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Question

Consider steady-state heat conduction across the thickness in a plane composite wall (as shown in the figure) exposed to convection conditions on both sides.
Given :hi=20 W/m2K; h=50 W/m2K; T,i=20C, T,=2Ck1=20 W/mK; k2=50 W/mK;L1=0.30 m and L2=0.15 m
Assuming negligible contact resistance between the wall surfaces, the interface temperature, T(in C), of the two walls will be

A

0.50
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B

2.75
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C

3.75
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D

4.50
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Solution

The correct option is C
3.75
Given data:
hi=20 W/m2K; h=50 W/m2K; T,=20Ck1=20 W/mK; k2=50 W/mK;L1=0.30 m; L2=0.15 m


Heat flow:

Q=T,iT,Rti+Rt1+Rt2+Rt

Q=T,iT,1hiA+L1k1A+L2k2A+1hA

QA=T,iT,1hi+L1k1+L2k2+1h

=20(2)120+0.3020+0.1550+150
=20+25+1.50+0.3+2100=22×1008.8=250 W

also QA=T,iT1hi+L1k1

250=20T120+0.320=20T0.320
250×0.320=20T
16.25=20T
or T=2016.25
=3.75C

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