Convective heat transfer downstream of a 3-D backward-facing step

Numerical solutions are obtained for fluid flow and heat transfer downstream of a 3-D backward-facing step within a duct. A heat flux is applied along the bottom surface downstream of the step. The dimensions downstream of the step are 30Hx12HxH, where H=1 cm (channel height); uniform flow enters a 20Hx12HxH/2 channel upstream of the step. The numerical model is based on a modified Petrov-Galerkin finite element technique that incorporates sparse storage solution with mass lumping. A projection algorithm is used to solve the primitive equations of motion. Upper and lower recirculation zones in the 3-D solutions are very different from 2-D results. Solutions obtained for Re = 400, 800, and 1200 are presented that illustrate changing recirculation and vortex zones. A time history shows the evolution of velocities along the centerline at Re = 800. Bulk Nusselt numbers converge to experimental values downstream of the step where the flow returns to a fully developed parabolic profile.