Exact formulation and solution of micropolar fluid dynamics in radiative and slip-influenced porous surface

The current investigation offers an exhaustive analysis of the complex behaviour of velocity slip in a fluid flow over a deformable porous surface, subject to both uniform and progressively elevated thermal conditions. Through the utilization of boundary layer approximations and the application of similarity transformations, the fundamental governing equations are reformulated as a system of coupled nonlinear differential equations. These equations are meticulously solved to derive exact solutions that capture the nuanced interplay between heat transfer and fluid dynamics across a wide spectrum of physically significant parameters. The existence, uniqueness, or multiplicity of these solutions hinges critically on key variables such as mass transfer rates and micropolar fluid effects. Specifically, the mass transfer parameter serves as a threshold, demarcating conditions where solutions may either exist or fail to emerge. In the case of a stretching surface, a singular solution is identified, while for a contracting surface, multiple distinct solutions are observed. Moreover, the study delves into exact solutions for heat transfer and fluid flow behaviour under select parametric scenarios, offering closed-form expressions for pivotal variables including skin friction, rotational velocity, heat flux, fluid velocity, and the reduced Nusselt number. These expressions are further visualized through detailed graphical representations, shedding light on the key physical phenomena governing the flow regime. Key findings of the research reveal that microstructural effects significantly enhance the rotational behaviour of the fluid, while thermal radiation notably alters the temperature distribution near the surface. Slip conditions lead to thinner boundary layers, affecting both heat and momentum transfer rates. These insights have practical implications in areas such as advanced thermal insulation, microfluidics, biomedical flows, and energy systems involving porous structures.