Unsteady Formulations for Stagnation Point Flow Towards a Stretching and Shrinking Sheet with Prescribed Surface Heat Flux and Viscous Dissipation

Okey Oseloka Onyejekwe

doi:10.11648/j.ijfmts.20170302.11

Abstract

The unsteady stagnation point flow and heat transfer with prescribed flux towards a stretching and shrinking sheet with viscous dissipation is studied. Similarity transformation is adopted to initially convert the governing differential equations into nonlinear ordinary differential equations. The two-point boundary value ordinary differential equations (ODE) are subsequently converted into partial differential equations by introducing a time-marching scheme. A Crank-Nicolson Newton-Richtmeyer scheme is employed to discretize the resulting equations. Initial guesses are made for the dependent variables and the solution advanced in time until temporal variations of the scalar profile are diminished and the steady-state solutions satisfy the similarity equations. A variation of the heat flux at one of the boundaries produced noticeable variations in the temperature field that can be related to the magnitude of the Prandtl number and velocity ratio parameter.

Highlights

The impact of a viscous fluid on a solid object (Fig. 1) constitutes a prototypical stagnation point flow
That is why the stagnation point flow is sometimes referred to as Hiemenz flow. He reduced the Navier-Stokes equations governing the flow to third order ordinary differential equations by using similarity transformations
One of the first attempts to look into the flow of incompressible fluid over a linearly stretching sheet was conducted by Crane [5] who provided similarity solutions for the case of a steady two-dimensional incompressible boundary layer flow produced by a stretching sheet that moves in its own plane

Summary

Introduction

The impact of a viscous fluid on a solid object (Fig. 1) constitutes a prototypical stagnation point flow. The heat transfer over a surface becomes quite interesting when the heat flux boundary condition is taken into account for those problems involving the cooling of electrical and nuclear components, space shuttle re-entry into the earth’s atmosphere, melt-spinning processes etc. This class of problems often encounters rapid heat-flux changes, and possible meltdown overheating and burnout constitute very important design considerations. Due to its fundamental nature and in combination with its practical importance, the classical problem has been generalized in several ways to include diverse physical effects These comprise viscous or inviscid, forward or reverse flows over surfaces. The heat transfer component of this study was carried out by Carragher and

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