Fractional order simulations for the thermal determination of graphene oxide <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:mi mathvariant="bold-italic">GO</mml:mi> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and molybdenum disulphide <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"> <mml:mrow> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:mrow> <mml:mi mathvariant="bold-italic">Mo</mml:mi> <mml:msub> <mml:mi mathvariant="bold-italic">S</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> nanoparticles with slip effects

In this thermal investigation, the mixed free convection Casson nanofluid along with heat transfer effects over a vertical plate is addressed. The thermal radiative phenomenon is also considered to improve the heat transfer rate. For base fluid, the engine oil is assumed for which the thermal enhancement is predicted with the suspension of graphene oxide (GO) and molybdenum disulphide (MoS2) nanoparticles. To construct the fractional model, the partial derivative with respect to time is exchanged by the recent definitions of fractional derivatives namely Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) time-fractional derivative and the Laplace scheme is applied to obtain the solution of governing equations. To enhance the innovation of this article different cases of velocity profiles are examined. The effects of different parameters are examined graphically and numerically by varying the values of parameters. The reported results claimed that the simulations performed via AB-time fractional are more stable as compared to the Caputo-Fabrizio time-fractional approach. The velocity profile declines with increasing the fractional parameters while increasing change in velocity has been observed for Grashof number. The nanoparticles temperature shows a lower change due to volume fraction coefficient.

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