A novel multi fractional comparative analysis of second law analysis of MHD flow of Casson nanofluid in a porous medium with slipping and ramped wall heating

Fractional calculus gets more attention in applied and pure science from the last two decay due to their valuable contribution. Due to extensive applications of fractional derivatives, the main aim of this article is focused on the multi fractional comparative study of entropy generation of magnetohydrodynamic (MHD) flow of Casson nanofluid with slipping and ramped wall heating effect on the plate. Set of partial differential equations forms governing equation and by using constant proportional–Caputo hybrid (CPC), Atangana–baleanu (AB) and Caputo Fabrizio (CF) fractional derivative generalized the model. Using the Laplace transform approach, a closed form of the solution is attained. Entropy production for Casson nanofluid is explored and compared using triple fractional modelled and for four different nanoparticles. Furthermore, the Bejan number is compared for the previously mentioned fractional derivatives. The graphs depict the effect of several parameters on the minimization and maximisation of multi generalised entropy generation. Instead of Atangana–baleanu and Caputo Fabrizio fractional operators, the newly proportional Caputo hybrid operator has a strong memory effect. It is concluded that CPC fractional model is more realistic then other two fractional model in case of ramped wall temperature while in case of isothermal wall temperature the results are vice versa.