Heat conduction with variable thermal conductivity (a) For steady-state heat conduction in solids, Eq. 11.2-5 becomes (
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 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).
Step by Step Answer:
Heat conduction with variable thermal conductivity First we obtain an express...View the full answer
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Conduction heat transfer is the transfer of heat through matter (i.e., solids, liquids, or gases) without bulk motion of the matter. In another ward, conduction is the transfer of energy from the more energetic to less energetic particles of a substance due to interaction between the particles. Conduction heat transfer in gases and liquids is due to the collisions and diffusion of the molecules during their random motion.
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