Optimal Sizing of Planar Thermal Spreaders

1994 ◽  
Vol 116 (2) ◽  
pp. 296-301 ◽  
Author(s):  
S. Hingorani ◽  
C. J. Fahrner ◽  
D. W. Mackowski ◽  
J. S. Gooding ◽  
R. C. Jaeger
Keyword(s):  
Heat Transfer ◽  
Flux Distribution ◽  
Environmental Temperature ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Two Dimensional ◽  
Heat Flux Distribution ◽  
Optimal Thickness ◽  
Dimensionless Variables ◽  
Biot Numbers

Two-dimensional cylindrical and three-dimensional Cartesian thermal spreaders are studied. One of the surfaces is convectively coupled to a uniform environmental temperature while the opposite surface is subjected to a uniform heat flux distribution over a portion of its boundary. The problem is generalized through the introduction of appropriate dimensionless variables, and analytical solutions for the temperature field are presented for each coordinate system. The solutions depend on the usual geometric and heat transfer groups. It is found that, for a range of realistic Biot numbers and a given ratio of the spreader to heater dimensions, a dimensionless spreader thickness exists for which the temperature of the heater reaches a minimum value. Optimal thickness curves are presented for these ranges.

Coupled Radiative and Conductive Heat Transfer in a Two-Dimensional Rectangular Enclosure With Gray Participating Media Using Finite Elements

1984 ◽  
Vol 106 (3) ◽  
pp. 613-619 ◽  
Author(s):  
M. M. Razzaque ◽  
J. R. Howell ◽  
D. E. Klein
Keyword(s):  
Heat Transfer ◽  
Flux Distribution ◽  
Conductive Heat Transfer ◽  
Conductive Heat ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Heat Flux Distribution ◽  
Distributed Energy ◽  
Participating Media ◽  
Rectangular Enclosure

A numerical solution of the exact equations of coupled radiative/conductive heat transfer and temperature distribution inside a medium, and of the heat flux distribution at all the gray walls of a two-dimensional rectangular enclosure with the medium having uniform absorbing/emitting properties, using the finite element method, is presented. The medium can also have distributed energy sources. Comparison is made to the results of the P-3 approximation method.

Ray-Thermal Sequential Coupled Heat Transfer ANALYSIS of Porous Media Receiver for Solar Dish Collector

2013 ◽  
Vol 442 ◽  
pp. 169-175 ◽  
Author(s):  
Fu Qiang Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Media ◽  
Flux Distribution ◽  
Heat Transfer Analysis ◽  
Uniform Heat Flux ◽  
Heat Flux Distribution ◽  
Uniform Heat ◽  
Distribution Boundary

For the sake of reflecting the concentrated heat flux distribution boundary condition as genuine as possible during simulation, the sequential coupled optical-thermal heat transfer analysis is introduced for porous media receiver. During the sequential coupled numerical analysis, the non-uniform heat flux distribution on the fluid entrance surface of porous media receiver is obtained by Monte-Carlo ray tracing method. Finite element method (FEM) is adopted to solve energy equation using the calculated heat flux distribution as the third boundary condition. The dimensionless temperature distribution comparisons between uniform and non-uniform heat flux distribution boundary conditions, various porosities, and different solar dish concentrator tracking errors are investigated in this research.

Determination of Outside Heating Distribution Using an Inverse Algorithm for an Industry Hydrothermal Autoclave With Three-Dimensional Flows

2004 ◽  
Author(s):  
Hongmin Li ◽  
Minel J. Braun ◽  
G.-X. Wang ◽  
Edward A. Evans
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Heat Conduction ◽  
Flux Distribution ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Heat Flux Distribution ◽  
Inverse Algorithm ◽  
Small Magnitude

Hydrothermal growth is the industry method of preference to obtain high quality single crystals. Due to the high pressure and high temperature growth conditions, growth process is carried out in closed containers. During a growth run, the only flow and heat transfer that control crystal growers have is the outside heating. An inverse algorithm, used to obtain the heating distribution for an autoclave with a two-dimensional flow, is further developed and used to determine the heating distribution for an industry autoclave with three-dimensional flows. A cross-section area average temperature distribution is set as a target. With the three steps, including CFD simulation of the fluid flow, heat conduction in the metal wall, and heat conduction in the insulation layer, the heater heat flux distribution is determined. The distributions appear close to linear from the median height to the top/bottom with small magnitude deviation in the circumferential direction. Linearly distributed heaters, based on the determined heat flux distribution, are then used and heat transfer and fluid flow is numerically simulated with a conjugate model. The achieved temperature agrees well with the targeted one. The distribution and heating rates of linearly distributed heaters can be applied to industry autoclaves.

scholarly journals A numerical study of the Bénard cell

1971 ◽  
Vol 45 (4) ◽  
pp. 805-829 ◽  
Author(s):  
André Cabelli ◽  
G. de Vahl Davis
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Numerical Method ◽  
Liquid Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
Critical Value ◽  
Two Dimensional ◽  
Surface Tension Forces ◽  
Biot Numbers

When a layer of liquid is heated from below at a rate which exceeds a certain critical value, a two- or three-dimensional motion is generated. This motion arises from the action of buoyancy and surface tension forces, the latter being due to variations in the temperature of the liquid surface.The two-dimensional form of the flow has been studied by a numerical method. It consists of a series of rolls, rotating alternately clockwise and anticlockwise, which are shown to be symmetrical about the dividing streamlines. As well as a detailed description of the motion and temperature of the liquid, and of the effects on these characteristics of variations in the Rayleigh, Marangoni, Prandtl and Biot numbers, a study has been made of the conditions under which the motion first starts, the wavelength of the rolls and the rate of heat transfer across the liquid layer.

scholarly journals Effect of buried depth on thermal performance of a vertical U-tube underground heat exchanger

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 327-330
Author(s):  
Li Yang ◽  
Bo Zhang ◽  
Jiří Jaromír Klemeš ◽  
Jie Liu ◽  
Meiyu Song ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Simplified Model ◽  
Two Dimensional ◽  
Construction Sites ◽  
Full Size ◽  
Unit Depth ◽  
Research Show

Abstract Many researchers numerically investigated U-tube underground heat exchanger using a two-dimensional simplified pipe. However, a simplified model results in large errors compared to the data from construction sites. This research is carried out using a three-dimensional full-size model. A model validation is conducted by comparing with experimental data in summer. This article investigates the effects of fluid velocity and buried depth on the heat exchange rate in a vertical U-tube underground heat exchanger based on fluid–structure coupled simulations. Compared with the results at a flow rate of 0.4 m/s, the results of this research show that the heat transfer per buried depth at 1.0 m/s increases by 123.34%. With the increase of the buried depth from 80 to 140 m, the heat transfer per unit depth decreases by 9.72%.

Computational and Experimental Study of Enhanced Laminar Flow Heat Transfer in Three-Dimensional Sinusoidal Wavy-Plate-Fin Channels

2003 ◽  
Author(s):  
Jiehai Zhang ◽  
Arun Muley ◽  
Joseph B. Borghese ◽  
Raj M. Manglik
Keyword(s):  
Heat Transfer ◽  
Flow Behavior ◽  
Computational Simulation ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Staggered Grid ◽  
Uniform Heat Flux ◽  
Complex Flow ◽  
Constant Property ◽  
Fin Efficiency

Enhanced heat transfer characteristics of low Reynolds number airflows in three-dimensional sinusoidal wavy plate-fin channels are investigated. For the computational simulation, steady state, constant property, periodically developed, laminar forced convection is considered with the channel surface at the uniform heat flux condition; the wavy-fin is modeled by its two asymptotic limits of 100% and zero fin efficiency. The governing equations are solved numerically using finite-volume techniques for a non-orthogonal, non-staggered grid. Computational results for velocity and temperature distribution, isothermal Fanning friction factor f and Colburn factor j are presented for airflow rates in the range of 10 ≤ Re ≤ 1500. The numerical results are further compared with experimental data, with excellent agreement, for two different wavy-fin geometries. The influence of fin density on the flow behavior and the enhanced convection heat transfer are highlighted. Depending on the flow rate, a complex flow structure is observed, which is characterized by the generation, spatial growth and dissipation of vortices in the trough region of the wavy channel. The thermal boundary layers on the fin surface are periodically disrupted, resulting in high local heat fluxes. The overall heat transfer performance is improved considerably, compared to the straight channel with the same cross-section, with a relatively smaller increase in the associated pressure drop penalty.

Three-Dimensional Natural Convection From Vertical Heated Plates With Adjoining Cool Surfaces

1992 ◽  
Vol 114 (1) ◽  
pp. 115-120 ◽  
Author(s):  
B. W. Webb ◽  
T. L. Bergman
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Control Volume ◽  
Three Dimensional ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Uniform Heat Flux ◽  
Infrared Thermal Imaging ◽  
Transfer Rates ◽  
Thermal Boundary Conditions

Natural convection in an enclosure with a uniform heat flux on two vertical surfaces and constant temperature at the adjoining walls has been investigated both experimentally and theoretically. The thermal boundary conditions and enclosure geometry render the buoyancy-induced flow and heat transfer inherently three dimensional. The experimental measurements include temperature distributions of the isoflux walls obtained using an infrared thermal imaging technique, while the three-dimensional equations governing conservation of mass, momentum, and energy were solved using a control volume-based finite difference scheme. Measurements and predictions are in good agreement and the model predictions reveal strongly three-dimensional flow in the enclosure, as well as high local heat transfer rates at the edges of the isoflux wall. Predicted average heat transfer rates were correlated over a range of the relevant dimensionless parameters.

Research on Heat Flux Distribution in Deep Grinding

2008 ◽  
Author(s):  
D. H. Zhu ◽  
B. Z. Li ◽  
J. G. Yang
Keyword(s):  
Heat Flux ◽  
Flux Distribution ◽  
Theoretical Expression ◽  
Uniform Heat Flux ◽  
Heat Transfer Mechanism ◽  
Heat Flux Distribution ◽  
Workpiece Surface ◽  
Quadratic Curve ◽  
Flux Model ◽  
Heat Flux Model

This paper studies the heat transfer mechanism in deep grinding process, especially the heat flux to the workpiece. On the basis of triangle moving heat source, a quadratic curve heat flux model in the grinding zone was developed to determine the heat flux distribution and to estimate the surface temperature of workpiece. From the calculated theoretical expression of heat flux to the workpiece, the quadratic curve heat flux can be understood as the superposition of square law heat flux, triangular heat flux and uniform heat flux in the grinding zone. Then four heat flux models using the determined amount of heat flux were applied to estimate the workpiece surface temperatures which were compared with that measured by the embedded thermocouple. It has been found that the quadratic curve heat flux distribution seems to give the best match with measured and theoretical temperature, although square law heat flux model is good enough to predict the temperature.

scholarly journals Thermal analysis in thin-film fluid regions of rectangular microgroove

2018 ◽  
Vol 22 (2) ◽  
pp. 899-897
Author(s):  
Xiaohong Gui ◽  
Xiange Song ◽  
Baisheng Nie
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Heat Flux ◽  
Contact Angle ◽  
Film Thickness ◽  
Flux Distribution ◽  
Total Heat ◽  
Heat Flux Distribution ◽  
Total Heat Transfer ◽  
Thin Film Thickness

The effects of contact angle and superheat on thin-film thickness and heat flux distribution occurring in a rectangle microgroove are numerically simulated. Accordingly, physical, and mathematical models are built in detail. Numerical results indicate that meniscus radius and thin-film thickness increase with the improvement of contact angle. The heat flux distribution in the thin-film region increases non-linearly as the contact angle decreases. The total heat transfer through the thin-film region increases with the improvement of superheat, and decreases as the contact angle increases. When the contact angle is equal to zero, the heat transfer in the thin-film region accounts for more than 80% of the total heat transfer. Intensive evaporation in the thin-film region plays a key role in heat transfer for the rectangle capillary microgroove. The liquid with higher wetting performance is more capable of playing the advantages of higher intensity heat transfer in thin- film region. The current investigation will result in a better understanding of thin- -film evaporation and its effect on the effective thermal conductivity in the rectangle microgroove.

scholarly journals Transient Heat Transfer in Rotating Cylinder - Thermography Measurement to Analyse Intense Heat Flux Distribution

2008 ◽  
Author(s):  
J.C. Batsale ◽  
J.P. Lasserre ◽  
M. Varenne-Pellegrini ◽  
V. Desormiere ◽  
L. Authesserre ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flux Distribution ◽  
Rotating Cylinder ◽  
Transient Heat Transfer ◽  
Heat Flux Distribution ◽  
Intense Heat
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