Coupling model of a generalized second grade fluid flow and fractional Cattaneo heat transfer with magnetic field and radiation

Abstract

This paper presents a comprehensive model that considers the effects of magnetic field and radiation on the coupling of flow and heat transfer in a generalized second-grade fluid influenced by an exponentially accelerating plate that extends to infinity. The classical Cattaneo law has been expanded to the heat transfer equation, and the constitutive relationship has been established using the fractional calculus technique. By utilizing the fractional Laplace transform and Cayley–Hamilton theorem, semi-analytical solutions in the Laplace domain are derived for both the velocity field and temperature field. To avoid contour integrals, the discrete Laplace transformations are calculated numerically using Matlab software. Graphical representations are provided to illustrate the numerical results of the velocity field and temperature field for different parameter values. The solutions for cases without a magnetic field, cases where the magnetic field only depends on the temperature gradient, cases without radiation, cases without energy anomalous diffusion in the generalized second-grade fluid, as well as cases for Newtonian fluid and classical second-grade fluid, are obtained as limiting cases. Finally, a detailed discussion is conducted regarding the effects of fractional parameters, magnetic force, radiation, and Prandtl number.

Keywords

• Generalized second grade fluid
• Fractional derivative
• Magnetic field
• Radiation
• Laplace transform