Computation of turbulent flow in mixed convection in a cavity with a localized heat source

A numerical simulation of the turbulent transport from an isolated heat source in a square cavity with side openings is presented in this work. The openings allow an externally induced air stream at ambient temperature to flow through the cavity and, thus, mixed convection arises. Results for the turbulent regime are obtained, by employing a suitable, high-Reynolds-number form of the K-E turbulence model. A stream function-vorticity mathematical formulation is used, along with the kinetic energy and dissipation rate equations and an expression for the eddy viscosity. A time-marching scheme is employed, using the ADI method. The values of the Reynolds number Re, associated with the external flow, and the Grashof number Gr, based on the heat flux from the source, for which turbulent flow sets in are sought. Two typical values of the Reynolds number are chosen, Re = 1000 and Re = 2000, and turbulent results are obtained in the range Gr = 5 < 10⁷-5 < 10⁸. For both values of Re, the average Nusselt number over the surface of the source is found to vary with Gr in a fashion consistent with previous numerical and experimental results for closed cavities, while the effect of Re in the chosen range of values was small.