TITLE.PM5

HEAT TRANSFER 789

dharm

\M-therm\Th15-1.pm5

Since the quantity of heat transmitted per unit time through each slab/layer is same, we
have

Q = kAt t

L

kAt t

L

kAt t

L

A

A

B

B

C

C

.( 12 − )=. ( 23 − )=. ( 34 − )

(Assuming that there is a perfect contact between the layers and no temperature drop occurs

across the interface between the materials).

Rearranging the above expression, we get

t 1 – t 2 = QL

kA

A

A

.

.

...(i)

t 2 – t 3 =

QL

kA

B

B

.

.

...(ii)

t 3 – t 4 =

QL

kA

C

C

.

.

...(iii)

Adding (i), (ii) and (iii), we have

(t 1 – t 4 ) = Q

L

kA

L

kA

L

kA

A

A

B

B

C

...C

L ++

N

M

O

Q

P

or Q =

At t

L

k

L

k

L

k

A

A

B

B

C

C

() 14 −

++

L

N

M

O

Q

P

...(15.27)

or Q =

()

...

()

[]

tt

L

kA

L

kA

L

kA

tt

A RRR

A

B

B

C

C

th A th B th C

14 − 14

++

L

N

M

O

Q

P

= −

−−−++

...(15.28)

If the composite wall consists of n slabs/layers, then

Q =

[]tt()

L

kA

n

n

11

1

− +

∑

...(15.29)

A

C

B

Q

kA kC kG

kB D

kD

F

kF

E

kE

G

Q

Composite wall

Rth–A

Rth–C

Rth–B

Rth–D

Rth–E

Rth–G

Rth F–

Fig. 15.5. Series and parallel one-dimensional heat transfer through a composite wall and electrical analog.