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Specific Heat Capacity

Find the rate...

Question

Find the rate of heat flow through a cross-section of the rod shown in figure $(T_{H} > T_{C})$ . Thermal conductivity of the material of the rod is K.

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Solution

Conductivity of the material of the rod is $= K$
$\frac{d Q}{d t} = \frac{K A (T_{H} - T_{e})}{x}$
The heat produced per unit time by the source is P. This heat is distributed over inner surface of the spherical shell having area $A = 4 π R^{2}$
Let $x$ be thickness of the shell.
The rate of heat transfer due to conduction is
$\frac{d Q}{d t} = \frac{K A T}{r}$

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