In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.