Consider a one-dimensional plane wall with constant properties and uniform internal generation . The left face is insulated, and the right face is held at a uniform temperature.

(a) Using the appropriate form of the heat equation, derive an expression for the x-dependence of the steady-state heat flux q"(x).
(b) Using a finite volume spanning the range 0 ≤ x ≤ ξ, derive an expression for q"(ξ) and compare the expression to your result for part (a).

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