Consider a plane vertical channel bounded by two parallel vertical planes and filled with viscous incompressible fluid. Steady convective flow is generated in the channel due to combined effect of internal heat generation and temperature difference between the planes. Heat is released in the fluid as a result of a chemical reaction. There is also a steady flow with constant velocity through permeable channel walls in the direction perpendicular to the convective flow. Steady convective flow in the channel is described by a nonlinear boundary value problem. For some values of the parameters the boundary value problem has two solutions. The solution with the smallest norm is selected as the base flow for the linear stability analysis. Base flow velocity and temperature profiles are found numerically. Linearizing the system of equations of thermal convection in the Boussinesq approximation around the base flow and using the method of normal modes we obtain an eigenvalue problem for a system of ordinary differential equations. Collocation method based on the Chebyshev polynomials is used to discretize the problem. Effect of cross-flow on the stability of the convective flow in the vertical direction is investigated numerically. Depending on the values of the parameters of the problem there exist regions of stabilization and destabilization of the base flow in the parameter space.