MATLAB Code for Exact Solutions of Generalized Couette Flow in a Micropolar Fluid with Couple Stresses under Different Boundary Conditions

The study investigates two distinct boundary value problems corresponding to different physical conditions at the walls: (I) vanishing bending moments and (II) vanishing shear stresses. The solutions are constructed using the Lin–Sidorov–Aristov ansatz, which eliminates the nonlinear convective term and reduces the governing equations to a biharmonic system.

The micropolarity parameter, representing the relative strength of couple viscosity, is systematically varied to reveal its profound influence on the flow structure. The code computes velocity profiles for both problem types across a wide range of the micropolarity parameter (from 0.05 to 2.0) and fixed dimensionless numbers (Reynolds number Re = 100, Taylor number Ta = 15). It generates five key figures that illustrate: (1) the fundamental difference between linear and nonlinear velocity profiles; (2) the shift of the velocity maximum toward the channel center and its magnitude increase, signaling the formation of a quasi-rigid core; (3) the wall shear stresses, which vanish identically in Problem II by construction, in contrast to the constant nonzero stresses in the classical Problem I; (4) the full two-dimensional velocity field contours, showing the transition from uniform shear to a core-annular structure; and (5) a direct comparison of the total velocity profiles at fixed transverse coordinates, highlighting the coupled effect of micropolarity and boundary conditions.