The impact of magnetohydrodynamics and heat transfer on the unsteady flow of Casson fluid in an oscillating cylinder via integral transform: A Caputo–Fabrizio fractional model

Abstract

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 researchers because 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.