The College of Science, Department of Mathematics, discussed a seminar entitled Rayleigh–Bénard Convection: Stability Analysis in Newtonian, Viscoelastic, and Porous Media Flows for postgraduate student Azhar Y. Abd Alhussein. This seminar provides a structured overview of mathematical fluid dynamics, commencing with Bénard's identification of regular hexagonal convection cells in a fluid layer heated from below. The Rayleigh number governs the initiation of thermal convection, and the Boussinesq approximation and Rayleigh's linear stability theory are presented. For Newtonian fluids, the Navier-Stokes equations are described; for non-Newtonian viscoelastic fluids, the Kelvin-Voigt model is introduced, where an elastic memory term raises the most important Rayleigh number, signifying flow stabilization. Darcy's law, the Brinkman equation, and their limiting instances explain flow through porous media.
