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Standard IX

Physics

Thermal Expansion

For the three...

Question

For the three-dimensional object shown in the figure below, five faces are insulated. The sixth face $(P Q R S),$ which is not insulated, interacts thermally with the ambient, with a convective heat transfer coefficient of $10 W / m^{2} K .$ The ambient temperature is $30^{\circ} C .$ Heat is uniformly generated inside the object at the rate of $100 W / m^{3} .$ Assuming the face $(P Q R S)$ to be at uniform temperature, its steady state temperature is

10^{\circ} C

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20^{\circ} C

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30^{\circ} C

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40^{\circ} C

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Solution

The correct option is D $40^{\circ} C$
Given Data:
$h_{\circ} = 10 W / m^{2} K T_{\circ} = 30^{\circ} C$

$q_{G} = 100 W / m^{3}$
Volume: $V = 2 \times 1 \times 2 = 4 m^{3}$
Heat generated,
$Q = q_{G} \times V = 100 \times 4 = 400 W$
Convection heat transfer from face $P Q R S,$
$Q = h_{\circ} A (T_{s} - T_{\circ}) 400 = 10 \times 2 \times 2 (T_{s} - 30) T_{s} - 30 = 10 T_{s} = 10 + 30 = 40^{\circ} C$

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The correct option is D 40∘CGiven Data: h∘=10 W/m2KT∘=30∘C qG=100 W/m3 Volume: V=2×1×2=4 m3 Heat generated, Q=qG×V=100×4=400 W Convection heat transfer from face PQRS, Q=h∘A(Ts−T∘)400=10×2×2(Ts−30)Ts−30=10Ts=10+30=40∘C