Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion

Ndolane Sene,Saima Arshed

doi:10.1155/2022/8785197

Abstract

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Highlights

Ey have used the Laplace transforms to get the analytical solutions of the proposed model
Samiulhaq et al [20] studied the magnetic field influence on unsteady free convection flow of a second-grade fluid near an infinite vertical Journal of Mathematics flat plate with ramped wall temperature embedded in a porous medium. e Laplace transform method has been used in the investigations related to the exact solutions of the model considered in the paper
Shah et al [21] proposed an investigation related to the influence of magnetic field on double convection problem of viscous fluid described by fractional-order derivative over an exponentially moving vertical plate

Summary

Introduction

Ey have used the Laplace transforms to get the analytical solutions of the proposed model. Vieru et al [29] first proposed an investigation related to the analytical solutions of the fractional model described free convection flow near a vertical plate with Newtonian heating and mass diffusion using Laplace transform. Note that we consider velocity v, temperature φ, and concentration θ satisfying the boundary conditions represented in the following relationships: v(0, t) 0, (34)

Results

Conclusion