Mixed convection along an isothermal vertical cylinder in porous media

Abstract

Mixed convection adjacent to a vertical cylinder in porous media is studied. The problem is solved using the nonsimilarity solution method for the case of uniform wall temperature (UWT). In the first approach, mixed convection is studied by examining separately the buoyancy effect on forced convection and the forced flow effect on free convection. These effects are represented, respectively, by RaJPex and PexlRax. Curvature is represented by gf = (xlr^Pe~* /2 in the forced-convection-dominated regime and by £„ = (x/r0)Raxl/2 in the free-convection-dominated regime. The second approach examines the entire regime of mixed convection by introducing the single parameter = [1 + (Rax/Pex)1/2]~l, where = I corresponds to pure forced convection and x = 0 to pure free convection. In this regime, the curvature is represented by £ = (xlr^[Pe*x2 + Ralx2]~*. In the analysis, the non-Darcian and thermal dispersion effects are neglected. The resulting nonsimilar systems of equations from the different approaches are solved using a finite difference method. Results are presented for temperature and velocity profiles, and local Nusselt number. Correlation equations are given for local and average Nusselt numbers in all regimes of mixed convection.