InterviewSolution
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Which of these equations represent the semi-discretized equation of a 2-D steady-state diffusion problem?(a) \(\int_A(\Gamma A\frac{\partial \phi}{\partial x})dA+\int_A(\Gamma A \frac{\partial\phi}{\partial y})dA+\int_{\Delta V} S\,dV=0\)(b) \(\int_A\frac{\partial}{\partial x}(\Gamma A \frac{\partial\phi}{\partial x})dA+\int_A\frac{\partial}{\partial y}(\Gamma A\frac{\partial\phi}{\partial y})dA+\int_{\Delta V}S\, dV=0\)(c) \(\int_A(\Gamma A\frac{d\phi}{dx})dA+\int_A(\Gamma A \frac{d\phi}{dy})dA+\int_{\Delta V}S\, dV=0\)(d) \(\frac{\partial \phi}{\partial t}+\int_A\frac{\partial}{\partial x}(\Gamma A \frac{\partial \phi}{\partial x})dA+\int_A\frac{\partial}{\partial y}(\Gamma A \frac{\partial \phi}{\partial y})dA+\int_{\Delta V}S\, dV=0\)This question was addressed to me during an online interview.My doubt stems from FVM for Multi-dimensional Steady State Diffusion in chapter Diffusion Problem of Computational Fluid Dynamics |
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Answer» Right choice is (a) \(\int_A(\Gamma A\frac{\PARTIAL \phi}{\partial x})dA+\int_A(\Gamma A \frac{\partial\phi}{\partial y})dA+\int_{\Delta V} S\,dV=0\) |
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