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Buoyancy driven convection in a square cavity induced by two mutually orthogonal arbitrarily placed heated thin plates is studied numerically under isothermal and isoflux boundary conditions. The flow is assumed to be two-dimensional. The coupled governing equations were solved by the finite difference method using the Alternating Direction Implicit technique and Successive Over Relaxation method. The steady state results are depicted in terms of streamline and isotherm plots. It is found that the resulting convection pattern is stronger for the isothermal boundary condition. A better overall heat transfer can be achieved by placing one of the plates far away from the center of the cavity for isothermal boundary condition and near the center of the cavity for isoflux boundary condition.

Natural convection heat transfer fluid flow past an inclined plate embedded in a fluid-saturated porous medium is investigated by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations by the scaling symmetries. From numerical results, it is found that the thermal and momentum boundary layer thicknesses are increased as the radiation parameter is increased. Also, it is observed that the velocity is increased and the temperature is decreased for increasing the buoyancy parameter and the porosity parameter.

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