Experimental and Analytical Study of the Combined Geometric Analog Computer

1968 ◽  
Vol 90 (3) ◽  
pp. 291-302 ◽  
Author(s):  
P. Razelos ◽  
H. G. Elrod ◽  
V. Paschkis
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Study ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Fundamental Solutions ◽  
Analog Computer ◽  
Infinite Medium ◽  
Diameter Ratio

A method for obtaining approximate solutions of transient three-dimensional heat-conduction problems has been investigated here analytically and experimentally. The method is based on the well-known principle of analogy between flow of heat and electricity and comprises a continuous resistance medium of resistivity ρe but discrete capacitances, which are introduced into the resistance medium through spherical electrodes. It has been shown that the internal behavior of the system is influenced only by the pitch diameter ratio λ of the spheres. Fundamental solutions for the infinite medium have been obtained and the analysis has shown that the system behaves like one having a resistivity ρe* which can be calculated from the actual resistivity of the liquid and the steady-state Green’s function of the fluid-sphere system. Experiments for the determination of the steady-state and transient Green’s functions are described. The accuracy of the method has also been investigated, and an illustrative example is given.

Simultaneous Determination of Steady Temperatures and Heat Fluxes on Surfaces of Three Dimensional Objects Using FEM

2001 ◽  
Author(s):  
Brian H. Dennis ◽  
George S. Dulikravich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Multiply Connected ◽  
Three Dimensional Objects ◽  
Solid Objects ◽  
System Solution

Abstract A finite element method (FEM) formulation is presented for the prediction of unknown steady boundary conditions in heat conduction on multiply connected three-dimensional solid objects. The present FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-specified on other boundaries. Details of the discretization, linear system solution techniques, regularization, and sample results for 3-D problems are presented.

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

2013 ◽  
Vol 5 (04) ◽  
pp. 510-527 ◽  
Author(s):  
Andreas Karageorghis ◽  
Daniel Lesnic ◽  
Liviu Marin
Keyword(s):  
Three Dimensional ◽  
Nonlinear Least Squares ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Void Detection ◽  
Spherical Parametrization ◽  
Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

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.

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 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.

Weldability Investigation of Temper-Grade Steels

2008 ◽  
Vol 589 ◽  
pp. 31-35
Author(s):  
Gábor Lengyel ◽  
Béla Palotás
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Heat Conduction ◽  
Heat Affected Zone ◽  
Three Dimensional ◽  
Cold Cracking ◽  
Crucial Importance ◽  
Preheat Temperature ◽  
Wide Range

The mechanical properties of temper-grade steels can be modified in a wide range by heat treatment. The principle of heat treatment lies in the good hardenability, so when such steels are welded it is very likely that the heat affected zone is hardened. Considering the fact that in the case of design simplifications it may be needed to weld temper-grade steels, as well therefore it is of crucial importance to eliminate cold cracking. There are many methods available to determine preheat temperature. The applicability of methods for determination of preheat temperature was checked by experimental welding for both two and three dimensional heat conduction. According to our experience the different methods cannot be applied in general namely they are valid only under certain conditions.

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