Numerical study on buoyancy and inclination effects on transient laminar opposing mixed convection in rectangular channels with symmetric and discrete heating

Detailed numerical simulations are carried out for transient laminar opposing mixed convection in a rectangular inclined channel with both walls suddenly subjected to discrete isothermal flush-mounted heat sources simulating electronic components. Using the vorticity-stream function formulation of the unsteady two-dimensional Navier-Stokes and energy equations, the governing equations are solved numerically using the control volume method. Simulations are performed for fixed values of the geometrical parameters, Reynolds number of Re = 500, Prandtl number of Pr = 7 and channel inclination of 0°≤γ≤90°. Results illustrate the effects of buoyancy strength or Richardson number Ri = Gr/Re² and channel inclination angle on the overall flow structure and nondimensional heat flux (Nusselt number) from the heated slabs. It is found that for the horizontal configuration (γ = 0°), due to the indirect effect of buoyancy, much higher threshold values of buoyancy strength are required for the appearance of the recirculation flows that take place downstream of the heated slabs. However, for increasing values of the inclination angle, vortex migration to higher positions inside the channel occurs and higher heat transfer rates are obtained. In addition, transition from steady to time-periodic flow takes place for values of the buoyancy parameter larger than a critical one, and the threshold value between the two regimes strongly depends on the value of the Reynolds number and channel orientation. The results include the effects of Reynolds and Prandtl numbers along with heat losses to the channel walls on the evolution of the final flow and thermal response.