1.

Which of these equations govern the problem of source-free one-dimensional steady-state heat conduction?(a) \(\frac{d}{dx}(k\frac{dT}{dx})\)(b) \(\frac{d}{dx}(k\frac{d\phi}{dx})\)(c) \(\frac{d}{dx}(\Gamma\frac{dT}{dx})\)(d) \(\frac{d}{dx}(\Gamma\frac{d\phi}{dx})\)The question was asked in final exam.My question is from FVM for 1-D Steady State Diffusion in division Diffusion Problem of Computational Fluid Dynamics

Answer»

The correct answer is (a) \(\frac{d}{dx}(k\frac{dT}{dx})\)

For explanation I would say: The GENERAL one-dimensional steady-state diffusion EQUATION is:

\(\frac{d}{dx}(\frac{\Gamma d\phi}{dx})+S=0 \)

For heat conduction problem, the diffusion constant is the heat conductivity (Γ=k) and the flow VARIABLE is temperature (Φ=T). As the given problem is source free, S=0. Therefore, the equation becomes

\(\frac{d}{dx}(k\frac{dT}{dx})=0\).


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