<p>The effect of using active and passive methods on convection flow has been studied in the present work. The examined chamber is containing with a power-law fluid, while a hot component for cooling is embedded inside it. According to the results of modeling by multiple relaxation time lattice Boltzmann method (MRT-LBM), by decreasing the power-law index, the imposed magnetic field influence can be made more significant. The mean Nusselt number value decreases by about 46% for shear thinning fluid and by about 21% for shear thickening fluid by enhancement of the Hartmann number value to the highest value. To achieve higher power current and higher average Nusselt number, the magnetic field can be applied non-uniformly, especially by applying it in a parabolic shape. The larger Hartmann Number value, the more pronounced the change in type of applied magnetic field. The impact of the change in the kind of applied magnetic field for the shear thickening fluid is minimal. By changing the design of the shape wall, it is possible to attain a flow with more strength and a higher Nusselt number. Although production of entropy by the smooth wall design is more, the mean Nusselt number value is about 37% and the flow power is about 62% more than the lozenge-shaped wall. The least influence of magnetic field is attained when the chamber is designed in a lozenge shape. The minimum amount of heat transfer, flow power and magnetic field effect is acquired when the chamber is at an angle of + 90^◦. Although increment of heat absorption/production coefficient reduces the mean Nusselt number value, it nevertheless enhances the flow strength and impact of magnetic field on entropy production. The Bejan Number value enhances with increasing heat absorption/production coefficient, enhancing the Hartmann number value and enhancing the power-law index.</p>