Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Abstract

In this paper, we consider the constructive equations of the fractional second-grade fluid. The considered fluid model is described by the Caputo derivative. The problem consists to determine the exact analytical solution using the Laplace transform method. The influence of the order of the used fractional operator has been presented in this paper. We also analyze the influence of the Prandtl number in the dynamics of the temperature distribution according to the variation of the order of the Caputo derivative. The impact of the second-grade parameter and the Grashof number in the dynamics of the velocity has been presented and discussed. The influences of the parameters used in the modeling have been interpreted in terms of a fractional context. In general, it is shown that the order of the fractional operator influences the diffusivity of the considered fluid. This influence can cause an increase or decrease in the temperature and velocity distributions. The main findings of the paper have been illustrated using the graphical representations of the considered distributions according to the order of the fractional operator.