scholarly journals A Monte Carlo Method of Solving Heat Conduction Problems

1980 ◽  
Vol 102 (1) ◽  
pp. 121-125 ◽  
Author(s):  
S. K. Fraley ◽  
T. J. Hoffman ◽  
P. N. Stevens
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Transport Equation ◽  
Heat Conduction Equation ◽  
Analytical Techniques ◽  
Conduction Equation ◽  
Geometric Complexity ◽  
New Approach ◽  
Temperature Distributions

A new approach in the use of Monte Carlo to solve heat conduction problems is developed using a transport equation approximation to the heat conduction equation. A variety of problems is analyzed with this method and their solutions are compared to those obtained with analytical techniques. This Monte Carlo approach appears to be limited to the calculation of temperatures at specific points rather than temperature distributions. The method is applicable to the solution of multimedia problems with no inherent limitations as to the geometric complexity of the problem.

Simulation of Nano-Scale Multi-Fingered PD/SOI MOSFETs Using the Boltzmann Transport Equation

Volume 4 ◽  
2004 ◽  
Author(s):  
Jose´ A. Pascual-Gutie´rrez ◽  
Jayathi Y. Murthy ◽  
Raymond Viskanta ◽  
Rajiv V. Joshi ◽  
Ching-Te K. Chuang
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Transport Equation ◽  
Heat Conduction Equation ◽  
Boltzmann Transport Equation ◽  
Conduction Equation ◽  
Temperature Fields ◽  
Boltzmann Transport ◽  
Nano Scale ◽  
Channel Temperature

This work uses a gray, a semi-gray, and a non-gray model based on the Boltzmann Transport Equation (BTE) in the relaxation time approximation to compute the temperature distribution in a nano-scale multi-finger, PD/SOI nMOSFET with copper interconnects. The BTE models were successfully incorporated in CFD software, Fluent 6.1. The BTE is used in the device layer, whereas in other regions of the device, such as the silicon substrate, buried oxide, gate oxide, poly-gate, and metal interconnects, the Fourier heat conduction equation is employed. The BTE is coupled with the heat conduction equation at the interfaces using the diffuse mismatch model (DMM). Heat dissipation in the channel region of the FET and in the metal lines of the device is specified based on circuit simulations for a clock buffer used in a microprocessor. The computed results for the temperature distribution in the multi-finger NFET using the different approaches are compared with simulations that employ the classical heat conduction equation in the entire domain. The comparisons demonstrate that the broad temperature fields in the transistor are primarily determined by the overall thermal resistances due to the various device structures; channel temperature, however, is determined in large part by sub-continuum effects. The need for direct measurements of channel temperature rather indirect gate temperature measurements is pointed out as well.

scholarly journals FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION

2016 ◽  
Vol 15 (1) ◽  
pp. 96
Author(s):  
E. Iglesias-Rodríguez ◽  
M. E. Cruz ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
R. Rodríguez-Ramos ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Small Parameter ◽  
Heat Conduction Equation ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Conduction Equation ◽  
Small Scale ◽  
Multiple Spatial Scales ◽  
Effective Coefficients ◽  
Reiterated Homogenization

Heterogeneous media with multiple spatial scales are finding increased importance in engineering. An example might be a large scale, otherwise homogeneous medium filled with dispersed small-scale particles that form aggregate structures at an intermediate scale. The objective in this paper is to formulate the strong-form Fourier heat conduction equation for such media using the method of reiterated homogenization. The phases are assumed to have a perfect thermal contact at the interface. The ratio of two successive length scales of the medium is a constant small parameter ε. The method is an up-scaling procedure that writes the temperature field as an asymptotic multiple-scale expansion in powers of the small parameter ε . The technique leads to two pairs of local and homogenized equations, linked by effective coefficients. In this manner the medium behavior at the smallest scales is seen to affect the macroscale behavior, which is the main interest in engineering. To facilitate the physical understanding of the formulation, an analytical solution is obtained for the heat conduction equation in a functionally graded material (FGM). The approach presented here may serve as a basis for future efforts to numerically compute effective properties of heterogeneous media with multiple spatial scales.

An Inverse Problem for the Heat Conduction Equation, III

1982 ◽  
Vol 108 (1) ◽  
pp. 73-78
Author(s):  
Gottfried Anger ◽  
Regine Czerner
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation
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