Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy gene
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Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation Zaim Abdel‑Nour1 · Abderrahmane Aissa2 · Fateh Mebarek‑Oudina3 · A. M. Rashad4 · Hafiz Muhammad Ali5 · M. Sahnoun2 · M. El Ganaoui6 Received: 18 March 2020 / Accepted: 9 April 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract The effect on the entropy production and MHD convection of the hybrid nanofluid Al2O3–Cu/water (water with Cu and Al2O3 nanoparticles) in a porous square enclosure is studied numerically via Galerkin finite element method. The enclosure used for flow and natural convection analysis is subjected to sinusoidal varying temperatures at the boundaries. Calculations were performed for specific parameters of the Rayleigh number (Ra = 103–106), porosity ratio (ε = 0.1–0.9), Darcy number (Da = 10−5–10−2), Hartmann number (Ha = 0–100) and nanoparticles concentration (φ = 0–0.08). The numerical results are presented by velocity profiles, isotherms, streamlines, and Nusselt number. They indicate that the isotherms subject to estimation variations under Ha boost from 0 to 100 as Ra enhances. At high Ha, the conduction transfer mechanism is more obvious. Also, it is seen that the convective heat transfer becomes stronger with the enhancement of the Ra while it detracts with the rise in Ha. Due to the Ra increase, the flow cell becomes stronger. For Ra = 106 and higher Hartmann numbers, the isotherms remain constant which is an indication of convection predominance. Keywords Entropy generation · Porous enclosure · Natural convection · Magnetic field · Hybrid nanofluid List of symbols Nu Nusselt number Da Darcy number L Height of cavity (m) Pr Prandtl number P Pressure K Thermal conductivity (W m−1 K−1) u, v Non-dimensional velocity components * Hafiz Muhammad Ali [email protected] 1
LSTE Laboratory, Faculty of Science and Technology, University of Mascara, Mascara, Algeria
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Laboratoire de Physique Quantique de la Matière et Modélisation Mathématique (LPQ3M), Université Mustapha Stambouli de Mascara, Mascara, Algeria
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Department of Physics, Faculty of Sciences, University of 20 août 1955-Skikda, Skikda, Algeria
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Department of Mathematics, Faculty of Science, Aswan University, Aswân 81528, Egypt
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Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Laboratoire énergétique de Longwy (FJV/LERMAB), Université de Lorraine, Longwy, France
L1 Width of cavity (m) W Length of cavity (m) x, y Coordinate W1 Width of cavity (m) Greeks symbols α Thermal diffusivity (m2 s−1) β Thermal expansion coefficient (K−1) θ Temperature ε Porosity μ Dynamic viscosity (kg m−1 s−1) φ Volume fraction ρ Density (kg m−3) Superscripts avg Average hnf Hybrid nanofluid c Cold loc Local s Solid particles
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Introduction Heat transfer forms the origin of many industrial processes that are present in our daily life. The magnification of these exchanges and the improvement o
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