A stabilized finite element method for incompressible flow and heat transfer: A natural derivation based on the use of local time-steps

In a recent paper the author introduced a stabilized finite element method suitable for the solution of incompressible viscous flows. In this work the method is extended to deal with problems involving coupled flow and heat transfer. Minimization of momentum and energy squared residuals are employed to obtain a stabilized finite element formulation suitable for the simulation of heat transfer problems in free, mixed and forced convection. Numerical solutions of some representative examples demonstrate the application of the proposed stabilized formulation.