Stabilized flux-based flow/thermal finite element representations with applications to convectively cooled structures

Stabilized flux-based finite element representations for steady two-dimensional incompressible flow/thermal problems with emphasis on subsequently applying such techniques to convectively cooled structures are described in this article. First, the discretized equations are derived from a mixed formulation using both primary and flux variables in conjunction with the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin features that are used to stabilize the solutions. The constitutive equations are then introduced into the discretized representations and the equations are finally solved for the primary variables. Equal-order linear quadrilateral interpolation functions are used for the velocities, pressure, and temperature. Numerical results are presented for a variety of situations, and finally emphasis is placed on applications to convectively cooled structures that are subjected to intense localized heating.