Temporal Stability and Entropy Generation in Rotational Micropolar Stagnation‐Point Flow Over a Biaxially Stretching/Shrinking Surface With Cattaneo–Christov Heat Flux

ABSTRACT This study examines steady three‐dimensional rotational stagnation‐point flow of an incompressible micropolar fluid over a biaxially stretching or shrinking surface. The energy model combines Cattaneo–Christov heat conduction with thermal radiation and viscous and microrotational dissipation. Similarity transformations reduce the governing partial differential equations to a coupled nonlinear boundary‐value problem that is solved with an adaptive collocation method. The objectives are to determine the dual‐solution region, identify the physically realizable branch through temporal stability analysis and quantify thermodynamic irreversibility through the entropy generation and Bejan numbers. Dual similarity solutions exist over a finite interval of the shrinking parameter and terminate at a critical bifurcation point. The smallest temporal eigenvalue is positive for the upper branch and negative for the lower branch, showing that only the upper branch is stable under small disturbances. Increasing the Brinkman number intensifies entropy generation and shifts the dominant irreversibility mechanism from heat transfer to fluid friction and microrotation. The model provides a theoretical basis for controlling heat transfer and irreversible losses in coating, polymer‐processing, lubrication, and microscale thermal systems that involve structured fluids near moving or deforming surfaces.