InterviewSolution
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InterviewSolution
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The thermal power of density `omega` is generated uniformly inside a uniform sphere of radius `R` and heat conductivity coefficient `x`. Find the temperature distribution in the sphere provided the steady-state temperature at its surface is eqal to `T_0`. |
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Answer» Here again `nabla^2 T = -(w)/(k)` So in spherical polar coordinates, `(1)/(r^2) (del)/(del r) (r^2 (del T)/(del r)) = -(w)/(k)` or `r^2 (del T)/(del r) = -(w)/(3 k) r^3 + A` or `T = B - (A)/( r) - (w)/(6 k) r^2` Again `A = 0` and `B = T_0 + (w)/(6k) R^2` so finally `T = T_0 + (w)/(6k)(R^2 - r^2)`. |
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