Viscous Fluid Flow
Graduate coursework exploring analytical and computational approaches to laminar viscous flows, boundary-layer theory, and Stokes-flow approximations.
Flow Classification and Dimensional Analysis
This introductory assignment reinforced fundamental distinctions between inviscid and viscous regimes, using scaling arguments and non-dimensionalization to identify dominant forces across Reynolds-number ranges. It emphasized how viscous terms become significant in the near-wall region and provided a foundation for interpreting later laminar-flow analyses.
Plane Poiseuille and Couette Flow
Analytical derivation and comparison of steady incompressible flow between parallel plates, including both pressure-driven (Poiseuille) and shear-driven (Couette) configurations. Solutions were obtained from simplified Navier–Stokes equations under fully developed assumptions, and validated using MATLAB plotting of velocity profiles and shear stresses. The analysis illustrated how velocity distributions evolve with channel aspect ratio and wall motion.
Boundary Layer on a Flat Plate
Focused on deriving and numerically evaluating the Blasius boundary-layer solution. The study demonstrated how streamwise velocity gradients and wall shear stress vary with Reynolds number, highlighting viscous diffusion’s role in momentum transfer. MATLAB-based discretization was employed to approximate the similarity ODE and visualize boundary-layer growth.
Creeping Flow around a Sphere
Examined Stokes flow at very low Reynolds numbers using the streamfunction–vorticity formulation in spherical coordinates. The derivation led to the biharmonic streamfunction equation \(E^4 \psi = 0\), with analytical solutions obtained through separation of variables and application of no-slip and far-field conditions. Velocity components and pressure distribution were recovered to quantify drag at \(Re \ll 1\).
Final Project — CPU Heat Sink CFD Analysis
A collaborative project applying the Navier–Stokes and energy equations to model forced convection in a plate-fin CPU heat sink using ANSYS Fluent. The study explored how the Nusselt–Reynolds number correlation varies across laminar flow regimes (\(Re = 170–800\)), verifying accuracy against flat-plate theory before extending to complex 3D geometries. Results established a geometry-specific power-law relation \(Nu = C Re^a\) for predicting thermal performance, linking theoretical viscous-flow principles with real-world thermal management.