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4

Problem Statement For notational simplicity, use the non-dimensional formulation described near the end of the question. (Doing so also facilitates comparison with results of a 2D approximation solved earlier.) The PDE is given by λh D[θw[x, y, z], x, x] + λc D[θw[x, y, z], y, y] + λz D[θw[x, y, z], z, z] == 0 over the domain {x, 0, 1}, {y, 0, 1}, {z, 0, ...


2

The nth root can be estimated from the common reasons - roots of Cot[x] exist in between (0,Pi) with period equal to Pi. Thus, one can use: n=6; (*Root number*) Rn = Rn/.FindRoot[Rn==Bi Cot[Rn], {Rn, (n-1+0.00001) Pi, (n-1) Pi, n Pi}]; Plot[{t, Bi Cot[t]}, {t, 0, n Pi}, Epilog -> {Red, PointSize[Large], Point@{Rn, Rn}}, PlotPoints -> ...


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