Analysis of Mixed Convection Flow Characteristics in Square Cavity with Uniformly Heated Bottom Wall by Finite Volume Method

Abstract — Mixed convection from a uniform heat source on the bottom of a square cavity is studied numerically. Two-dimensional forms of non-dimensional Navier-Stokes equations are solved by using control volume based finite volume technique. Three typical values of the Reynolds numbers are chosen as Re = 1, 10, and 100 and steady, laminar results are obtained in the values of Richardson number as Ri = 0, 1 and 10 and the values of Prandtl numbers as Pr = 0.1, 0.71, 1 and 10. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented based on the value of Re and Pr. The computational results indicate that the heat transfer is strongly affected by Reynolds number and Richardson number. In the present investigation, bottom wall is uniformly heated while the two vertical walls are maintained at constant cold temperature and the top wall is well insulated. A complete study on the effect of Ri shows that the strength of circulation increases with the increase in the value of Ri irrespective of Re and Pr. As the value of Ri increases, there occurs a transition from conduction to convection dominated flow at Ri =1. A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Ri and Pr