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 numerical and experimental investigation of free convection from vertical, isothermal, parallel-walled channels has been undertaken to explore the heat transfer enhancement obtained by adding adiabatic extensions of various sizes and shapes. Investigations were carried out for air (Pr= 0.7) over a wide range of wall heating conditions. In all cases, the adiabatic extensions were able to increase heat transfer. The increase varied from 2.5 at low Ra* to 1.5 at high Ra*. The experimental and numerical results are in excellent agreement. A single correlation accounting for the channel aspect ratio Lh /b , expansion ratio, B/b , modified Rayleigh number, Ra* and heated length ratio, Lh /L is presented.

Heat Transfer Enhancement From a Vertical, Isothermal Channel Generated by the Chimney Effect

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

Experiments and computations are presented to quantify the convective heat transfer and the hydraulic loss that is obtained by forcing water through blocks of graphitic foam (GF) heated from one side. Experiments have been conducted in a small-scale water tunnel instrumented to measure the pressure drop and the temperature rise of water passing through the foam and the base temperature and heat flux into the foam block. The experimental data were then used to calibrate a thermal non-equilibrium finite-volume model to facilitate comparisons between GF and aluminum foam. Comparisons of the pressure drop indicate that both normal and compressed aluminum foams are significantly more permeable than GF. Results of the heat transfer indicate that the maximum possible heat dissipation from a given surface is reached using very thin layers of aluminum foam due to the inability of the foam to entrain heat into its internal structure. In contrast, graphitic foam is able to entrain heat deep into the foam structure due to its high extended surface efficiency and thus much more heat can be transferred from a given surface area. The higher extended surface efficiency is mainly due to the combination of moderate porosity and higher solid-phase conductivity.

Forced Convection Heat Transfer and Hydraulic Losses in Graphitic Foam

Experiments are presented to quantify the convective heat transfer and hydrodynamic loss that is obtained by forcing water through blocks of porous carbon foam (PCF) heated from one side. The experiments were conducted in a small-scale water tunnel instrumented to measure the pressure drop and temperature rise of the water passing through the blocks and the base temperature and heat flux into the foam block. In comparison to similar porosity aluminum foam, the present results indicate that the pressure drop across the porous carbon foam is higher due to the large hydrodynamic loss associated with the cell windows connecting the pores, but the heat transfer performance suggests that there may be a significant advantage to using PCF over aluminum foam for extended surface convection elements in recuperators and electronic cooling devices.

Anthony G. Straatman

Papers

Heat Transfer Enhancement From a Vertical, Isothermal Channel Generated by the Chimney Effect

Modeling Forced Convection in Finned Metal Foam Heat Sinks

Forced Convection Heat Transfer and Hydraulic Losses in Graphitic Foam

Characterization of Porous Carbon Foam as a Material for Compact Recuperators

CFD study of the hydraulic and thermal behavior of spherical-void-phase porous materials