TITLE.PM5

HEAT TRANSFER 791

dharm

\M-therm\Th15-1.pm5

t 1

t 2

hcf

hhf

Hot fluid film

Q Q

thf

1

Metal wall

Cold fluid film

tcf

2

L

thf t 1 t 2 tcf

1

h.Ahf

L

k.A

1

h.Acf

k

Fig. 15.7. The overall heat transfer through a plane wall.

The equations of heat flow through the fluid and the metal surface are given by

Q = hhf. A(thf – t 1 ) ...(i)

Q = kt t

L

A() 12 − ...(ii)

Q = hcf. A(t 2 – tcf) ...(iii)

By rearranging (i), (ii) and (iii), we get

thf – t 1 =

Q

hAhf. ...(iv)

t 1 – t 2 =

QL

kA. ...(v)

t 2 – tcf =

Q

hAcf. ...(vi)

Adding (iv), (v) and (vi), we get

thf – tcf = Q

11

hA

L

hf.. .kA h Acf

++

L

N

M

M

O

Q

P

P

or Q =

At t

h

L

kh

hf cf

hf cf

()−

(^11) ++
...(15.31)
If U is the overall coefficient of heat transfer, then
Q = U.A (thf – tcf) =
At t
h
L
kh
hf cf
hf cf
()−
(^11) ++
or U =
1
11
h
L
hf khcf
++
...(15.32)