

tcf

AA

AB

Fig. 15.18. Cross-section of a composite cylinder.

The rate of heat transfer is given by,

Q = hhf. 2πr 1. L(thf – t 1 ) =

kLtt

rr

A.( )

ln ( / )

(^212)
21
π−
= kLtt
rr
B.( )
ln ( / )
(^223)
32
π− = h
cf. 2πr 3. L(t 3 – tcf)
Rearranging the above expression, we get
thf – t 1 =
Q
hr Lhf.. 12 π ...(i)
t 1 – t 2 =
Q
kL
rr
A.
ln ( / )
2
21
π ...(ii)
t 2 – t 3 =
Q
kL
rr
B.
ln ( / )
2
32
π ...(iii)
t 3 – tcf =
Q
hr Lcf.. 3 2 π ...(iv)
Adding (i), (ii), (iii) and (iv), we have
Q
2 πL^
L
N
M
M
M
11 11
1
32
hr k 3
rr
k
rr
hf. ABhrcf
ln ( ln ( )
.
+++
21 /) /
O
Q
P
P
P
= thf – tcf