Casson fluid flow has numerous functional applications in food processing, metallurgy, drilling and bio-engineering operations. The significance of Casson fluid in cylindrical coordinates has recently attracted researchersbecause of the numerical and experimental analyses of the fluid. Due to the lack of fractional analytical approaches, this paper is trying to examine the magnetic effect and thermal effect on Casson fluid with oscillatory boundary conditions in cylindrical coordinates. The constitutive model of Casson fluid is solved by using the Caputo–Fabrizio time fractional derivative approach. The fluid moves in the vertical oscillating cylinder under the influence of a transverse applied magnetic field. Closed-form solutions are obtained via integral transforms (Laplace and Hankel transformations) for velocity and temperature distributions. Graphical results are shown for various physical parameters such as the Casson fluid parameter $\beta$, magnetic parameter $M$, Grashoff number Gr, Prandtl number Pr and fractional parameter $\alpha$. The corresponding expressions for Nusselt number are also evaluated for various embedded parameters in a tabular form.

In the present era of research, entropy generation is one of the most important topics, which is used to control the irreversibility phenomena during heat transfer. Due to the important application in engineering, atomic reactors and cooling process in different fields, this work aims to study the second law analysis of Casson fluid. Vertical plate geometry was considered, where the plate at the boundary exhibits arbitrary wall shear stress and the fluid lies above the plate. Exponential type heating was produced at the bounding plate whereas natural convection is caused because of buoyancy force. Magnetohydrodynamic (MHD) analysis was also considered perpendicular to the plate. The usual Darcy’s law of Newtonian fluid was modified to Darcy’s law for Casson fluid. The exact analysis was performed using the Laplace transform technique to establish exact solutions for the velocity field and temperature distribution. Results are interpreted physically using various plots and discussed in detail.