The proportional Caputo operator approach to the thermal transport of Jeffery tri-hybrid nanofluid in a rotating frame with thermal radiation

Abstract

AbstractEngine Oil is a widely used fluid in engineering problems, particularly to enhance the rate of heat transfer when these working fluids play a fundamental role. We consider engine oil as a base fluid and the suspension of different shaped (Spherical cylindrical and platelet) nanoparticles dispersed uniformly in the base fluid to enhance the working capability of engine oil. The spherical shape $${\text{CuO}}$$ CuO , platelet shape $${\text{Al}}_{2} {\text{O}}_{3}$$ Al 2 O 3 and cylindrical shape $${\text{TiO}}_{2}$$ TiO 2 nanoparticles are added in engine oil to constitute tri-hybrid nanofluid aiming at obtaining better thermal performance. Furthermore, we also analyze the Jeffery tri-hybrid nanofluid in a rotating frame over an infinite vertical plate. More precisely, the classical model of Jeffery tri-hybrid nanofluid is transformed into a time-fractional model by applying the newly developed constant proportional Caputo fractional derivatives. Sharp numerical results are obtained applying a Laplace transform steered approach. All the flow parameters are highlighted through graphs via MATHCAD. Furthermore, a comparative analysis between nanofluid, hybrid nanofluid and tri-hybrid nanofluid has been performed showing that tri-hybrid nanofluid has good thermal performance. The solutions of the constant proportional operator are discussed classically by taking fractional parameter α → 1. Moreover, some engineering quantities have been calculated and presented in tables. During the analysis we dispersing the mixture of nanoparticles in engine oil base fluid enhanced the heat transfer up-to18.72% which can efficiently improve the lubricity of the engine oil.