The stability of natural convection in a horizontal porous channel with uniform heat generation and concentration gradients was considered by using numerical method and Garlerkin methods. Attention is focused on cases where the fluid and solid phases are not in local thermal equilibrium

and standard linearized stability theory is used to analysis how the criterion for the onset of convection varies with the inter-phase heat transfer coefficient

H

the porosity-modified thermal conductivity ratio

g

the size of the temperature gradient in the vertical direction of the porous layer

and the distribution of heat source in the fluid phase and solid phase. We also get the expressions of the critical Rayleigh number of heat source. The results show that

the forming region of natural convection mainly located in the upper half of the area when the heat source is positive from the distribution of the velocity field

while the forming region of natural convection mainly located in the lower half of the area when the heat source is negative. The heat source is always to promote the occurrence of natural convection. Effective thermal conductivity ratio

internal heat transfer coefficient of fluid and solid phases and the distribution of heat source in the fluid and solid phase

mutual coupling

affects the stability of natural convection.