Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al 2 O 3 -water nanofluid wit
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2652-8
Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2 O3 -water nanofluid with discrete heating∗ C. REVNIC1 , T. GROS¸AN2,† , M. SHEREMET3 , I. POP2 1. Faculty of Pharmacy, University of Medicine and Pharmacy, Cluj-Napoca 400012, Romania; 2. Department of Mathematics, Babe¸s-Bolyai University, Cluj-Napoca 400084, Romania; 3. Department of Theoretical Mechanics, Tomsk State University, Tomsk 634050, Russia (Received Mar. 2, 2020 / Revised Jun. 10, 2020) Abstract We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid (Cu-Al2 O3 -water). The upper and bottom walls of the cavity have a wavy shape. The temperature of the vertical walls is lower, the third part in the middle of the bottom wall is kept at a constant higher temperature, and the remaining parts of the bottom wall and the upper wall are thermally insulated. The magnetic field is applied under the angle γ, an opposite clockwise direction. For the numerical simulation, the finite element technique is employed. The ranges of the characteristics are as follows: the Rayleigh number (103 Ra 105 ), the Hartmann number (0 Ha 100), the nanoparticle hybrid concentration (φAl2 O3 , φCu = 0, 0.025, 0.05), the magnetic field orientation (0 γ 2π), and the Prandtl number P r, the amplitude of wavy cavity A, and the number of waviness n are fixed at P r = 7, A = 0.1, and n = 3, respectively. The comparison with a reported finding in the open literature is done, and the data are observed to be in very good agreement. The effects of the governing parameters on the energy transport and fluid flow parameters are studied. The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement. When the Rayleigh number is raised, the Nusselt number is increased, too. For moderate Rayleigh numbers, the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid, followed by the Al2 O3 -nanofluid. The nature of motion and energy transport parameters has been scrutinized. Key words magnetohydrodynamics, natural convection, hybrid nanofluid, heat transfer, bottom heater, wavy top and bottom enclosure Chinese Library Classification O362 2010 Mathematics Subject Classification
76R10, 76R50, 75D05
∗ Citation: REVNIC, C., GROS ¸ AN, T., SHEREMET, M., and Pop, I. Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2 O3 -water nanofluid with discrete heating. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2652-8 † Corresponding author, E-mail: [email protected] c Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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C. REVNIC, T. GROS ¸ AN, M. SHEREMET, and I. POP
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