ABSTRACT

A theoretical approach is presented to analyze the onset of instability in a porous medium. It can predict not only the stationary convection but also the oscillatory convection. Results show the symmetric variation of the wave number and the Rayleigh number with the change of imaginary part of the eigenvalue from positive to negative values. Due to decrease of the activation energy parameter and the mass diffusion parameter the magnitude of the critical Rayleigh number decreases, however, the magnitude of the critical wave number increases. Moreover the critical Rayleigh number decreases with higher values of the conduction-radiation parameter and the heat release parameter. The remarkable finding is that when the Lewis number is increased from a lower value to a higher value, the stationary convection changes to oscillatory convection. An increase in the product of the porosity and the ratio of the density and the heat capacity of the fluid to the porous material causes a decrease in the magnitudes of the critical Rayleigh number. Under consideration of the surface radiation, a maximum value of the heat release parameter and a minimum value of the mass diffusion parameter and the activation energy parameter are required for the onset of convection in a porous medium. A comparison is made with a past study for the critical wave number and the critical Rayleigh number which provides a good agreement.