Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid

Meraj Mustafa

doi:10.1063/1.4917306

Abstract

In this paper Cattaneo-Christov heat flux model is used to investigate the rotating flow of viscoelastic fluid bounded by a stretching surface. This model is a modified version of the classical Fourier’s law that takes into account the interesting aspect of thermal relaxation time. The boundary layer equations are first modeled and then reduced to self-similar forms via similarity approach. Both analytical and numerical solutions are obtained and found in excellent agreement. Our computations reveal that velocity is inversely proportional to the viscoelastic fluid parameter. Further fluid temperature has inverse relationship with the relaxation time for heat flux and with the Prandtl number. Present consideration even in the case of Newtonian fluid does not yet exist in the literature.

Highlights

The classical Fourier’s heat conduction law[1] has been the most successful model for the description of heat transfer mechanism in various pertinent situations
Let us consider the flow of upper-convected Maxwell (UCM) fluid bounded by a linearly stretching surface
Rotating flow of upper-convected Maxwell fluid is examined with the consideration of CattaneoChristov heat flux model that accounts for the effects of thermal relaxation time

Summary

INTRODUCTION

The classical Fourier’s heat conduction law[1] has been the most successful model for the description of heat transfer mechanism in various pertinent situations. It is seen that such consideration produces hyperbolic energy equation for temperature field and it allows for the transportation of heat through the propagation of thermal waves having finite speed Such kind of heat transportation has exciting practical applications that span from nanofluid flows to the modeling of skin burn injury Christov[4] replaced the time derivative in Maxwell-Cattaneo’s model with the Oldroyd’s upper-convected derivative in order to preserve the material-invariant formulation. This model is recognized in the literature as Cattaneo-Christov heat flux model. Han et al.[7] studied the slip flow and heat transfer in Maxwell fluid through Cattaneo-Christov model They solved the governing problem analytically by homotopy analysis method (HAM). The behavior of involved parameters especially the thermal relaxation time is thoroughly emphasized by graphical illustrations

PROBLEM FORMULATION

ANALYTIC SOLUTIONS BY HAM

Convergence of the series solutions

CONCLUSIONS