When we are handling prescribed flux conditions, we have an equation that allows us calculating the temperature inside the fictitious volume. When this equation is applied on the adjacent volume it must return us the flux value at the interface.


The fluxes perpendicular to h and x lines are given by, respectively:

= flux per unit area;

= length over a line h and over x respectively;

k  = thermal diffusivity coefficients;

= coordinates transformation metrics and the Jacobian determinant, given by Eq. (3.4) to (3.7), respectively.


Below we have the equations for the fictitious volumes of the prescribed flux.

It is important to notice that for the East and North faces the right faces of the flux equation there is no minus sign, this means that the flux is always considered positive when it is entering in the control volume.