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

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.

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

“…The motion of the fluid is considered in x direction. The system of equations which governs the CSNF flow is given as [32][33][34]:…”

“…The system of equation which govern the CSNF flow under the above assumptions along with initial and boundary conditions are given as [32][33][34]:…”

“…Arif et al [33] calculated the exact solutions of CSF for generalized couette flow using CF fractional derivative. In an another paper, Arif et al [34] investigated the solutions for the heat transfer of CSF through a channel . Sheikh et al [35] derived the closed form solutions for the CF fractional model of second-grade fluid flow over a fluctuating plate.…”

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