Unsteady thermal transport flow of Maxwell clay nanoparticles with generalized Mittag-Leffler kernel of Prabhakar's kind

Abstract

The present work deals with an unsteady flow of a Maxwell fluid including clay nanoparticles via Prabhakar fractional operator. Thermal conductivity and viscosity coefficients for nanoparticles depends upon the Brinkman and Maxwell-Garnett models are computed analytically. The fractional mathematical model is developed through constitutive laws and transformed into non-dimensional form with suitable dimensionless parameters. Laplace transform is applied to obtain the generalized results for temperature and velocity distributions. The influence of volume fraction, dimensionless numbers and different fractional parameters depending upon temperature and velocity profile are justified and made up by MATHCAD software. We find several limiting solutions and compare them to the most recent literature. Furthermore, significant outcomes for clay nanoparticles with various base fluids have been reported. As a result, it is found that generalized Mittag-Leffler kernel with three parameters exhibits stronger than power law kernel and Mittag-Leffler kernel with one parameter. Water based nanoparticles shown maximum velocity with distinctive peak near the plate. For greater values of time and fractional parameters fluid properties like temperature and velocity can be enhanced.