A Characteristic-based Solution of Forced and Free Convection in Closed Domains with Emphasis on Various Fluids

Document Type : Original Article


1 Department of Mechanical Engineering, University of Bonab, Bonab, Iran

2 Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

3 Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran


In this paper, forced and free convection in the cavity is simulated numerically with complex boundary conditions. Temperature changes sinusoidally at the upper and right walls and the temperature of the other walls is kept at zero. The effects of Prandtl and Grashof numbers variations on flow patterns are surveyed. A wide range of materials, e.g. molten metals, gases, water, and coolant liquid are considered. For this purpose, an in-house code is written in FORTRAN-95 within the finite volume framework. For time discretization, the fifth-order Rung-Kutta method is applied. The convective terms are calculated by a novel characteristic-based scheme along with artificial compressibility. The flow is assumed to be incompressible, laminar and two dimensional. It was found that higher Nusselt numbers have affected increasing Grashof numbers. The effect of Gr on Nu at the upper wall is stronger than that of the down wall. However, the effect of Pr on Nu at upper wall is almost equal with that of the down wall.