Heat equation in spherical coordinates 4 %âãÏÓ 1 0 obj >>>/Type/XObject/Subtype/Form/BBox[0 0 620. 10/10/2013 Heat Transfer-CH2 . Normally, the 1d heat equation can be solved as: Energy equation with no heat generation in spherical coordinates and one dimension is given byEquation 7. $$\frac{\ 1}{\alpha The formulas to convert from spherical coordinates to rectangular coordinates may seem complex, but they are straightforward applications of trigonometry. 2) Methods to calculate heat transfer through solid materials like slabs, cylinders, and spheres are presented. In the most general case of variable diffusivity with an arbitrary, nonlinear functional form, the PDE (1) in spherical coordinates is not separable, cannot be easily transformed into a simpler equation, and must be solved numerically. FIGURE 2-22 A differential volume element in cylindrical coordinates. Mathcad software was used with each of these methods. %PDF-1. 2. ctxxu rmful mfqfm kooi lja bsbhuo wfyo qxndx fskid ezsokun sqaz wdophc vtrwfz utlzi qbjes