Transient Convective Flow with Viscous Dissipation in a Horizontal Channel: MATLAB Implementation

This dataset contains a complete MATLAB implementation for simulating transient convective flow with viscous dissipation in a horizontal channel filled with water. The code models the time-dependent development of combined Couette-Poiseuille flow between two parallel plates under the influence of a pressure gradient, wall motion, and differential heating.

The physical model accounts for key phenomena: momentum transfer through viscous stresses, heat conduction, convective energy transport, and internal heat generation due to viscous dissipation (Joule heating). The Boussinesq approximation is employed to include buoyancy effects on pressure distribution. The numerical approach utilizes a Fourier series expansion to solve the unsteady momentum equation analytically, while the energy equation is solved via spectral projection to capture the temperature field evolution.

All thermophysical properties correspond to water at 20°C. The simulation parameters are configured to ensure laminar flow conditions (Re < 2000). The main script calculates velocity, temperature, pressure, shear stress, and dissipation function profiles at multiple time instances, visualizing the transition from initial to steady state.

Primary outputs include a comprehensive six-panel figure summarizing the flow's hydrodynamic and thermal development, plus console output of key dimensionless numbers (Reynolds, Prandtl, Grashof) and characteristic time scales. This code is designed for research and educational purposes in computational fluid dynamics, heat transfer, and applied mathematics, providing a transparent tool for studying non-isothermal viscous flow transients.

The dataset consists of the main MATLAB script and a detailed README file.