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An extended answer. For more arbitrary meshes you have to consider that generally CFD/FEM solvers rely on generic data-structures with element and side lists: Element list Side list Consider the following pictures, which is the standard case for simple Cartesian meshes. Since there is a single plus and a single minus side on each face, the definition is ...


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When dealing with conservation laws like your case, you can often make use of the divergence theorem (as you did). You can then express the fact that the total mass within your integration region is preserved by the following surface integral: $$\oint_{\partial \Omega} k \nabla T \cdot \mathbf{n} ~\partial S = 0$$ Now, as it stands, it is irrelevant which ...


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Normal direction depends on the cell that you are writing equation for. the word outward is relative to the cell under study. In order to write equation for each of cells, i.e. $\Sigma \nabla T.n S_f=0$, stick to this : $\nabla T_{face}=\frac{T_c-T_i}{r_c-r_i}$ and assume $n$ as outward pointing normal vector for that face. I think your problem is that you ...


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