In this research, a square chamber filled by a ternary hybrid nanofluid is used to analyze conjugate MHD (Magnetohydrodynamic) free convection. Except for the bottom horizontal wall, which has a finite thickness and thermal conductivity, the thickness of the remaining three walls is assumed to be zero. The chamber’s lower wall is heated uniformly, while the left vertical wall is heated linearly. In contrast, the upper chamber wall is adequately insulated, and the right vertical wall is cooled. Utilizing finite element analysis, numerical simulations are conducted to examine the heat and fluid flow as dictated by the Navier-Stokes and heat energy equations. Various governing parameters, including the ratio of thermal conductivities ( 0.1 ≤ R k ≤ 10 ) , the volume percentage of ternary hybrid nanoparticles ( 0 ≤ δ thnp ≤ 0.03 ) , the Rayleigh number ( 10 3 ≤ Ra ≤ 10 6 ) , and the Hartmann number ( 0 ≤ Ha ≤ 100 ) , have been found to impact the system’s thermal properties. Streamlines and isotherms show the qualitative results of this study. Nusselt number and entropy production are used to present the quantitative results. It is found that the average entropy production due to heat transfer can be increased using ternary nanofluid for both cases of presence as well as absence of magnetic fields. This increase is comparatively minimum (which is approximately 5.9% for Ha = 0 and 4.8% for Ha = 50) for the case of Rk = 0.1 than the other cases of Rk = 1 and Rk = 10. Highest heat transfer rate can be accomplished using the ternary fluid as performing fluid than base fluid. This is comparatively significant for Rk = 0.1 in the nonappearance of magnetic field than the other cases. The rate of heat transfer and average entropy production can be reduced by decreasing Ra.