Mixed Convection Heat Transfer in a Lid-Driven Square Cavity with Heated Circular Obstacles

The current manifestation is utilized to explain the inspiration of mixed convection heat transfer in lid-driven square enclosure with heated circular obstacles of non-dimensional radii R = 0.15 having coordinates (0.28, 0.5) and (0.72, 0.5) respectively. To be more specific, bottom and vertical walls are kept cold temperatures (Tc = 0), while the circular obstacles are treated as linearly and non-linearly hot temperature (Th= 1 or sinπx). The no-slip velocity boundary conditions are specified at obstacles surfaces. On the other hand, the top wall is moved with a velocity ULid and is thermally adiabatic. The governing equations for fluid flow and heat transfer are resolved using a finite element approach based on Galerkin's weighted residual method. To show the consistency of the implemented numerical technique, the parametric study is designed based on the most relevant non-dimensional parameters, namely, the Reynolds number (Re) changing from 50 to 5000, the Richardson number (Ri) ranging from 0.01 to 104, and the non-dimensional radii (R) varing from 0.05 to 0.20 respectively. A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Re and Ri (Gr/Re2) respectively. Velocity streamlines, isotherms, stream functions, average Nusselt numbers, and average fluid temperatures are computed for different Richardson and Prandtl numbers.Heat transfer around circular obstacles depends on Re and Ri, with uniformly heated obstacles performing better, especially at low Re and Ri.