Petroleum University of Technology Verification of Conduction Heat Transfer Equation in Spherical Coordinates So many friends of mine asked me about conduction heat equation in spherical coordinates and how to prove it, since there was not a good resource on the net. So I tried to prove as easiest as possible. Hope to be useful. We start by selecting a control volume dV, as indicated in the figure: .. Also, the following identity is useful: sin Taylor series is used as well: ⋯ Radial Direction , . 1 2 1 2 2 ⟹ From Taylor series we have: