Suppose that the specific heat is a function of position and temperature, c(x, u). (a)
Chapter 1, Problem 1.2.6(choose chapter or problem)
Suppose that the specific heat is a function of position and temperature, c(x, u). (a) Show that the heat energy per unit mass necessary to raise the temperature of a thin slice of thickness x from 0 to u(x, t) is not c(x)u(x, t), but instead u 0 c(x, u) du. (b) Rederive the heat equation in this case. Show that (1.2.3) remains unchanged.
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