Convection in a porous medium with variable internal heat source and variable gravity

The qualitative effect of variable internal heat source and variable gravity on the onset of convection in a horizontal fluid saturated sparsely packed porous layer is investigated using linear stability analysis. The single term Galerkin technique is used to compute the value of the critical Rayleigh number and the corresponding wave number. Three different sets of variable gravity and heat source functions are chosen and their influence on the onset of convection is discussed. The eigenvalues are obtained for free-free velocity boundary conditions with isothermal temperature conditions on the boundaries. The influence of porous parameter on the onset of convection is brought out. It is found that the variable heat source and variable gravity does not affect the shape and size of the convective cell at the onset of convection. However the porous parameter do so.