This research attempts to study the thermal activity of suspension consisting of water and NEPCM elements inside a cavity with a trapezoidal cross-section. In addition, the cavity center contains a cold circular object rotating at a constant speed. The cavity is thermally characterized by the following: the upper and lower walls are thermally insulated (adiabatic), while the two lateral walls have a high temperature. The purpose of this study is to find out how the suspension interferes with the transfer of heat from hot walls to the cold body through the intervention of some initial conditions, which are: The effects of rotating cylinder speed (Re = 1 -500), medium permeability (Da = 10-5 – 10-2) and the magnetic field strength (Ha= 0 -100). The study used a digital simulation by solving the differential equations related to fluid mechanics and heat transfer using the Galerkin finite element (GFEM) method.to understand the influences of studied parameters (Re, Da and Ha numbers), the contours of isotherms, heat capacity and pathlines are presented in terms of these parameters. The findings indicated that as the rotation speed of the obstacle increased, the forced convection became dominant, and the thermal transmission rate improved. The improvement of the thermal transfer rate was also observed for higher Da numbers. Increasing the strength of the magnetic field hiders the fluid motion and reduces the thermal activity. At the highest studied Re, increasing Da from 10-5 to 10-2 augmented the Nusselt number by 10 times, while augmenting Ha from 0 to 100 reduced the Nu by 46%.
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