A Time Fractional Model With Non-Singular Kernel the Generalized Couette Flow of Couple Stress Nanofluid

Muhammad Arif,Farhad Ali,Kottakkaran Sooppy Nisar,Ilyas Khan

doi:10.1109/access.2020.2982028

Abstract

The aim of the present work is to calculate the closed form solutions of the unsteady couple stress nanofluids flow in a channel. Couple stress nanofluids (CSNF) is allowed to pass through the parallel plates separated by a distance $h$ . In this study, we choose blood as base fluid with gold nanoparticles suspension. The lower plate is at rest and the upper plate is suddenly moved with constant velocity $U_{0} $ . Recently, Atangana–Baleanu (AB) introduced a new definition of fractional derivatives. This AB definition of fractional derivative has been applied to the present couple stress nanofluid (CSNF) model. The closed form solutions of present CSNF model via AB approach are obtained by using the Laplace and finite Fourier sine transforms. Exact results of velocity and temperature are displayed and discussed for different parameters of interest. Solutions obtained here are reduced to three different cases in limiting sense i.e. (i) fractional couple stress nanofluid without external pressure gradient. (ii) ordinary couple stress nanofluid. (iii) regular couple stress fluid. Finally, skin friction and Nusselt number are evaluated at lower and upper plates and listed in tabular forms. The results show that increasing external pressure gradient, CSNF velocity increases whereas decreases by increasing Reynolds number. Increasing volume fraction slow down the CSNF velocity. The velocity of Newtonian viscous fluid is higher than CSNF velocity.

Highlights

There are many kind of fluids in nature one is Newtonian and the other one are non-Newtonian fluids which have a lot of industrial and daily life applications in many physical, practical and different engineering processes
He noticed that couple stresses are the simplest generalization theory of the classical fluids which allows for the effect of polar such as the presence of couple stress forces and body couples
In this paper he shows the applications of Couple stress fluid (CSF) and different real world problems which are calculated by many researchers

Summary

INTRODUCTION

There are many kind of fluids in nature one is Newtonian and the other one are non-Newtonian fluids which have a lot of industrial and daily life applications in many physical, practical and different engineering processes. The problems related to couple stress fluids (CSFs) in a channel have useful engineering and industrial applications. CSF theory and mathematical model have many daily life applications, like pumping phenomena when the fluids synthesis lubricants and problems related to biological process and animal blood and many other example. The definitions of fractional derivative explained the viscoelastic and viscoplastic behavior of different materials Due to these practical life applications like, Bio-engineering, kinetics of polymers and in many other areas of modern science and technologies the scientists are focused to discussed different phenomena using fractional calculus and fractional operators. Many researchers work on nanofluid and use these fluid in different circumstances like, Gireesha et al [42], [43] investigated heat and mass transfer phenomena in chemically reacting Casson nanofluid model. Skin fraction for (CSNF) for the lower and upper plate are calculated and presented the numerical values in tabular form

MATHEMATICAL MODELING AND SOLUTION OF THE PROBLEM

SOLUTIONS OF MOMENTUM EQUATION

SPECIAL CASES

CLASSICAL MODEL OF REGULAR COUPLE STRESS FLUID

RESULTS AND DISCUSSION