Abstract Numerical Investigations are carried out to study the thermal performance of the magnetohydrodynamics laminar mixed convection in a triangular cavity with a circular enclosure. The present work analysis is carried out on a triangular cavity with circular blockage by varying the Re (200-600), Ri (0.01-1), and Gr (4000-36000), respectively. The working system is a triangular cavity filled with water with a circular block. Non-linear partial differential equations are the governing equations that use the finite element method. The moving upper wall and temperature difference contribute to the convection heat transfer. The upper wall is heated and maintained at high temperatures. The other walls are kept as adiabatic. The obstacle at the center is kept at a low temperature. The physical parameters are non-dimensional numbers like the Reynolds, Richardson, and Hartmann numbers that influence the heat transfer rate. The Richardson and Reynolds numbers impact positively, and the Hartmann numbers tend to decrease heat transfer rates.