1.

Which of these equations represent 1-D steady state diffusion?(a) div(Γ grad Φ)+S=0(b) \(\frac{d}{dx}(\Gamma\frac{d\phi}{dx})+S=0\)(c) \(\frac{d\phi}{dt}+\frac{d}{dx}(\Gamma\frac{d\phi}{dx})+S=0\)(d) \(\frac{d\phi}{dt}+div(\Gammagrad\phi)+S=0\)This question was posed to me during an online interview.The question is from FVM for 1-D Steady State Diffusion topic in chapter Diffusion Problem of Computational Fluid Dynamics

Answer»

The CORRECT option is (b) \(\frac{d}{dx}(\Gamma\frac{d\phi}{dx})+S=0\)

Best explanation: The TERM div(Γ GRAD Φ) REPRESENTS diffusion in all three directions. One-dimensional diffusion is given by the equation \(\frac{d}{dx}(\Gamma\frac{d\phi}{dx}.\frac{d\phi}{dt})\) is the TRANSIENT term. So, this should not be present in the steady-state equation. Considering all these, the correct equation is

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


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