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On Laminar Mixed Convection Flow in a Vertical Porous Stratum with Asymmetric Wall Heating Conditions
J.C. Umavathi, Mallikarjun B. Patil and I. Pop

The steady fully developed laminar mixed convection flow in a vertical channel embedded in a porous medium with asymmetric wall heating conditions in the presence of heat generation and heat absorption effects is analyzed in this paper. The flow is modeled using Brinkman equation model. The viscous and Darcy dissipation terms are also included in the energy equation. Through proper choice of non-dimensional variables and parameters, the governing equations are developed and three types of thermal boundary conditions are prescribed. These thermal boundary conditions are isothermal-isothermal, isoflux-isothermal and isothermal-isoflux for the left-right walls of the channel. The velocity and temperature fields are obtained analytically by perturbation series method and numerically by finite difference method. In addition, closed form expressions for the Nusselt numbers and reversal flow conditions at both the left and right channel walls are derived. Results are presented graphically illustrating the effects of the various parameters such as porous parameter, product of Brinkman number and the Grashof number and the ratio of Grashof number and Reynolds number on velocity and temperature fields. It is also found that both the analytical and numerical solutions agree very well for small values of the perturbation parameter e ( = Br Gr ).

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