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Engineering
Physics
Thermodynamics
Conduction of Heat
Thermal Expansion
Question

Two parallel plates A and B are joined together to form a compound plate as shown in figure. The thickness of the plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 100 cm2 for each plate. The thermal conductivities are KA = 200 Wm–1°C–1 and KB = 400 Wm–1°C–1. The outer surface of plate A is maintained at 100°C and the outer surface of plate B is maintained at 0°C.

Ratio of thermal resistance of plate A to the equivalent thermal resistance is 0.76

The equivalent thermal conductivity of the compound plate is 548 Wm–1°C–1

The rate of heat flow through any cross-section is 3810 W

The temperature at the interface is 24°C

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Solution
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RA=ℓAKAA

=4 × 10−2m200 Wm−1°C−1 × 100 × 10−4 m2

= 2 × 10–2 °CW–1

RB=58×10−2

H=ΔTRA+RB≅3810

Req=ΔTH=100°C3809.5W

RA :  Req=2 × 10−21003809.5

=2 × 10−2 × 3809.5100=7619.0×10−4

RA : Req = 0.76

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