Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al 2 O 3 -Cu/H 2 O hy
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2642-6
Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al2 O3 -Cu/H2 O hybrid nanofluid∗ N. A. ZAINAL1,2 , R. NAZAR1,† , K. NAGANTHRAN1 , I. POP3 1. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia; 2. Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Durian Tunggal 76100, Melaka, Malaysia; 3. Department of Mathematics, Babe¸s-Bolyai University, Cluj-Napoca 400084, Romania (Received Feb. 8, 2020 / Revised May 20, 2020)
Abstract The characteristics of heat transfer in the three-dimensional stagnationpoint flow past a stretching/shrinking surface of the Al2 O3 -Cu/H2 O hybrid nanofluid with anisotropic slip are investigated. The partial differential equations are converted into a system of ordinary differential equations by valid similarity transformations. The simplified mathematical model is solved computationally by the bvp4c approach in the MATLAB operating system. This solving method is capable of generating more than one solutions when suitable initial guesses are proposed. The results are proven to have dual solutions, which consequently lead to the application of a stability analysis that verifies the achievability of the first solution. The findings reveal infinite values of the dual solutions at several measured parameters causing the non-appearance of the turning points and the critical values. The skin friction increases with the addition of nanoparticles, while the escalation of the anisotropic slip effect causes a reduction in the heat transfer rate. Key words
anisotropic slip, three-dimensional flow, stagnation-point, hybrid nanofluid
Chinese Library Classification O361 2010 Mathematics Subject Classification
76D10, 34B15
Nomenclature A, B, Cf , cp , (pcp ), k,
dimensionless slip parameters; coefficient of skin friction; specific heat at constant pressure; heat capacitance of the fluid; fluid thermal conductivity;
N1 , N2 , N ux , P r, Rex , t,
constants; local Nusselt number; Prandtl number; local Reynolds number; time;
∗ Citation: ZAINAL, N. A., NAZAR, R., NAGANTHRAN, K., and POP, I. Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al2 O3 Cu/H2 O hybrid nanofluid. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2642-6 † Corresponding author, E-mail: [email protected] ©Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
2
N. A. ZAINAL, R. NAZAR, K. NAGANTHRAN, and I. POP
T, Tw , T∞ , S, u, v, w,
temperature of the fluid; temperature of the surface; ambient temperature; constant mass flux parameter; velocity components in the x-, y-,
x, y, z,
and z-directions, respectively; velocity components of the free stream along the x-, y-, and z-axes, respectively; Cartesian coordinates.
ν, ρ, τ, τw , φ1 ,
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