Non-Darcy regime mixed convection on vertical plates in saturated porous media with lateral mass flux

Summary A unified treatment is presented of mixed convection on vertical plates embedded in fluid saturated porous media with prescribed variable plate temperature or surface heat flux for the case of non-Darcy limiting regime. The plates are permeable with lateral mass flux. By suitable similarity transformations, it is shown that the two problems of prescribed temperature and prescribed heat flux lead to identical differential equations with two common boundary conditions and third boundary condition differing in the two cases. The effect of lateral mass flux and the free stream on the Nusselt number and the energy transport by the boundary layer is investigated. The unified approach to the mixed convection problem includes free convection problem as a special case. Exact analytical solutions are obtained for two cases of free convection problem.Notation b inertial coefficient - c specific heat - D_p pore diameter - E rate of upward energy transport - Ê dimensionless rate of energy transport - f dimensionless stream function - f_w mass flux parameter - g acceleration due to gravity - k thermal conductivity - K permeability of the porous medium - m exponent in the variation of heat flux - M mixed convection parameter - Nu_x Nusselt number - Pe_x Peclet number - q_w surface heat flux - Ra_x local Rayleigh number - Ra_x^* modified local Rayleigh number - T temperature - T_e ambient temperature - T_w plate temperature - T_w temperature difference=T_w-T_e - u velocity in thex-direction - u_e free stream velocity - v velocity in they-direction - v_w lateral velocity at the plate - x coordinate along the plate in the upward direction - y coordinate normal to the plate - equivalent thermal diffusivity =k/c_e - coefficient of thermal expansion - porosity - dimensionless variable - dimensionless temperature - viscosity - fluid density - _e ambient density - exponent in the variation of plate temperature - stream function