Influence of Soret and Dufour effects on unsteady 3D MHD slip flow of Carreau nanofluid over a slendering stretchable sheet with chemical reaction

Reddy Reddisekhar Reddy,J Chamkha,Polu Bala Anki Reddy

doi:10.15388/na.2019.6.1

Abstract

This paper presents a numerical exploration on the unsteady three-dimensional hydromagnetic flow of Carreau nanofluid over a slendering stretchable sheet in the presence of thermal radiation and chemical reaction. Furthermore, the effects of velocity slip, thermal slip, solutal slip, Soret and Dufour are taken into account. The prevailing time-dependent partial differential equations are metamorphosed into a system of coupled nonlinear ordinary differential equations by using the appropriate similarity transformations. The resultant nonlinear coupled differential equations are solved numerically by using the Runge–Kutta fourth-order method along with shooting scheme. The sway of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient has been premeditated, and numerical results are presented graphically and in tabular form. Comparison amid the previously published results, and the current numerical results are made for the limiting cases, which are found to be in a virtuous agreement.

Highlights

Nanofluids are solid-liquid materials, which contain nanometer-sized solid particles or else nanofibers with sizes 1–100 nm dispersed in a liquid such as oil, ethylene glycol, lubricants, water, biofluids and polymer solutions
Weissenberg number (We) measured the values of nondimensional parameters as We = 0.5, n = 0.6, τ1 = 0.2, λ = 0.7, M = 0.5, n∗ = 0.3, Prandtl number (Pr) = 0.72, R = 0.2, Nb = 0.3, Nt = 0.1, τ2 = 0.2, Dufour number (Dr) = 0.2, Soret number (Sr) = 0.4, Schmidt number (Sc) = 0.6, τ3 = 0.2 and Γ = 0.5
It is perceived that the velocities of fluid decreases for hefty values of Weissenberg number in shear thinning fluid for both the cases of steady and unsteady

Summary

Introduction

Nanofluids are solid-liquid materials, which contain nanometer-sized solid particles or else nanofibers with sizes 1–100 nm dispersed in a liquid such as oil, ethylene glycol, lubricants, water, biofluids and polymer solutions. The phenomenon of thermo-diffusion in liquids was presented by Soret in 1879, and the difference of temperature caused by the gradient of species concentration was developed by Dufour in 1872 These effects play an important role in the field of geosciences, oceanography, chemical engineering and air pollution. Keeping in view its important applications, combined thermophoresis, Brownian motion and Dufour effects on natural convective heat transfer on nanofluids were investigated simultaneously by Pakravan and Yaghoubi [19]. Inspired by the above-mentioned applications, the authors has focused on the problem, which addresses the numerical exploration on the unsteady three-dimensional MHD flow of Carreau nanofluid over a slendering stretchable sheet with thermal radiation and chemical reaction. The effects of velocity slip, thermal slip, solutal slip, Soret and Dufour are taken into account

Governing equations and mathematical formulation

Discussion

Main findings