Boundary and thermal non-equilibrium effects on the onset of Darcy-Brinkman convection in a porous layer

A local thermal non-equilibrium model for the temperature representing the solid and fluid phases separately is used to study the onset of free convection in a sparsely packed porous layer using the Brinkman-extended Darcy model. The lower boundary of the porous layer is considered to be rigid and isothermal, while the upper isothermal boundary is assumed to be either rigid or free. The Galerkin method is used to obtain the eigenvalue equation, which is then solved numerically. The effects of thermal non-equilibrium and other physical parameters on the onset of convection are analyzed and compared for two types velocity boundary conditions considered. Besides, some known results available in the literature are compared with those obtained from the present study and good agreement is found.