The magnetohydrodynamics (MHD) mixed convection of nano-encapsulated phase change material (NEPCM) contained within a double lid-driven hexagonal porous chamber contacting a square-shaped obstacle is numerically examined in this study. The enclosure's upper and lower walls are moving at the same speed; while the square-shaped obstacle is hot, the side walls are stationary and cold. The Galerkin Finite Elements method (GFEM) was applied to deal with the governing equations and their boundary conditions. The flow and thermal fields are presented and discussed in relation to the effects of the moving wall direction, moving wall velocity, magnetic field strength, and chamber permeability. These studied factors are examined in these ranges: Ha = 0 to 100, Da = 10–5 to 10–2, ø = 0 % to 5 % and Re = 1 to 500. The results showed that the heated body is surrounded by a circular flow when the two walls move in opposite directions. However, thermal activity is enhanced and strengthened when the upper and lower walls move in the same direction. According to the findings, the concentration of NEPCM particles has little effect on the quality of the thermal transfer and decreasing the space's permeability makes it more difficult for the suspension to move and reduces the amount of thermal energy transferred between the cold and hot surfaces. Additionally, a decrease in thermal transfer occurs when the intensity of the magnetic field is increased, which has a negative impact on the suspension's movement.
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