Stability analysis and heat transfer in Darcy–Forchheimer micropolar fluid flow with dissipation effects: Triple local similarity solutions

The research investigated the local triple solutions of similarity in a Darcy–Forchheimer micropolar fluid flow with dissipation effects on an exponentially shrinking sheet using the bvp4c solver on the MATLAB platform for computational analysis. This study contributes to our fundamental understanding of micropolar fluid flow in porous media, particularly in the presence of complicated boundary conditions (BCs) and other physical phenomena like heat dissipation. Systems that use these fluids can benefit from the study's findings in terms of both design and operation. The objective of the research focuses on the behavior of the coefficient of skin friction, the coefficient of couple stress, heat transfer rate, and mass transfer rate for micropolar material against the suction effect. In addition, the impacts of the micro‐gyration parameter, the Darcy–Forchheimer, the velocity slip, the viscous dissipation, and the Schmidt number parameters were taken into consideration. There are numerous solutions, including triple solutions and a single solution, in light of the findings. The first and second solutions dropped, whereas the third solution improved. A boost in the micropolar fluid parameter raises the concentration rate. The heat transfer rate falls in the first and second solutions but increases in the third solution. As a consequence of micropolar fluid characteristics and behavior. Upon conducting a stability analysis of triple solutions, it was discovered that the first solution is the only one that is physically viable to be stable. In advanced engineering systems incorporating fluid motion through porous media, the study of heat transfer in Darcy–Forchheimer micropolar fluid flow with dissipation effects has crucial practical applications. It also plays an important role in the design of industrial heat exchangers, biomedical devices, and microfluidic systems, where correct modeling of heat production caused by viscous dissipation and micro‐rotation improves system efficiency. The combination of Darcy–Forchheimer drag factors, as well as micropolar and thermal effects, provides a complete framework for optimizing heat and mass transmission in porous settings.