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Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al2O3-Cu/H2O hybrid nanofluid

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Abstract

The characteristics of heat transfer in the three-dimensional stagnation-point flow past a stretching/shrinking surface of the Al2O3-Cu/H2O 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.

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Abbreviations

A, B :

dimensionless slip parameters

C f :

coefficient of skin friction

c p :

specific heat at constant pressure

(pcp):

heat capacitance of the fluid

k :

fluid thermal conductivity

N1, N2 :

constants

Nu x :

local Nusselt number

Pr :

Prandtl number

Re x :

local Reynolds number

t :

time

T :

temperature of the fluid

T w :

temperature of the surface

T ∞ :

ambient temperature

S :

constant mass flux parameter

u,v,w, :

velocity components in the x-, y-, and z-directions, respectively

ue, ve, we :

velocity components of the free stream along the x-, y-, and z-axes, respectively

x, y, z :

Cartesian coordinates.

β :

coefficient of the thermal expansion

ω :

eigenvalue

ω 1 :

smallest eigenvalue

η :

similarity variable

θ :

dimensionless temperature

κ :

stretching/shrinking parameter

μ :

dynamic viscosity of the fluid

ν :

kinematic viscosity of the fluid

ρ :

density of the fluid

τ :

dimensionless time variable

τ w :

wall shear stress

ϕ 1 :

Al2O3 nanoparticle volume fraction

ϒ 2 :

Cu nanoparticle volume fraction.

f:

base fluid

nf:

nanofluid

hnf:

hybrid nanofluid

s1:

Al2O3 solid component

s2:

Cu solid component.

′:

differentiation with respect to η.

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Acknowledgements

The principal author wishes to acknowledge Universiti Kebangsaan Malaysia (UKM), Ministry of Higher Education (MoHE) Malaysia, and Universiti Teknikal Malaysia Melaka (UTEM) in support of the scholarship, and all authors wish to acknowledge the research university grant (No. DIP-2017-009).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, 43600, Bangi, Selangor, Malaysia

    N. A. Zainal, R. Nazar & K. Naganthran

  2. Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Durian Tunggal, 76100, Melaka, Malaysia

    N. A. Zainal

  3. Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania

    I. Pop

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  1. N. A. Zainal
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Correspondence to R. Nazar.

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Zainal, N.A., Nazar, R., Naganthran, K. et al. Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al2O3-Cu/H2O hybrid nanofluid. Appl. Math. Mech.-Engl. Ed. 41, 1401–1416 (2020). https://doi.org/10.1007/s10483-020-2642-6

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