Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

A Mushtaq,A Alsaedi,T Hayat,M Mustafa,S Abbasbandy

doi:10.1063/1.4940133

Abstract

Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i) the shooting method and (ii) the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.

Highlights

Non-Newtonian fluid mechanics has been gaining considerable fame in research community since the last decade primarily due to its multidisciplinary applications in chemical and biomedical industry
The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr
The Deborah number is important for viscoelastic materials

Summary

Introduction

Non-Newtonian fluid mechanics has been gaining considerable fame in research community since the last decade primarily due to its multidisciplinary applications in chemical and biomedical industry. It is well established argument that almost all the industrial and biological fluids do not exhibit linear relationship between stress and the rate of deformation. Researches have shown that rheological characteristics of these fluids cannot be predicted solely through single constitutive relationship. The shear-thinning/thickening behaviors can be addressed through the well-known power-law model. This model is unable to explain the visco-elastic effects in the flow. Some recent investigations pertaining to the flow and heat transfer characteristics in Maxwell fluid can be found in Refs. 1–13

Methods

Results

Conclusion