Exact solutions of non-singularized MHD Casson fluid with ramped conditions: A comparative study

The study of magnetohydrodynamic (MHD) fluids has significant implications across various scientific disciplines, particularly in understanding complex phenomena in astrophysics, engineering, and geophysics. The Casson fluid model stands as a crucial tool for describing non-Newtonian behaviors observed in certain fluid systems. The current work shows an analytical analysis to determine the ramped effect on the fractionalized MHD Casson fluid over an vertical plate. Fractional partial differential equations are used to formulate the problem along with initial and boundary conditions. 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 closed form solution of the dimensionless governing equation analytically. 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.