Fractional modeling of bioconvection in Jeffrey nanofluids with gyrotactic organisms

Abstract

AbstractThe current study examines how mass and heat transfer affect mobility of Jeffrey fluid while taking sun radiation across the vertical plate into account. In the polyvinyl alcohol water base fluid, the study combines gyrotactic organisms with copper nanoparticles. Microorganisms classified as gyrotactic respond to gravitational and viscous forces by swimming and orienting themselves, which results in the formation of patterns known as bioconvection, which is the result of the collective movement of these microorganisms. The main goals are to address the growing uses of solar plates by creating a unique mathematical model for flow and thermal properties of the parabolic trough solar collector (PTSC) installed on solar panel. Sunlight is directed onto a single focal line by curved mirrors in PTSCs, which heat the fluid moving over the plate at this focused line. The momentum, heat, and mass equations are solved by the model using Fourier and Fick's laws. The Laplace transform is then used to convert the solution sets into dimensionless Partial differential equation (PDE) for the velocity, energy, and mass fields. The innovative aspect of this model is its in‐depth examination of non‐Newtonian nanofluids, which are boosted by the addition of gyrotactic organisms and copper nanoparticles to increase heat transfer efficiency. The impacts of several factors on flow characteristics, including the Lewis number, mass Grashof number, Grashof number for bioconvection, magnetic and electric parameters, Peclet number, chemical reaction parameter, and Prandtl number, are shown graphically. Increasing the radiation parameters and volume fraction results in a noticeable improvement in the temperature profile. By demonstrating the superior heat transfer capabilities of non‐Newtonian nanofluids in solar energy applications, this work advances the field. It is particularly relevant to microchip cooling, solar energy systems, and thermal energy systems. In summary, the work provides a comprehensive model that advances our understanding of heat and mass transfer in non‐Newtonian nanofluids that are exposed to ambient sunlight. In the future, the model will be employed in real solar energy systems to confirm its effectiveness. The findings have applications in the development of temperature control technology and solar energy systems that are more effective.