Effect of Local and Non-Local Kernels on Heat Transfer of Mixed Convection Flow of the Maxwell Fluid

M B Riaz,Maryam Asgir,Hafte Amsalu Kahsay,A Atangana,Muhammad Altaf Khan,Erhan Set

doi:10.1155/2021/9914408

Abstract

The heat transfer study of mixed convection flow of the Maxwell fluid is carried out here. The fluid flow is demonstrated by the system of coupled partial differential equations in the dimensionless form firstly. Then, its fractional form is developed by using the new definition of the noninteger-order derivative with the singular kernel (Caputo/C) and nonsingular kernels (Caputo–Fabrizio/CF and Atangana–Baleanu (nonlocal)/ABC). The hybrid-form solutions are obtained by applying the Laplace transform, and for the inverse Laplace transform, the problem is tackled by the numerical algorithms of Stehfest and Tzou. The C, CF, and ABC solution comparison under the effects of considered different parameters is depicted. The physical aspects of the considered problem are well explained by C, CF, and ABC in comparison to the integer-order derivative due to its memory effects. Furthermore, the best fit model to explain the memory effects of velocity is CF. The solutions for the Newtonian fluid and ordinary Maxwell fluid are considered as a special case and found in the literature.

Highlights

The best fit model to explain the memory effects of velocity is CF. e solutions for the Newtonian fluid and ordinary Maxwell fluid are considered as a special case and found in the literature
Introduction e combination of natural and forced convection is called mixed convection. is phenomenon gained a lot of popularity in recent years due to its vast applications in many fields of engineering, such as nuclear, chemical, food, aerospace, electrical, fluid dynamics, and astrophysics. e combined convection process comes into reality when free or forced convection alone is not enough to describe the heat transfer process properly
Maxwell fluid is one of the widely studied non-Newtonian fluids due to its diversity and rheological properties [5]. e nature of the viscoelastic fluids is best described by the noninteger/fractional derivative due to the history of fluid flow

Summary

Solutions for Temperature

By implementing the Laplace transform on equation (16), z2φ(η, zη s). The solution of the above equation is given as φ(η, s) 1e−η√ Pr s α. Laplace transform of equation (19) is b0s s+c φ(η, s). E above differential equation solution after applying the transformed boundary conditions of φ(η, s) from (6) and (7) is φ(η, s) 1e−η􏽰 ( ( b0 s) /( s +c ) ),. Applying the Laplace transform on equation (22), b0sα sα + c φ(η, s)

Solutions for Velocity

Solutions for Shear Stress

Results and Discussion