Hydrothermal Mixed Convection in a Split-Lid-Driven Triangular Cavity Suspended by NEPCM

Obai Younis, Sameh E. Ahmed (), Aissa Abderrahmane, Abdulaziz Alenazi and Ahmed M. Hassan
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Obai Younis: Department of Mechanical Engineering, College of Engineering in Wadi Addwasir, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Sameh E. Ahmed: Department of Mathematics, Faculty of Science, King Khaild University, Abha 62529, Saudi Arabia
Aissa Abderrahmane: Laboratoire de Physique Quantique de la Matière et Modélisation Mathématique (LPQ3M), University of Mascara, Mascara 29000, Algeria
Abdulaziz Alenazi: Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia
Ahmed M. Hassan: Department of Mechanical Engineering, Future University in Egypt, New Cairo 11835, Egypt

Mathematics, 2023, vol. 11, issue 6, 1-17

Abstract: 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 X -axis and the right part moves in the opposite direction (1(+−)), Case 2, where the two parts move in the positive direction of the X -axis (2(++)), Case 3, where the two parts move in the negative direction of the X -axis (3(− −)), and Case 4, where the left part moves in the negative direction of the X -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 ( 1 ≤ R e ≤ 100 ) , the inclination angle of the elliptic heat source ( 0 ≤ γ ≤ 90 ) , the nanoparticles volume fraction ϕ ( 0 % ≤ ϕ ≤ 8 % ) 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 ( γ = 0 ) to vertical ( γ = 90 ) 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.

Keywords: mixed convection; GFEM; elliptic heat source; magnetic field; NEPCM (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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