Conjugate Mixed Convection in a Differentially Heated Lid-Driven Square Cavity With Rotating Cylinders

Abstract

Abstract Conjugate mixed convection in a lid-driven differentially heated square cavity with two heat-conducting rotating cylinders is numerically investigated. The right and the left walls of the enclosure, respectively, are maintained at a constant higher temperature (Th) and lower temperature (Tc), keeping the horizontal walls adiabatic. Both the cylinders are rotating in the counterclockwise direction. Only the left wall is moving downwards with a constant velocity. The governing nondimensional partial differential equations are resolved by means of Galerkin weighted residual finite element formulation. The average Nusselt number (Nu) is calculated along the right vertical heated wall. Flow and thermal fields are presented via streamlines and isotherms. Parametric simulations are performed for various pertinent parameters which are Grashof number (Gr), Reynolds number based on lid velocity (Re), Reynolds number based on cylinders’ peripheral velocity (Rec), and Richardson number (Ri). At first, the effects of variation of cylinders’ diameter are observed by considering six different cases for a particular peripheral velocity. It is found that the maximum Nu is obtained when the diameters of both cylinders are 0.1L. Further simulation is done for varying the Rec in the range of 5 to 50, to observe the effect of cylinders’ rotational speed. It has been found that for a particular Re, Nu increases with increasing rotational speed, but the effect is more pronounced at low Re. Finally, the combined effects of both Re and Gr on Nu have been investigated, keeping the Ri in the laminar mixed convection region. It has been demonstrated that when the Ri is increased from 0.1 to 10, the Nu enhances about 395.7%.