A fractional model for the kerosene oil and water-based Casson nanofluid with inclined magnetic force

[Display omitted] •Comparative thermal aspect of nanofluid with kerosene oil and water base fluid subject to the inclined magnetic force is addressed.•The inclined surface induced the flow.•Newtonian heating with nonlinear relations are accounted.•Analytical solutions are obtained through Laplace transform. This investigation deals with comparative thermal aspect of nanofluid with kerosene oil and water base fluid subject to the inclined magnetic force. The inclined surface induced the flow. The Newtonian heating with nonlinear relations are also focused to modify the analysis. The fractional model of non-dimensional leading equations is formulated by utilizing a recent definition of fractional derivative technique namely Atangana-Baleanu (AB) time fractional derivative. The semi-analytical solution of energy and momentum profile is described by utilizing the mathematical technique Laplace transform and different numerical algorithms are utilized for the inverse of Laplace i.e. Stehfest and Tzou’s schemes via MATLAB computational software. The behavior of different parameters with changed values is analyzed and plotted graphically for energy and momentum profiles. The comparative thermal analysis for the kerosene oil and water base material is presented. It is observed the enhancement in heat transfer is comparatively higher for the water-based nanofluid as compared to kerosene oil-based nanofluid. The change is velocity is more progressive for the viscous case as compared to the Casson fluid. Moreover, the rate of velocity is larger for the ordinary derivative model as compared to fractional model derivative.