If aPΦP=aEΦP+aWΦW+aNΦN+aSΦS+S is the general form of a 2-D steady-state diffusion problem, what is aE by considering the following stencil?(a) \(\frac{\Gamma_E A_E}{\delta y_{PE}}\)(b) \(\frac{\Gamma_E A_E}{\delta y_{PE}}\)(c) \(\frac{\Gamma_E A_E}{\delta x_{PE}}\)(d) \(\frac{\Gamma_E A_E}{\delta x_{WP}}\)The question was asked in unit test.My doubt is from FVM for Multi-dimensional Steady State Diffusion in section Diffusion Problem of Computational Fluid Dynamics

If aPΦP=aEΦP+aWΦW+aNΦN+aSΦS+S is the general form of a 2-D steady

1.	If aPΦP=aEΦP+aWΦW+aNΦN+aSΦS+S is the general form of a 2-D steady-state diffusion problem, what is aE by considering the following stencil?(a) \(\frac{\Gamma_E A_E}{\delta y_{PE}}\)(b) \(\frac{\Gamma_E A_E}{\delta y_{PE}}\)(c) \(\frac{\Gamma_E A_E}{\delta x_{PE}}\)(d) \(\frac{\Gamma_E A_E}{\delta x_{WP}}\)The question was asked in unit test.My doubt is from FVM for Multi-dimensional Steady State Diffusion in section Diffusion Problem of Computational Fluid Dynamics
Answer» Right answer is (c) \(\FRAC{\Gamma_E A_E}{\DELTA x_{PE}}\) Explanation: FLUX in the EASTERN DIRECTION is given by \(\Gamma_E A_E\frac{\partial\phi}{\partial x}\Big\|_e=\Gamma_E A_E\frac{(\phi _E-\phi _P)}{\delta x_{PE}}\) \(\Gamma_E A_E\frac{\partial\phi}{\partial x}\Big\|_e=\Gamma _e A_E\frac{\phi_E}{\delta x_{PE}}-\Gamma_E a_E\frac{\phi_P}{\delta x_{PE}}\) Expanding this while forming the general equation, we will get \(a_E=\frac{\Gamma_E A_E}{\delta x_{PE}}\).

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