MHD Stagnation-point Flow over a Stretching/ Shrinking Sheet in Nanofluids

Nor Hathirah Abd Rahman,Haliza Rosali,Norfifah Bachok

doi:10.13189/ujme.2019.070406

Nor Hathirah Abd Rahman, Haliza Rosali + Show 1 more

Open Access

https://doi.org/10.13189/ujme.2019.070406

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Abstract

In this study, we investigated the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow over a linearly stretching/shrinking sheet in nanofluids. There are three types of metallic nanoparticles considered such as copper (Cu), alumina (Al2O3) and titania (TiO2) in the base fluid of water with the Prandtl number Pr = 6.2 to investigate the effect of the nanoparticles volume fraction parameter φ of the nanofluids. In this problem, the governing nonlinear partial differential equations are transformed into the nonlinear ordinary differential equations by using a similarity transformation and then solved numerically using the boundary value problems solver bvp4c in Matlab software. The influence of magnetic field parameter, M on the skin friction coefficient Cf, local Nusselt number Nu and the velocity and temperature profiles are presented graphically and discussed. The results show that the velocity and temperature are influenced by the magnetic field and nanoparticles volume fraction. The dual solutions exist for shrinking sheet case and the solutions are non-unique, different from a stretching sheet. The numerical values of and for M=0 are also computed, which show a favourable agreement with previous work.

Highlights

In the boundary layer problem, the stagnation-point flow effect has been attracted the interest of many researchers due to its applications in industry such as flows over the tips of aircraft, submarines, etc
The nonlinear ordinary differential equations (7) and (8) subjected to the boundary conditions (9) have been solved numerically using the function bvp4c from Matlab due to its effectiveness in solving the boundary value problems which are much harder than initial value problems
The effects of nanoparticles volume fraction of nanofluid φ, the Prandtl number Pr and the magnetic field parameter M are analysed for three different types of nanofluids which are copper (Cu), alumina (Al2O3) and titania (TiO2) as the working fluids and water as the base working fluid

Summary

Introduction

In the boundary layer problem, the stagnation-point flow effect has been attracted the interest of many researchers due to its applications in industry such as flows over the tips of aircraft, submarines, etc. Hiemenz [1] was the first researcher who studied the steady two-dimensional stagnation-point flow towards a stationary semi-infinite wall and obtained an exact solution of the governing Navier-Stokes equations. The problem has been extended to the axisymmetric stagnation-point flow case by Homann [2]. Mahapatra and Gupta [3,4] have been investigated the heat transfer in the stagnation-point flow over a stretching surface through a viscoelastic fluid, respectively. Wang [5] who is the first introduced the flow past a shrinking sheet by considering both two-dimensional and axisymmetric cases of stagnation-point flow. Ishak et al [6], Bhattacharyya and Layek [7], Bhattacharyya [8], Bachok et al [9], and Lok et al [10] have extended the work by Wang [5] by focusing different effect characteristics such as the thermal radiation, homogeneous-heterogeneous reactions and magnetic fields effect

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