MIXED CONVECTION FROM A LOCALIZED HEAT SOURCE IN A CAVITY WITH CONDUCTING WALLS: A NUMERICAL STUDY

Abstract

Mixed convection is studied numerically in the case of an isolated, constant source of heat input within a rectangular enclosure. An external flow enters the enclosure through an opening in the left vertical wall and exits from another opening in the right vertical wall. This configuration leads to a conjugate heat transfer problem and simulates the air cooling of electronic components. Various parameters arise in this problem, particularly the Reynolds number, the buoyancy parameter Gr/Re², the ratio of the thermal conductivity of the wall material to that of the fluid taken as air, and several geometric parameters. The time-dependent continuity and Navier-Stokes equations are transformed into a system of equations with the stream function and the vorticity as the dependent variables. The energy equation is solved over the entire domain, using the corresponding properties for the solid and fluid regions. The control volume approach is employed in order to discredit the governing equations for their numerical solution. A time marching procedure is followed, until steady state is reached. Results art presented for different values of the buoyancy parameter in the laminar regime, and the critical value of Gr/Re², i.e., the highest value that leads to a convergent steady solution, is determined. Oscillatory results characterized by a single frequency were observed as this value was exceeded, up to a point where the oscillations showed irregular patterns, indicating that the flow was approaching the turbulent regime. Of particular interest here is the heat transfer, from the heat source to the fluid and from all the inner walls (solid-fluid interfaces) to the fluid, expressed in terms of the corresponding Nusselt numbers.