Exploring the Impact of Prabhakar Fractional Derivatives on Bioconvection Flow of Nanofluids with Applications in Solar Energy

Abstract

The current research explores how entropy generation, heat, and mass transfer impact the motion of a second-grade fluid when exposed to solar radiation on a vertical plate. This study employs a base fluid composed of polyvinyl alcohol-water and considers the presence of copper nanoparticles and gyrotactic microorganisms. Given the increasing utilization of solar plates in various devices, there is a need to develop an effective numerical model for the flow and thermal characteristics of a parabolic trough solar collector (PTSC) mounted on a solar plate. Parabolic trough solar collectors (PTSCs) are solar energy systems that utilize curved mirrors, resembling parabolic troughs, to concentrate sunlight onto a single focal line. This focused sunlight heats the fluid flowing through a plate aligned along the focal line. The governing equations for heat, mass, and momentum, based on Fourier's and Fick's laws, have been established, and mathematical modeling is carried out. The Laplace transform method is applied to derive non-dimensional partial differential equations for the energy, mass, and velocity fields. The graphical analysis primarily focuses on the significant impact of key parameters, including the bioconvection Lewis number, magnetic field parameter, Prandtl number, electric field parameter, Grashof number, mass Grashof number, chemical reaction parameter, and Peclet number, related to the flow properties. Increasing the volume fraction and radiation parameter of nanoparticles is shown to enhance the temperature profile. Non-Newtonian nanofluids exhibit great potential for enhancing heat transfer processes and find diverse applications in solar energy systems, thermal energy systems, and microchip cooling. These nanofluids not only exhibit exceptional thermal properties but also unexpected thermal behavior. By incorporating nanoparticles into fluids, we can augment both solar energy storage and heat transfer capabilities.