Transient natural convection in differentially heated porous enclosures

The problem of steady, laminar, hydromagnetic heat and mass transfer by nat ural convection flow over a vertical cone and a wedge embedded in a uniform porous medium is investigated. Two cases of thermal boundary conditions, n amely the uniform wall temperature (UWT) and the wall heat flux (UHF), are considered. A nonsimilarity transformation for each case is employed to tra nsform the governing differential equations to a form whereby they produce their own initial conditions. The transformed equations for each case are s olved numerically by an efficient implicit, iterative, finite-difference sc heme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects; heat generation or absorption; lateral wall mass fl ux; concentration to thermal buoyancy ratio; and the Lewis number on the fl uid velocity, temperature, and concentration as well as the Nusselt and the Sherwood number decreases owing to the imposition of the magnetic field, i t increases as a result of the fluid's absorption effects. Also, both the l ocal Nusselt and Sherwood numbers increase as the buoyancy ratio increase. This is true for both uniform wall temperature and heat flux thermal condit ions. Furthermore, including the porous medium inertia effect in the mathem atical model is predicted to decrease the local Nusselt number for both the isothermal and isoflux wall cases.