| Summary: | A numerical investigation of the magnetohydrodynamics of a mixed convection of nano-enhanced phase change material (NEPCM) within a triangular chamber containing an elliptical heat source is presented in this article. The forced convection has resulted from the movement of the upper cavity, while the free convection is due to the temperature difference between the heat source and cold inclined sidewalls. Four cases are considered based on the directions of the moving of the upper wall parts, namely, Case 1, where the left part is moving in the positive direction of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>X</mi></semantics></math></inline-formula>-axis and the right part moves in the opposite direction (1(+−)), Case 2, where the two parts move in the positive direction of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>X</mi></semantics></math></inline-formula>-axis (2(++)), Case 3, where the two parts move in the negative direction of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>X</mi></semantics></math></inline-formula>-axis (3(− −)), and Case 4, where the left part moves in the negative direction of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>X</mi></semantics></math></inline-formula>-axis and the right part moves in the negative direction (4(−+)). The Galerkin finite element method (GFEM) is employed for addressing the governing equations of the system under study. The impacts of the Reynolds number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>≤</mo><mi>R</mi><mi>e</mi><mo>≤</mo><mn>100</mn></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, the inclination angle of the elliptic heat source <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>≤</mo><mi>γ</mi><mo>≤</mo><mn>90</mn></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, the nanoparticles volume fraction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo> </mo><mrow><mo>(</mo><mrow><mn>0</mn><mo>%</mo><mo>≤</mo><mi>ϕ</mi><mo>≤</mo><mn>8</mn><mo>%</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and the movement directions of the parts of the upper wall (four cases) are presented and discussed. The results suggested that increasing Re enhanced the heat transfer rate, while increasing Ha reduced it. The vertical positions of the elliptical heat source resulted in the maximum heat transmission rate. At the highest Re, changing the location of the heat source from horizontal (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>) to vertical (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>90</mn></mrow></semantics></math></inline-formula>) enhanced the average Nusselt number by 60%, while choosing Case 1 for upper wall movement increased the average Nusselt number by 300% compared to Cases 2 and 3.
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