Write in detail the expression for ((boldsymbol{v} cdot abla) T) in spherical coordinates. Also write in detail

Question:

Write in detail the expression for $(\boldsymbol{v} \cdot abla) T$ in spherical coordinates. Also write in detail the expression for the Laplacian, and thereby complete the temperature equation for spherical coordinates. What simplifications result for an axisymmetric case, i.e., when the temperature has no dependence on the $\phi$ direction?

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