Derive the following corresponding expression for the Laplacian in spherical coordinates: [begin{equation*}abla^{2} T=frac{1}{r^{2}} frac{partial}{partial r}left(r^{2} frac{partial T}{partial
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Derive the following corresponding expression for the Laplacian in spherical coordinates:
\[\begin{equation*}abla^{2} T=\frac{1}{r^{2}} \frac{\partial}{\partial r}\left(r^{2} \frac{\partial T}{\partial r}\right)+\frac{1}{r^{2} \sin \theta} \frac{\partial}{\partial \theta}\left(\sin \theta\frac{\partial T}{\partial \theta}\right)+\frac{1}{r^{2} \sin ^{2} \theta} \frac{\partial^{2} T}{\partial \phi^{2}} \tag{1.58}\end{equation*}\]
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Advanced Transport Phenomena Analysis Modeling And Computations
ISBN: 9780521762618
1st Edition
Authors: P. A. Ramachandran
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