Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

Nor Dzulkifli,Nor Yacob,Norihan Md Arifin,Norfifah Bachok,Haliza Rosali

doi:10.3390/app8112172

Abstract

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution.

Highlights

The stagnation-point flow is a flow that explains the behavior of the fluid motion near the stagnation region
Magnetohydrodynamics (MHD) boundary layer flow over an exponential stretching sheet in a porous medium immersed in nanofluid was investigated by Rao et al [5]
The purpose of this study is to propose a new model that investigates the behavior of the flow and heat transfer for an unsteady stagnation-point flow over an exponential stretching/shrinking sheet in the presence of suction/injection and the velocity slip parameter immersed in nanofluid

Summary

Introduction

The stagnation-point flow is a flow that explains the behavior of the fluid motion near the stagnation region. This type of flow happens when the flow hits the solid surface and the fluid velocity at the stagnation-point equals zero. Zaib et al [4] studied the unsteady boundary layer flow and heat transfer passes through an exponential shrinking sheet in a Copper water nanofluid with the presence of a suction effect. The effects of joule heating and thermal radiation on the Magnetohydrodynamics (MHD) boundary layer flow over an exponential stretching sheet in a porous medium immersed in nanofluid was investigated by Rao et al [5]. Aleng et al [6] applied

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