Exact solutions for free convection flow of generalized Jeffrey fluid: A Caputo-Fabrizio fractional model

Abstract

The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of free convection flow of Jeffrey fluid over a vertical static plate. The free convection is caused due to the temperature gradient. Therefore, heat transfer is considered for free convection. The classical model for Jeffrey fluid is written in dimensionless form with the help of non-dimensional variables. Furthermore, the dimensionless model is converted into a fractional model called as a generalized Jeffrey fluid model. The governing equations of generalized Jeffrey fluid model have been solved analytically using the Laplace transform technique. The recovery of existing solutions in the open literature is possible through this work in terms of classical Jeffrey fluid, fractional Newtonian fluid as well as classical Newtonian fluid. For various embedded parameters, the physics of velocity and temperature profiles is studied by means of numerical computation. This report provides a detailed discussion as well as a graphical representation of the obtained results. Keywords: Caputo-Fabrizio fractional derivatives, Generalized Jeffrey fluid, Free convection, The Laplace transform, Exact solutions