## fourier's law heat conduction

1. The problem statement, all variables and given/known data

a) A slab of thickness L and constant thermal conductivity $$\lambda$$ generates heat at a constant rate throughout of g W m–3. The heat is dissipated from both sides of the slab by convection into the ambient air at a temperature Tf with a heat transfer coefficient h. The expression for the steady state temperature profile throughout the slab is given by

$$T(x) = \frac{g}{8 \lambda} L^{2}( 1- (\frac{2x^{2}}{L})) + \frac{gL}{2h} + T_{f}$$

where symbols have their usual meaning in this context.

(i) Derive an expression for the heat flux as a function of position x.

Should I differentiate with respect to 'x'?
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