A Parametric Study of Laminar Mixed Convection in a Square Cavity Using Numerical Simulation Techniques

A parametric study is conducted using numerical experimentation to construct an empirical Nusselt number correlation in terms of Richardson and Prandtl numbers for laminar mixed convection in a square cavity. The square cavity under study is assumed to be filled with a compressible fluid. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is pulled at constant speed. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, mathematical model is adopted to predict the momentum and heat transfer inside this rectangular cavity. This physics based mathematical model consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary and initial conditions. The compressibility of the working fluid is represented by an ideal gas relation. The thermodynamic and transport properties of the working fluid are assumed to be constant. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing (based on Taylor expansion) for the time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried to determine the accuracy of the square mesh adopted for the present study. Two benchmark cases (driven cavity and rectangular channel flows) were studied to verify the accuracy of the CMSIP. Numerical experiments were then carried out to simulate the heat transfer characteristics of mixed convection flow for different Richardson numbers in the range of 0.036<Ri<1.00 where the Reynolds number is kept less than 2000 to ensure laminar flow conditions inside the cavity. The velocity vector field maps (circulation patterns) and temperature contours, and temperature profiles along the horizontal axes were generated for different Prandtl numbers ranging from 0.3 to 1. Wall heat fluxes and Nusselt numbers were determined for each parametric study. The collected data from the numerical experiments were then used to construct an empirical Nusselt number correlation in terms of Richardson and Prandtl numbers.