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

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.