Couette-Poiseuille Reactive Fluid Flow with Variable Thermophysical Properties

Applied mathematics research on modeling reactive fluid flow with variable viscosity and thermal conductivity using coupled nonlinear PDEs, perturbation methods, and finite difference numerics.

Institution: Federal University of Technology Akure  ·  Year: 2018  ·  View PDF

Overview

This undergraduate thesis investigated Couette-Poiseuille flow — the combined pressure-driven and shear-driven flow between parallel plates — under reactive conditions with variable fluid properties (viscosity, thermal conductivity) that depend on temperature.

Problem Formulation

Classical Couette-Poiseuille flow assumes constant fluid properties, which breaks down when the fluid undergoes exothermic chemical reactions that significantly alter local temperature and, consequently, local viscosity. The thesis formulated a coupled system of nonlinear PDEs governing:

  • Momentum equation: with variable viscosity as a function of temperature
  • Energy equation: including viscous dissipation and Arrhenius-type reaction term
  • Constitutive relations: linking viscosity and thermal conductivity to temperature via exponential (Vogel-type) dependence

Methods

  • Analytical approach: Perturbation expansion for limiting cases (small reaction parameter, large activation energy)
  • Numerical approach: Finite difference discretization with iterative solution of the coupled nonlinear system; convergence analysis and grid refinement
  • Stability analysis: Examination of temperature runaway conditions (thermal explosion criterion)

Significance

The variable-property reactive flow problem is relevant to polymer processing, combustion, and geophysical flows. The mathematical challenge — coupled nonlinear PDEs with temperature-dependent coefficients — develops core skills in applied analysis and scientific computing that underpin computational ML methods.

Connection to research: Rigorous training in numerical analysis, coupled nonlinear systems, and applied PDE theory from this thesis informs how I approach ML research — particularly in areas that involve optimization landscapes, iterative algorithms, and understanding when learned models generalize vs. fail.