The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

The flow of homogeneous fluids through porous media: analogies with other physical problems

Respiratory Physiology—the essentials

A review of the composite phase change materials: Fabrication, characterization, mathematical modeling and application to performance enhancement

Entropy Generation Minimization

A mathematical and numerical model for the treatment of conjugate fluid flow and heat transfer problems in domains containing pure fluid, porous, and pure solid regions is presented. The model is general and physically reasoned, and allows for local thermal nonequilibrium in the porous region. The model is developed for implementation on a simple collocated finite-volume grid. Special attention is given to the matching of the interfacial heat flux, the approximation of advected variables at the interface between pure fluid and porous regions, the pressure–velocity coupling at such an interface, and the estimation of pressure values at the interface.

A Nonequilibrium Finite-Volume Model for Conjugate Fluid/Porous/Solid Domains

A unit-cube geometry model is proposed to characterize the internal structure of porous carbon foam. The unit-cube model is based on interconnected sphere-centered cubes, where the interconnected spheres represent the fluid or void phase. The unit-cube model is used to derive all of the geometric parameters required to calculate the heat transfer and flow through the porous foam. An expression for the effective thermal conductivity is derived based on the unit-cube geometry. Validations show that the conductivity model gives excellent predictions of the effective conductivity as a function of porosity. When combined with existing expressions for the pore-level Nusselt number, the proposed model also yields reasonable predictions of the internal convective heat transfer, but estimates could be improved if a Nusselt number expression for a spherical void phase material were available. Estimates of the fluid pressure drop are shown to be well-described using the Darcy-Forchhiemer law, however, further exploration is required to understand how the permeability and Forchhiemer coefficients vary as a function of porosity and pore diameter.

A Unit Cube-Based Model for Heat Transfer and Fluid Flow in Porous Carbon Foam

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.

Anthony G. Straatman

Papers

A Nonequilibrium Finite-Volume Model for Conjugate Fluid/Porous/Solid Domains

A Unit Cube-Based Model for Heat Transfer and Fluid Flow in Porous Carbon Foam

Two-equation Turbulence Modeling of Pulsatile Flow in a Stenosed Tube

Carbon-foam finned tubes in air¿water heat exchangers

Thermal characterization of porous carbon foam—convection in parallel flow