Numerical study on conjugate effect of conduction and mixed convection flow in a rectangular ventilated cavity with a heat generating circular block

Abstract

The mixed convection flow and heat transfer characteristics inside a rectangular ventilated cavity with a heat-generating solid circular block have been investigated numerically. The inlet opening is at the bottom of the left wall, while the outlet one is at the top of the right wall and all the walls of the cavity are considered to be adiabatic. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. Using a class of appropriate transformations, the governing equations along with the boundary conditions are transformed into non-dimensional form, which are then solved by employing a finite-element scheme based on the Galerkin method of weighted residuals. Results are presented in terms of streamlines, isotherms, average Nusselt number and drag force on the solid block surface, average temperature of the fluid in the cavity for different combinations of the governing parameters namely diameter of the solid block D, solid and fluid thermal conductivity ratio K, heat generating parameter Q, Reynolds number Re, Prandtl number Pr, locations of the inner block and cavity aspect ratio AR at the three values of Richardson number Ri, varying from 0.01 to 5. The results indicate that the flow and thermal fields as well as the heat transfer rate, the drag force and the average fluid temperature in the cavity depend significantly on the above mentioned parameters.