Heat Conduction in a Rectangular Tube With Eccentric Hot Spots

2010 ◽  
Author(s):  
Bo Dan ◽  
James F. Geer ◽  
Bahgat G. Sammakia
Keyword(s):  
Heat Conduction ◽  
Hot Spots ◽  
Analytical Study ◽  
Three Dimensional ◽  
Rectangular Domain ◽  
Current Paper ◽  
Dominant Factor ◽  
Rectangular Tube ◽  
Convection Boundary ◽  
Steady State Heat

The current paper presents the results of an analytical study of steady state heat conduction in a rectangular tube with eccentric hot spots on both the top and the bottom surfaces. The rectangular domain is assumed to be adiabatic on the lateral surfaces and a single or multiple eccentric hot spots can be applied on the top and bottom surfaces. Isothermal, heat flux or convection boundary conditions can be applied on the hot spots. Because the hot spots are eccentric, the spreading resistance becomes a dominant factor in heat conduction in the tube. The multiple hot spots, multiple layer and combination problems are also studied in the current paper. The solutions can be applied to the thermal management of three-dimensional stacks of electronic devices, the interconnect layers and the thermoelectric devices.

Heat Conduction in a Rectangular Tube With Eccentric Hot Spots

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Bo Dan ◽  
James F. Geer ◽  
Bahgat G. Sammakia
Keyword(s):  
Heat Conduction ◽  
Hot Spots ◽  
Analytical Study ◽  
Three Dimensional ◽  
Rectangular Domain ◽  
Current Paper ◽  
Dominant Factor ◽  
Rectangular Tube ◽  
Convection Boundary ◽  
Steady State Heat

The current paper presents the results of an analytical study of steady state heat conduction in a rectangular tube with eccentric hot spots on both the top and the bottom surfaces. The rectangular domain is assumed to be adiabatic on the lateral surfaces and a single or multiple eccentric hot spots can be applied on the top and bottom surfaces. Isothermal, heat flux, or convection boundary conditions can be applied on the hot spots. Because the hot spots are eccentric, the spreading resistance becomes a dominant factor in heat conduction in the tube. The multiple hot spots, multiple layers and combination problems are also studied in the current paper. The solutions can be applied to the thermal management of three-dimensional stacks of electronic devices, the interconnect layers and the thermoelectric devices.

Heat Conduction in Three Dimensional Stacked Packages

2005 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Heat Conduction ◽  
Thermal Management ◽  
Heat Generation ◽  
Analytical Study ◽  
Three Dimensional ◽  
The Other ◽  
Heat Generation Rate ◽  
Potential Applications ◽  
Steady State Heat ◽  
Spatially Varying

This paper presents the results of an analytical study of steady state heat conduction in multiple rectangular domains. Any finite number of such domains may be considered in the current study. The thermal conductivity and thickness of these domains may be different. The entire geometry composed of these connected domains is considered as adiabatic on the lateral surfaces and can be subjected to uniform convective cooling at one end. The other end of the geometry may be adiabatic and a specified, spatially varying heat generation rate can be applied in each of the domains. The solutions are found to be in agreement with known solutions for simpler geometries. The analytical solution presented here is very general in that it takes into account the interface resistances between the layers. One application of this analytical study relates to the thermal management of a 3-D stack of devices and interconnect layers. Another possible application is to the study of hotspots in a chip stack with non uniform heat generation. Many other potential applications may also be simulated.

Heat Conduction in Multilayered Rectangular Domains

2007 ◽  
Vol 129 (4) ◽  
pp. 440-451 ◽  
Author(s):  
James Geer ◽  
Anand Desai ◽  
Bahgat Sammakia
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Generation ◽  
Analytical Study ◽  
Three Dimensional ◽  
Thermal Boundary Conditions ◽  
Wide Range ◽  
Potential Applications ◽  
Steady State Heat ◽  
Spatially Varying

This paper presents the results of an analytical study of steady state heat conduction in multiple rectangular domains. Any finite number of domains that are equally sized (in plane) may be considered in the current analysis. The thermal conductivity and thickness of these domains may be different. The entire geometry composed of these connected domains is considered as adiabatic on the lateral surfaces and can be subjected to a wide range of thermal boundary conditions at the top and bottom. For example, the bottom of the stack may be adiabatic, while the top of the stack may be exposed to a uniform heat transfer coefficient. Spatially varying heat generation rates can be applied in each of the domains. The solutions are found to be in agreement with known solutions for simpler geometries. The analytical solution presented here is very general in that it takes into account the interface resistances between the layers. One application of this analytical study relates to the thermal management of three-dimensional stacks of computer devices and interconnect layers. The devices would have spatially nonuniform power dissipation within them, and the interconnect layers would have a significantly lower thermal conductivity than the devices. Interfacial defects, such as delamination or air voids, between the devices and the interconnect layers may be included in the model. Another possible application is to the study of hot spots in a chip stack with nonuniform heat generation. Many other potential applications may also be simulated.

Three-Dimensional, Steady-State Heat Conduction in Cylinders of General Anisotropic-Media

1979 ◽  
Vol 101 (3) ◽  
pp. 548-553 ◽  
Author(s):  
Y. P. Chang ◽  
K. C. Poon
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Fourier Transforms ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Anisotropic Media ◽  
State Heat ◽  
Change Of Variables ◽  
Steady State Heat ◽  
Kummer's Equation

This paper provides the analytical solution of three-dimensional steady-state heat conduction in solid and hollow cylinders of general anisotropic-media. By the use of Fourier transforms and a change of variables the partial differential equation is reduced to Kummer’s equation. Some calculated results for a solid cylinder are shown and discussed. A parameter γ is found to represent the coupling effect of three-dimensional anisotropy. For small values of γ, an approximate solution is recommended. The inequality σ > 0 which was found in an earlier paper is further discussed.

A Numerical Method for Heat Conduction Problems

1974 ◽  
Vol 96 (3) ◽  
pp. 307-312 ◽  
Author(s):  
M. J. Reiser ◽  
F. J. Appl
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Steady State ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Singular Integral ◽  
Integral Method ◽  
Two Dimensional ◽  
Convection Boundary ◽  
Steady State Heat

A singular integral method of numerical analysis for two-dimensional steady-state heat conduction problems with any combination of temperature, gradient, or convection boundary conditions is presented. Excellent agreement with the exact solution is illustrated for an example problem. The method is used to determine the solution for a fin bank with convection.

Experimental Measurements of Temperature Distribution in Three Dimensional Stacked Package

2007 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Experimental Study ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Distribution ◽  
Numerical Model ◽  
Analytical Solution ◽  
Three Dimensional ◽  
Power Input ◽  
Experimental Measurements ◽  
Steady State Heat

This paper presents the results of an experimental study of steady state heat conduction in a three dimensional stack package. The temperatures are measured at different interfaces within the stacked package. Delphi devices are used in the experiment which enables controlled power input and surface temperature of the devices. The experiment is carried out for three different boundary conditions on the package. The power input in varied to study its effects. A numerical model is created to compare to the experimental results. The results are also compared with the analytical solution presented in Desai et al [5] and Geer et al [6]. The results indicate that the experimental, numerical and analytical solutions follow the same trend. The agreement between the experimental and numerical results improves when the lateral losses are taken into account.

Calculation of three-dimensional nearly singular boundary element integrals for steady-state heat conduction

2015 ◽  
Vol 60 ◽  
pp. 137-143 ◽  
Author(s):  
Guizhong Xie ◽  
Liangwen Wang ◽  
Jianming Zhang ◽  
Dehai Zhang ◽  
Hao Li ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Boundary Element ◽  
Three Dimensional ◽  
Singular Boundary ◽  
State Heat ◽  
Steady State Heat
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