MHD analysis of tangent hyperbolic micropolar fluid flow over a permeable stretching surface

This investigation analyzes the effects of micropolar tangent hyperbolic hybrid nanofluid flow over a porous stretching sheet. Additionally, the influences of magnetohydrodynamics and heat source/sink effects are also considered into the analysis. The angular momentum equation is employed to examine the micro-rotation characteristics of the fluid flowing, whereas the enhancement in heat transport performance is evaluated through the inclusion of hybrid nanoparticles. These equations are subsequently reduced to a system of ordinary differential equations using suitable similarity transformations. The resulting nonlinear system is solved numerically using the Runge-Kutta-Fehlberg 45 (RKF-45) method in conjunction with a shooting technique. The effects of relevant physical parameters are illustrated through graphical representations, highlighting their physical significance. Graphical representations depict the physical significance of relevant parameters. Validation of numerical results is performed by comparing them with previously published data. The main conclusions of the study are as follows: (1) a gradual reduction in fluid velocity is observed with an increase in Weissenberg number $$\:(We=0.0,\:0.5,\:1.0)$$ , and permeability parameter $$\:\:(K=0.0,\:0.4,\:0.8)$$ , while the surface condition parameter is fixed at $$\:n\:=\:0.5$$ , (2) the skin friction coefficient shows a pronounced decrease as the permeability parameter increases $$\:(K=0.0,\:0.5,\:1.0)$$ , (3) the wall couple stress exhibits an increasing trend with rising values of the micro-rotation parameter $$\:({\Psi\:}=0.0,\:2.0,\:4.0)$$ . Owing to the unique rheological behavior, tangent hyperbolic fluids are widely applicable in engineering and biomedical systems, where they facilitate controlled transport in food processing, polymer technology, oil recovery, and blood flow analysis.