Question: Heat conduction with variable thermal conductivity (a) For steady-state heat conduction in solids, Eq. 11.2-5 becomes ( q) = 0, and insertion of Fourier's

Heat conduction with variable thermal conductivity

(a) For steady-state heat conduction in solids, Eq. 11.2-5 becomes (∆ ∙ q) = 0, and insertion of Fourier's law gives (∆ ∙ k∆ T) = 0. Show that the function F = fkdT + const. satisfies the Laplace equation V²F = 0, provided that k depends only on T.

(b) Use the result in (a) to solve Problem 10B.12 (part a), using an arbitrary function k(T).

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