Series solution of time-fractional mhd viscoelastic model through non-local kernel approach

The study of ramped condition in the context of unsteady incompressible magnetohydrodynamic Casson fluid flow over a moving vertical plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. In this study, Casson fluid is considered unsteady under the influence of magnetic field. The fractional mathematical model is proposed by considering the effect of chemical reaction parameter of the flowing fluid. The governing equations are transformed into the dimensionless form and developed fractional models like Caputo-Fabrizio and Atangana-Baleanu Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for velocity, energy and momentum balances developed in terms of series. MATHCAD software is being used for numerical computations and the physical attributes of material and fractional parameters are discussed. To analyze their behavior clearly, two-dimensional graphical results are plotted for velocity profile and temperature as well. It has been concluded that the fluid’s velocity are reduced for larger values of the fractional parameter and Prandtl number and is maximum for small values of both parameters. Further, the velocity behavior becomes larger for isothermal condition as compared to ramped conditions.