New YAC time-fractional derivative approach for water-based hydromagnetic chemically reacting radiative flow of nanofluid with copper nanoparticles past an upright plate

Abstract

The current article utilizes the novel application of the Yang-Abdel-Cattani (YAC) fractional derivative to analyze the Casson nanofluid flow. Water nanofluid suspended with copper nanoparticles is considered in the flow phenomenon. Primarily, the dimensionless governing equations are converted to a fractional model by using a new description of fractional derivative, i.e. YAC fractional derivative. These fractional equations are then transformed and solved using the Laplace method. Finally, the solutions of these transformed equations are obtained in terms of a series of Prabhakar functions. The comparative results for Newtonian and non-Newtonian fluids are obtained using the analytical solutions and presented in the form of graphs. The effect of the chemical reaction, Casson parameter, radiation parameter, orders of the time-fractional derivative, and magnetic strength on velocity, temperature, and concentration fields is investigated. The fluid behavior of both Newtonian and Casson fluids is analyzed and presented in the form of graphs. Fluid temperature is enhanced by 5.22% with the use of copper nanoparticles with a 4% volume fraction. With the advancement of chemical reaction, the velocity and concentration of the nanofluid are observed to be decreasing.