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A review of the literature revealed that nanofluids are more effective in transferring heat than conventional fluids. Since there are significant gaps in the illumination of existing methods for enhancing heat transmission in nanomaterials, a thorough investigation of the previously outlined models is essential. The goal of the ongoing study is to determine whether the microscopic gold particles that are involved in mass and heat transmission drift in freely. The current study examines heat and mass transfer on 3D MHD Darcy–Forchheimer flow of Casson nanofluid-induced bio-convection past a stretched sheet. The inclusion of the nanoparticles is a result of their peculiar properties, such as remarkable thermal conductivity, which are important in heat exchangers and cutting-edge nanotechnology. The gyrotactic microorganisms must be included to prevent the potential deposition of minute particles. The proposed flow dynamics model consists of an evolving nonlinear system of PDEs, which is subsequently reduced to a system of dimensionless ODEs utilizing similarity approximations. MATLAB software was utilized to create an effective code for the Runge-Kutta technique using a shooting tool to acquire numerical results. This method is extensively used to solve these issues since it is accurate to fourth order, efficient, and affordable. The influence of submerged factors on the velocity, temperature, concentration, and density of motile microorganisms is shown in the figures. Additionally, tables and bar charts are used to illustrate the physical characteristics of the Nusselt and Sherwood numbers for the densities of both nanoparticles and motile microorganisms. The dimensionless velocities are observed declining when the casson, magnetic, porosity, and forchheimer parameters grow, whereas the dimensionless temperature and concentration rise as the thermophoresis parameter rises. This work provides insights into practical applications such nanofluidic, energy conservation, friction reduction, and power generation. Furthermore, in a concentration field, the Brownian and thermophoresis parameters exhibit very distinct behaviours. However, the work makes a significant point that the flow of a Casson fluid including nanoparticles can be regulated by appropriately modifying the Casson parameter, thermophoresis parameter, and Brownian motion parameter.

Numerical Study on 3D MHD Darcy-Forchheimer Flow Caused by Gyrotactic Microorganisms of the Bio-Convective Casson Nanofluid across a Stretched Sheet