<p>Hydromagnetic fluid flows experience the drag due to the porous medium and the Lorentz force. Porous medium and magnetic field affect fluid flows and hence the transfer of heat in the fluids. Viscoplastic fluids are encountered in several engineering applications and, therefore, have the potential to be studied. The flow of viscoplastic fluid and heat transfer are modeled by considering the magnetic field and the Darcy-Forchheimer porous medium. The basic conservation laws provide a set of PDEs, and the no-slip theory provides a set of boundary conditions. Due to the development of boundary layer flow, boundary layer approximations are used for the simplification of PDEs, which are further transformed into a system of ODEs. The system of ODEs with boundary conditions is numerically solved using the finite element method (FEM). Mesh analysis is performed, and convergence is ensured. Numerical solutions are further used for studying the dynamics of the Nusselt number and the skin friction coefficient. Darcy-Forchheimer porous medium has an increasing effect on the temperature of the hybrid nano-viscoplastic fluid. This increasing effects on temperature of hybrid nanofluid is greater than on the temperature of the mono nano-viscoplastic fluid. The viscoelasticity has a significant increasing effect on the velocity of the fluid. Thus, fluids exhibiting higher yield stress experience a higher effect of boundary. The Darcy-Forchheimer porous medium is responsible for lowering the rate of transfer of heat from the heated surface to the fluid. It is also noted that the Nusselt number decreases when the resistive force of the porous medium increases, because convective transport of heat becomes slow due to decrease in the velocity.</p>