The study of flow through bidisperse porous media (BDPM) has attracted the attention of many researchers because of its potential applications in industrial, physical, and hydrological problems. In this project, we have studied numerically the problem of two-dimensional, incompressible, laminar, steady flow through a BDPM over a flat semi-infinite plate along the vertical direction with a uniform magnetic field applied normal to the flow direction using the framework of the Boussinesq approximation. We have studied two different models: Darcy- Boussinesq model and DarcyBrinkman-Forchheimer-Boussinesq model. In both models, we considered two-velocity and two- temperature equations. The physical models are governed by the linear as well as nonlinear coupled partial differential equations which cannot be solved analytically. To follow the numerical approach we first made the governing equations dimensionless using a suitable transformation of variables. The simulation was carried out using the very robust computer algebra software MATLAB. Comparisons with previously published works were performed which gave acceptable agreement among the results. In both physical models, particular efforts have been focused on the effects of the Rayleigh number, Hartmann number, modified thermal diffusivity ratio, ratio of permeabilities, and the inter-phase momentum transfer parameter on the flow and thermal fields. The results iii corresponding to the dimensionless velocity and temperature profiles are displayed graphically for various pertinent parameters and discussed them from the physical points of view. The role of the various model parameters is identified to know the effects of them in the momentum and thermal boundary layers thicknesses which will help in controlling the physical system. The results show that for the Darcy and non-Darcy models the velocity in the f-phase (macrophase) increases with the increment of the Rayleigh number and the modified thermal diffusivity ratio, while the velocity in pphase (microphase) rises with the growth of the Rayleigh number, the ratio of permeabilities and inter-phase momentum transfer parameter. The increment of these model parameters caused the momentum boundary layer thickness to decline. Besides, the temperature in the f-phase increased with the enlargement of the Hartmann number and ratio of the permeabilities, whereas the temperature in the p-phase escalates with the expansion of the Hartmann number, modified thermal diffusivity ratio, and f-phase volume fraction. The thickness of the thermal boundary layer evolved with the increase of these model parameters. In the Darcy-Brinkman-Forchheimer-Boussinesq model which is valid for the high velocity due to the high permeability, particular efforts have been given on the inertial parameters too. The result shows that for lower values of the permeability ratio, the heat transfer rate in the p-phase is decreased the large values of Gp and Gf . In contrast, for higher values of the permeability ratio, the rate of heat transfer in the p-phase increased for large values of Gp and declined for large values of Gf .