Under nonisothermal conditions, besides the calculation of velocity and pressure, the simulation of FIC requires the evaluation of:

These four quantities (, , x, and T) obey partial differential equations and require appropriate boundary conditions. Under isothermal assumption, ignore temperature T. Presently we also ignore the quantity since it is evaluated on the basis of an algebraic equation.

The equations that respectively govern , , and x are hyperbolic of the first order. They require boundary conditions only at the inlet of the computational domain. Those inlet boundary conditions are automatically imposed when you select the inflow boundary condition. In particular, vanishing inlet conditions are imposed for x.

For the simulation of a flow involving FIC under nonisothermal conditions, evaluate the temperature field T. It obeys the energy equation, which is of the second order, so that conditions are required on all boundaries Within the present context of FIC, the most appropriate thermal boundary conditions are as follows:

Considering the expected temperature convection involved in the flow, do not assign a temperature at the exit of the computational domain. The equations are coupled to the momentum and incompressibility (mass conservation) equations. The momentum equation that governs the velocity field also requires conditions on all boundaries. They are expressed in terms of contact forces or velocity components.

Within the present context of FIC, the most appropriate flow boundary conditions are: