Double-Diffusive Natural, Mixed, and Forced Convection Characterization in a Single Lid-Driven Rectangular Cavity: Effect of Heat and Mass Diffusion Rates Difference

This paper studies mixed double-diffusive convection inside a sliding top-wall rectangular enclosure submitted along the vertical walls to constant thermal and solutal fluxes and containing a Newtonian fluid. The paper put forward two approaches for solving the problem at hand, a numerical one based on the finite difference method and an analytical approach using the parallel flow approximation. The investigation shows that the convection main controlling parameters are: thermal Rayleigh number \({\text{Ra}}_{T} ,\) buoyancy ratio \(N,\) Lewis number \({\text{Le}},\) and Peclet number \({\text{Pe}}\) with both approaches showing perfect agreement for wide ranges of governing parameters. To shed further light on the effects of mentioned parameters on convection phenomena, an acceptable criterion is adopted to delineate natural, mixed, and forced convections dominance regions, and that separately for heat transfer and mass transfer. The parameters \({\text{Pe}}\) and \({\text{Ra}}_{T}\) significantly impact the shift from one convective regime to another. As for \({\text{Le}},\) varying it affects the main mechanism driving heat and mass transfer; thus, strongly influences transfer rates. Further, increasing \({\text{Le}}\) enhances forced regime contribution in overall convection while stretching the range for which mixed regime occurs. Unexpectedly though, heat and mass diffusion rates difference \(\left( {{\text{Le}}\, \ne \,1} \right)\) have no significant effect on boundaries delimiting mixed regime for heat and mass transfer separately.