In many chemical processes, porous medium is usually used as a catalyst and mixing of reactants that may generate heat in thermal chemical processes. In this study, a cavity with cool walls was exerted to cool the porous medium using free convection process. A hot elliptical porous medium made of nickel with 0.98 porosity was located in the center of a square chamber with cold vertical walls, which was filled with ethylene glycol and titanium oxide nanoparticles. Moreover, A magnetic field was also applied to control the flow and heat transfer mechanisms. In present investigation, a number of cases were simulated for porous Rayleigh number (10 2≤ R a p≤ 10 6), Hartmann number (0≤ H a≤ 150), and volume fraction 0≤ φ≤ 9%. The findings showed that increment of Hartmann number decreased h a v g in all of the porous Rayleigh numbers and volume fractions except 9%. Moreover, adding oxide titanium nanoparticles to ethylene glycol enhanced h a v g by small amount for all of the porous Rayleigh numbers and Hartmann numbers except H a= 0.