A Comparative Study of Natural Convection Flow of Fractional Maxwell Fluid with Uniform Heat Flux and Radiation

Aamir Farooq,Muhammad Imran Qureshi,Jia-Bao Liu,Atila Madureira Bueno,Muhammad Kamran,Asfand Fahad,Ruihua Tang,Sadique Rehman

doi:10.1155/2021/9401655

Abstract

This paper focuses on the comparative study of natural convection flow of fractional Maxwell fluid having uniform heat flux and radiation. The well-known Maxwell fluid equation with an integer-order derivative has been extended to a non-integer-order derivative, i.e., fractional derivative. The explicit expression for the temperature and velocity is acquired by utilizing the Laplace transform (LT) technique. The two fractional derivative concepts are used (Caputo and Caputo–Fabrizio derivatives) in the formulation of the problem. Utilizing the Mathcad programming, the effect of certain embedded factors and fractional parameters on temperature and velocity profile is graphically presented.

Highlights

To specify the performance of non-Newtonian fluids, numerous models have been applied. e Maxwell fluid is the first viscoelastic rate type fluid, which is extensively utilized. e differential form and rate type models have gotten a lot of attention among them
Taking Laplace transform (LT) on equation (13) and related initial-boundary conditions and substituting equation (22) for S(ζ, q), we find that u(ζ, q)
Numerical Discussion and Graphs e aim of this research is to study the Maxwell fluid’s natural convection flow with radiation and consistent heat flow. e differential model is developed into fractional order. ere are two fractional derivative concepts that we used (Caputo and Caputo–Fabrizio derivatives)

Summary

Introduction

To specify the performance of non-Newtonian fluids, numerous models have been applied. e Maxwell fluid is the first viscoelastic rate type fluid, which is extensively utilized. e differential form and rate type models have gotten a lot of attention among them. Khan et al [5] researched on heat transfer of Maxwell fluid through an infinite vertical plate In this study, they obtained the analytical solutions for temperature and velocity via LT. They obtained the analytical solutions for temperature and velocity via LT Such a model was studied by Khan et al [6] using fractional CF derivative. Aman et al [7] discussed about heat, velocity, and shear stress of fractional Maxwell model in a flexible medium using numerical LT. E semianalytical solutions for Maxwell fluid with fractional derivative were discussed in [8, 9]. Mohi [14] discussed the closed-form solution of fractional Maxwell of MHD effects using Laplace and Fourier transform. We observe the graphical representation of various embedded parameters like Maxwell fluid factor, fractional parameter, and Grashof and Prandtl numbers

Mathematical Statement

Preliminaries

Temperature Profile with CF Derivative

Velocity Profile with CF Derivative

12. Shear Stress with Caputo–Fabrizio Time Fractional Derivative