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

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Numerical Heat Transfer And Fluid Flow

Respiratory Physiology—the essentials

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

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Principles Of Heat Transfer In Porous Media

A numerical study has been undertaken to explore the details of forced convection heat transfer in finned aluminum foam heat sinks. Calculations are made using a finite-volume computational fluid dynamics (CFD) code that solves for the flow and heat transfer in conjugate fluid/porous/solid domains. The results indicate that using unfinned blocks of porous aluminum results in low convective heat transfer due to the relatively low effective thermal conductivity of the porous aluminum. The addition of aluminum fins to the heat sink significantly enhances the heat transfer with only a moderate pressure drop penalty. The convective enhancement is maximized when thermal boundary layers between adjacent fins merge together and become nearly developed for much of the length of the heat sink. It is found that the heat transfer enhancement is due to increased heat entrainment into the aluminum foam by conduction. A model for the equivalent conductivity of the finned/foam heat sinks is developed using extended surface theory. This model is used to explain the heat transfer enhancement as an increase in equivalent conductivity of the device. The model is also shown to predict the heat transfer for various heat sink geometries based on a single CFD calculation to find the equivalent conductivity of the device. This model will find utility in characterizing heat sinks and in allowing for quick assessments of the effect of varying heat sink properties.

Modeling Forced Convection in Finned Metal Foam Heat Sinks

Drag Reduction Due to Streamwise Grooves in Turbulent Channel Flow

A numerical model for computing fluid flow and heat transfer, under the assumption of local thermal nonequilibrium, is proposed for use with general unstructured, nonorthogonal grids. This model introduces novel interface conditions which are physically-reasoned and ensure strong coupling between the pressure and velocity fields. Special attention is given to the numerical approximation of diffusive and advective fluxes, pressure forces in the momentum equations, pressure–velocity coupling, and gradient reconstruction at interfaces while maintaining second-order accuracy. The resulting model is very robust and is shown to produce physically reasonable results for high laminar Reynolds numbers on nonorthogonal grids.

Christopher T. DeGroot

Papers

Modeling Forced Convection in Finned Metal Foam Heat Sinks

Drag Reduction Due to Streamwise Grooves in Turbulent Channel Flow

A Finite-Volume Model for Fluid Flow and Nonequilibrium Heat Transfer in Conjugate Fluid-Porous Domains Using General Unstructured Grids

Numerical Results for the Effective Flow and Thermal Properties of Idealized Graphite Foam

Thermal characterization of porous graphitic foam - Convection in impinging flow