Analytical Investigation of the Heat Transfer Effects of Non-Newtonian Hybrid Nanofluid in MHD Flow Past an Upright Plate Using the Caputo Fractional Order Derivative

Abstract

The objective of this paper is to examine the augmentation of the heat transfer rate utilizing graphene (Gr) and multi-walled carbon nanotubes (MWCNTs) as nanoparticles, and water as a host fluid in magnetohydrodynamics (MHD) flow through an upright plate using Caputo fractional derivatives with a Brinkman model on the convective Casson hybrid nanofluid flow. The performance of hybrid nanofluids is examined with various shapes of nanoparticles. The Caputo fractional derivative is utilized to describe the governing fractional partial differential equations with initial and boundary conditions on the flow model. Exact solutions are obtained for flow transport, temperature distribution besides that heat transfer rate and friction drag in terms of Mittag-Leffler function by using Fourier sine and Laplace techniques as hybrid methods. Further, we provided the limiting case solutions for classic partial differential equations on obtained governing fluid flow models. The influence of various physical parameters with different fractional orders are investigated on hybrid nanofluid’s fractional momentum and energy by plotting velocity and energy curves. Few of the findings suggest that fractional parameters have significant effect on flow parameters and that blade-shaped nanoparticles have a high heat transfer rate. The graphical results reveal that the Grashof number shows a symmetry effect in the case of cooling and heating the plate. Furthermore, the performance of hybrid nanofluid is considerably more effective with the Caputo-fractional derivatives rather than in the classic derivative approach.