MATLAB code for the exact solution of viscous dissipative Oberbeck–Boussinesq equations: Ostroumov–Birikh flow generalization

This repository contains a complete MATLAB software package for computing and visualizing an exact analytical solution to the Oberbeck-Boussinesq equations for viscous, incompressible fluid flow. The solution generalizes the classical Ostroumov-Birikh type flow by fully incorporating the effects of viscous dissipation (via the Rayleigh dissipation function) and an external pressure gradient.

The core achievement of this code is the calculation of a three-dimensional temperature field generated solely by viscous heating, even under isothermal boundary conditions and in the absence of external temperature gradients. The velocity field is linear in the transverse coordinate, while the induced temperature field has a quadratic structure.

Key functionalities of the software include:

Calculation of steady-state velocity and temperature fields based on user-defined physical, geometrical, and boundary parameters.

Support for custom fluid properties (viscosity, thermal diffusivity, heat capacity).

Automatic derivation of all integration constants from the specified boundary conditions.

Comprehensive visualization: profiles of velocity components and temperature modes, 2D contour plots, and 3D surface plots of the temperature distribution across the fluid layer.

Built-in verification of boundary condition satisfaction and calculation of integral flow characteristics (maximum/average temperature, dissipation power).

The package serves as a valuable tool for validating CFD solvers, analyzing thermal effects in microfluidic and shear flows, and for educational purposes in advanced fluid dynamics and heat transfer courses.