Analysis of efficient partial differential equations model for nano-fluid flow through wedge involving minimal energy and thermal radiation

This research explores the groundbreaking integration of nanoparticles with microorganisms, leveraging their wedge-shaped configuration for enhanced functionality. To model this phenomenon mathematically, a framework of partial differential equations, coupled with boundary conditions, has been formulated. The system of linked nonlinear ordinary differential equations reduced to the nonlinear partial differential equations by the implementation of appropriate transformations. Then this model is numerically solved using the bvp4c built-in tool of MATLAB. A comprehensive computational analysis evaluates the effects of critical control parameters on temperature, velocity, nanofluid concentration, and microorganism density profiles. Furthermore, the study reveals that higher values of parameters such as Eckert number and Radiation, while an opposite pattern is observed for the Prandtl number. Furthermore, it is concluded that the concentration of nanoparticles is increased by increasing the Schmidt number, thermophoresis, and chemical reaction parameter. The bioconvection process induced by the microorganism density, creating a pronounced microorganism concentration near the wedge surface. The acquired results have various applications in the domains of thermal engineering, seismology, and mechanical engineering. The domain of used parameters is fixed as, 0.1 < M < 0.7 , 0.1 < R b < 2 . 4 , 0 . 1 < R d < 0 . 4 , 0 . 1 < Q < 0 . 4 , 0 . 5 < P r < 0 . 8 , 0 . 1 < E c < 1 . 5 , 0 . 1 < Ω < 4 . 5 , a n d 0 . 1 < P e < 3 . 0 for generating the optimal results.