Exact solutions on magnetohydrodynamic Casson nanofluid EG-GO and EG-MWCNT over a vertical plate with shape factors: Caputo fractional derivative

The aim of the present work is to apply the Caputo-fractional derivative to the heat transformation of unsteady incompressible magnetohydrodynamic (MHD) Casson nanofluid flow. Ethylene Glycol-Graphene oxide and Ethylene glycol-Multiwall Carbon nanotubes considered as nanofluids. The current study helps in understanding the fluid dynamics involved in water purification, energy conservation, solar energy, coolants, cancer therapies, and physiological fluid dynamics. By using appropriate non-dimensional variables, the leading PDE of the problem are non dimensionalized. The governing equations are solved by the combined integral transforms of Fourier sine and Laplace transform technique. For an extensive study of the problem, graphical illustrations and tables are developed by using the MATLAB software. The effects of the order of the Caputo derivative, thermal Grashof number, viscous dissipation, and Casson parameter oscillations on the fractional heat and momentum equations are inspected. The thermal and velocity profiles are increased for thermal Grashof number and Casson parameter. Symmetry phenomena are also observed in the case of cooling and heating plate for thermal Grashof number. Different shapes of nanoparticles are performed for ordinary fractional parameters which is increased for temperature as well as velocity.