Natural Convection in Rectangular Enclosure Due to Flux Density of Heat Prescribed to its Water-Saturated Vertical Porous Wall

Unsteady natural convection in a rectangular enclosure with a vertical saturated porous wall is studiednumerically. The governing equations using Boussinesq approximation for the treatment of buoyancyterm in the momentum equation and the Darcy model are expressed using the stream functionvorticityformulation. Equations are discretized with the implicite finite-difference method. Thomasalgorithm and Gauss-Seidel method are used to solve the resultant algebraic system equations.Results are presented in terms of streamlines, isotherms and isoconcentrations. The increase of theporous wall permeability leads to a more intensive buoyancy-driven flow through the porous wall andconsequently an increase of heat and mass transfer occurs in the enclosure. Nusselt and Sherwoodnumbers are expressed as functions of dimensionless parameters as Darcy number, modified Grashofnumber and the enclosure aspect ratio.