The energy balance equation for rectangular coordinates is given by

In Example 3.1, there is no convective flow, consequently there is no heat convection, and the following terms are canceled:

Example 3.1

The variables and parameters used in this example are as follows: p = density, c_p = heat capacity, q = heat flux, k = thermal conductivity, A = cross-sectional area, S = source strength (J m⁻³ s⁻¹).

Insertion of these terms into the balance equation yields

PCP aT at aT +ux +Uy + uz ax aT z = k ( 2T 2 + 32 + az2 + S.