MATLAB Code for Exact Solutions of Generalized Couette Flow in a Micropolar Fluid with Couple Stresses under Different Boundary Conditions
Description
This dataset contains MATLAB source code and numerical results, and ready visualizations for the exact analytical solutions of generalized Couette flow in a micropolar fluid with couple (moment) stresses. 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. All figures are saved in both PNG (for immediate use) and FIG (for further editing) formats. The computational results are also saved in a MAT file for reproducibility and further analysis. This dataset provides a complete, self-contained resource for researchers studying complex fluids with internal microstructure, serving as a benchmark for numerical simulations and experimental validation in micropolar fluid dynamics.
Files
Steps to reproduce
To reproduce the results, follow these steps: 1. Environment Setup: Ensure MATLAB R2023b (or a compatible version) is installed. No additional toolboxes are required, as the code uses only core MATLAB functions. 2. Run the Main Script: Execute the provided MATLAB script (`couette_flow_publication_results.m`). The script is fully self-contained and begins by defining the problem parameters: the micropolarity parameter range (`s_values = [0.05, 0.1, 0.3, 0.5, 1.0, 2.0]`), Reynolds number (`Re = 100`), Taylor number (`Ta = 15.0`), and the dimensionless coordinates (`Z` and `Y`). 3. Solution Computation: The code analytically solves the fourth-order ODE system for both boundary value problems: - Problem I (vanishing bending moments) yields the classical linear velocity profile. - Problem II (vanishing shear stresses) computes the nonlinear profile using the derived closed-form expression involving hyperbolic functions, for each value of the micropolarity parameter `s`. 4. Data Generation: The script systematically evaluates the solutions across the specified parameter ranges and computes derived quantities, such as the position and magnitude of the velocity maximum, and wall shear stresses. 5. Figure Generation: The code automatically generates five publication-ready figures: - Fig1: Comparison of base velocity profiles `U(Z)` for both problems. - Fig2: Parametric dependence of the velocity maximum's location and value on `s`. - Fig3: Wall shear stresses at both boundaries as a function of `s`. - Fig4: Contour plots of the full 2D velocity field `Vx(Y,Z)` for a representative `s = 0.3`. - Fig5: Direct comparison of the total velocity profiles `Vx(z)` at fixed transverse coordinates (`Y = -1, 0, 1`). 6. Output: All figures are saved in both PNG (for immediate use) and FIG (for further editing) formats. The complete numerical data (coordinate arrays, velocity profiles, parameters) is saved in a single MAT file (`couette_flow_publication_results.mat`) for full reproducibility and post-processing. No user input is required. The execution will produce all figures and data files listed in the repository, allowing for direct verification and extension of the published results.
Institutions
- Samara State Technical University
- Ural'skij federal'nyj universitet imeni pervogo Prezidenta Rossii B N El'cina