Convection heat–mass transfer of generalized Maxwell fluid with radiation effect, exponential heating, and chemical reaction using fractional Caputo–Fabrizio derivatives

Abstract

Abstract This article is directed to analyze the transfer of mass and heat in a generalized Maxwell fluid flow unsteadily on a vertical flat plate oscillating in its respective plane and heated exponentially. It explains the transfer of mass and heat using a non-integer order derivative usually called a fractional derivative. It is a generalization of the classical derivatives of the famous Maxwell’s equation to fractional non-integer order derivatives used for one-dimensional flow of fluids. The definition given by Caputo–Fabrizio for the fractional derivative is used for solving the problem mathematically. The Laplace transform method is used for finding the exact analytical solution to a problem by applying it to a set of non-integer order differential equations that are dimensionless in nature. These equations contain concentration, temperature, and velocity equations with specific initial and boundary conditions. Solutions of the three equations are graphically represented to visualize the effects of various parameters, such as the radiation parameter (Nr), the thermal Grashof number, the fractional parameter (α), the mass Grashof number, Prandtl effective number, Schmidt number, Prandtl number, the chemical reaction ( η 2 ) ({\eta }_{2}) , mass, and the temperature during fluid flow.