The Green Function and Its Application to Heat Transfer in a Low Permeability Porous Channel

1999 ◽  
Vol 122 (3) ◽  
pp. 274-278 ◽  
Author(s):  
C. Cui ◽  
X. Y. Huang ◽  
C. Y. Liu
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Green Function ◽  
Porous Channel ◽  
Low Permeability ◽  
Heat Sources ◽  
Point Heat Source ◽  
Analytical Technique ◽  
Discrete Heat Sources ◽  
The Green Function

This paper describes an analytical technique for heat transfer in a low permeability porous channel with initially a point heat source and then multiple discrete sources. The solution of the temperature field for the point source is derived as a Green function, from which the temperature field for other geometrical heat sources can be obtained by using the Green integral. An application of the Green function and Green integral to the porous channel with discrete heat sources is presented. The results are compared with the existing numerical results and good agreements are achieved. [S1043-7398(00)01503-6]

Forced Convection in a Porous Channel With Discrete Heat Sources

2000 ◽  
Vol 123 (2) ◽  
pp. 404-407 ◽  
Author(s):  
C. Cui ◽  
X. Y. Huang ◽  
C. Y. Liu
Keyword(s):  
Heat Transfer ◽  
Reynolds Numbers ◽  
Heat Fluxes ◽  
Experimental Results ◽  
Porous Channel ◽  
Heat Sources ◽  
Nusselt Numbers ◽  
Discrete Heat Sources ◽  
Flow Through ◽  
Good Agreement

An experimental study was conducted on the heat transfer characteristics of flow through a porous channel with discrete heat sources on the upper wall. The temperatures along the heated channel wall were measured with different heat fluxes and the local Nusselt numbers were calculated at the different Reynolds numbers. The temperature distribution of the fluid inside the channel was also measured at several points. The experimental results were compared with that predicted by an analytical model using the Green’s integral over the discrete sources, and a good agreement between the two was obtained. The experimental results confirmed that the heat transfer would be more significant at leading edges of the strip heaters and at higher Reynolds numbers.

Analytical Formulation for the Temperature Profile by Duhamel’s Theorem in Bodies Subjected to an Oscillatory Heat Source

2005 ◽  
Vol 129 (2) ◽  
pp. 236-240 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Heat Source ◽  
Temperature Profile ◽  
Rectangular Domain ◽  
Temperature Fields ◽  
Heat Sources ◽  
Point Heat Source ◽  
Analytical Formulation ◽  
Analytical Technique

An analytical technique is presented for treating heat conduction problems involving a body experiencing oscillating heat flux on its boundary. The boundary heat flux is treated as a combination of many point heat sources, each of which emits heat intermittently based on the motion of the flux. The working function of the intermittent heat source with respect to time is evaluated by using the Fourier series and temperature profile of each point heat source is derived by using the Duhamel’s theorem. Finally, by superposition of the temperature fields over all the point heat sources, the temperature profile due to the original moving heat flux is determined. Prediction results and verification using finite element method are presented for an oscillatory heat flux in a rectangular domain.

Experimental Study of Transient Heat Transfer Process in a Submerged Radial Jet

2006 ◽  
Author(s):  
Maria Cely ◽  
Antonio Bula ◽  
Antonio Ramos
Keyword(s):  
Heat Transfer ◽  
Data Acquisition System ◽  
Heat Transfer Process ◽  
Heat Sources ◽  
Cooling Process ◽  
Plate Temperature ◽  
Discrete Heat Sources ◽  
Stable Temperature ◽  
Set Up ◽  
The Heat Transfer Coefficient

A transient cooling process using a submerged radial water jet is considered. The experiment set up consists of a submerged radial jet exiting from a nozzle located over a thin plate. The plate is made out of aluminum alloy and it has two discrete heat sources located symmetrically at the opposite side of the impinging surface. The temperature variation in the plate is captured using a data acquisition system. The plate is allowed to reach a stable temperature before the radial jet system is generated. The results obtained present the temperature distribution for the plate and the heat transfer coefficient at the fluid-solid interface, for different nozzle heights and initial plate temperature.

Confined Liquid Jet Impingement on a Plate With Discrete Heating Elements

2005 ◽  
Author(s):  
Muhammad M. Rahman ◽  
Santosh K. Mukka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Jet Impingement ◽  
Liquid Jet ◽  
Heat Sources ◽  
Average Heat Transfer Coefficient ◽  
Average Heat ◽  
Discrete Heat Sources ◽  
Solid Region

The primary focus of this paper is the conjugate heat transfer during vertical impingement of a two-dimensional (slot) submerged confined liquid jet using liquid ammonia as the working fluid. Numerical model for the heat transfer process has been developed. The solid region has been modeled along with the fluid region as a conjugate problem. Discrete heat sources have been used to study the overall effect on convective heat transfer. Simulation of discrete heat sources was done by introducing localized heat fluxes at various locations and their magnitudes being varied. Simulations are performed for two different substrate materials namely silicon and stainless steel. The equations solved in the liquid region included the conservation of mass, conservation of momentum, and conservation of energy. In the solid region, only the energy equation, which reduced to the heat conduction equation, had to be solved. The solid-fluid interface temperature showed a strong dependence on several geometric, fluid flow, and heat transfer parameters. The Nusselt number increased with Reynolds number. For a given flow rate, a higher heat transfer coefficient was obtained with smaller slot width and lower impingement height. For a constant Reynolds number, jet impingement height and plate thickness, a wider opening of the slot provided higher average heat transfer coefficient and higher average Nusselt number. A higher average heat transfer coefficient was seen at a smaller thickness, whereas a thicker plate provided a more uniform distribution of heat transfer coefficient. Higher thermal conductivity substrates also provided a more uniform heat distribution.

scholarly journals Transport in Flat Heat Pipes at High Heat Fluxes From Multiple Discrete Sources

2004 ◽  
Vol 126 (3) ◽  
pp. 347-354 ◽  
Author(s):  
Unnikrishnan Vadakkan ◽  
Suresh V. Garimella ◽  
Jayathi Y. Murthy
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Heat Pipe ◽  
Three Dimensional ◽  
Heat Pipes ◽  
Density Change ◽  
Heat Sources ◽  
Discrete Heat Sources ◽  
Energy Equations

A three-dimensional model has been developed to analyze the transient and steady-state performance of flat heat pipes subjected to heating with multiple discrete heat sources. Three-dimensional flow and energy equations are solved in the vapor and liquid regions, along with conduction in the wall. Saturated flow models are used for heat transfer and fluid flow through the wick. In the wick region, the analysis uses an equilibrium model for heat transfer and a Brinkman-Forchheimer extended Darcy model for fluid flow. Averaged properties weighted with the porosity are used for the wick analysis. The state equation is used in the vapor core to relate density change to the operating pressure. The density change due to pressurization of the vapor core is accounted for in the continuity equation. Vapor flow, temperature and hydrodynamic pressure fields are computed at each time step from coupled continuity/momentum and energy equations in the wick and vapor regions. The mass flow rate at the interface is obtained from the application of kinetic theory. Predictions are made for the magnitude of heat flux at which dryout would occur in a flat heat pipe. The input heat flux and the spacing between the discrete heat sources are studied as parameters. The location in the heat pipe at which dryout is initiated is found to be different from that of the maximum temperature. The location where the maximum capillary pressure head is realized also changes during the transient. Axial conduction through the wall and wick are seen to play a significant role in determining the axial temperature variation.

Forced Convection in a Porous Channel With Localized Heat Sources

1994 ◽  
Vol 116 (2) ◽  
pp. 465-472 ◽  
Author(s):  
A. Hadim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Pressure Drop ◽  
Heat Source ◽  
Forced Convection ◽  
Numerical Study ◽  
Porous Channel ◽  
Heat Sources ◽  
Porous Layers ◽  
Channel Configuration

A numerical study is performed to analyze steady laminar forced convection in a channel filled with a fluid-saturated porous medium and containing discrete heat sources on the bottom wall. Hydrodynamic and heat transfer results are reported for two configurations: (1) a fully porous channel, and (2) a partially porous channel, which contains porous layers above the heat sources and is nonporous elsewhere. The flow in the porous medium is modeled using the Brinkman-Forchheimer extended Darcy model. Heat transfer rates and pressure drop are evaluated for wide ranges of Darcy and Reynolds numbers. Detailed results of the evolution of the hydrodynamic and thermal boundary layers are also provided. The results indicate that as the Darcy number decreases, a significant increase in heat transfer is obtained, especially at the leading edge of each heat source. For fixed Reynolds number, the length-averaged Nusselt number reaches an asymptotic value in the Darcian regime. In the partially porous channel, it is found that when the width of the heat source and the spacing between the porous layers are of the same magnitude as the channel height, the heat transfer enhancement is almost the same as in the fully porous channel while the pressure drop is significantly lower. These results suggest that the partially porous channel configuration is a potentially attractive heat transfer augmentation technique for electronic equipment cooling, an end that motivated this study.

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