scholarly journals MATHEMATICAL MODELLING IN ELECTRICAL ENGINEERING

2005 ◽  
Vol 10 (3) ◽  
pp. 257-274
Author(s):  
L. Hacia
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Integral Equations ◽  
Current Density ◽  
Radiative Heat ◽  
Electrical Engineering ◽  
Fredholm Integral Equations ◽  
Conduction Theory

Various problems of electrical engineering lead to mathematical models being difference, differential or integral equations. In this paper some mathematical models in certain problems of electrical engineering are presented. Our considerations are restricted to the radiative heat transfer and density theory (Fredholm integral equations). Respecting time in current density problems we get integro‐differential equations or generally Volterra‐Predholm integral equations (heat‐conduction theory). The new numerical method for these equations is analysed. Daugelio elektros inžinerijos problemu sprendimui tenka sudaryti matematinius modelius, kurie dažniausiai būna aprašomi skirtuminemis, diferencialinemis ar integralinemis lygtimis. Šiame darbe apžvelgiami kai kurie modeliai, skirti konkrečiu elektros inžinerijos uždaviniu sprendimui. Apsiribojama šilumos perdavimo proceso su spinduliuote modeliavimu ir tankio pasiskirstymo teorija (Predholmo integralines lygtys) .Ivedus laika, lygtys tankiui tampa integr‐diferencialinemis arba Volteros‐Predholmo integralinemis lygtimis. Darbe pateikiamas ir nagrinejamas naujas skaitinis tokiu lygčiu sprendimo metodas.

Radiative Heat Transfer in Multidimensional Emitting, Absorbing, and Anisotropic Scattering Media—Mathematical Formulation and Numerical Method

1989 ◽  
Vol 111 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Zhiqiang Tan
Keyword(s):  
Heat Transfer ◽  
Integral Equations ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Numerical Technique ◽  
Mathematical Formulation ◽  
Internal Heat ◽  
Anisotropic Scattering ◽  
Scattering Media ◽  
Zonal Method

Thermal radiative transmission in multidimensional emitting, absorbing, and anisotropic scattering media is studied in this paper. In the first part, starting from basic formulae of radiative heat transfer, a set of integral equations for the problem is derived. Then the product-integration method is applied to discretize the integral equations. This method, while analogous to Hottel’s zonal method or Razzaque’s finite element method, requires evaluation of only three or two-dimensional integrals for three-dimensional systems. Finally the formulation and the numerical technique are applied to the problems of thermal radiation in emitting, absorbing, and linearly anisotropic scattering planar and square media with gray surfaces and with or without internal heat generations. Computed results are discussed and compared with available data.

Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles

1996 ◽  
Vol 118 (3) ◽  
pp. 539-545 ◽  
Author(s):  
G. Chen
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Particle Temperature ◽  
Approximate Expression ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Host Medium ◽  
Conduction Theory ◽  
Fourier Heat Conduction ◽  
Thermal Phenomena

Heat transfer around nanometer-scale particles plays an important role in a number of contemporary technologies such as nanofabrication and diagnosis. The prevailing method for modeling thermal phenomena involving nanoparticles is based on the Fourier heat conduction theory. This work questions the applicability of the Fourier heat conduction theory to these cases and answers the question by solving the Boltzmann transport equation. The solution approaches the prediction of the Fourier law when the particle radius is much larger than the heat-carrier mean free path of the host medium. In the opposite limit, however, the heat transfer rate from the particle is significantly smaller, and thus the particle temperature rise is much larger than the prediction of the Fourier conduction theory. The differences are attributed to the nonlocal and nonequilibrium nature of the heat transfer processes around nanoparticles. This work also establishes a criterion to determine the applicability of the Fourier heat conduction theory and constructs a simple approximate expression for calculating the effective thermal conductivity of the host medium around a nanoparticle. Possible experimental evidence is discussed.

Ultrasensitive Bimaterial Cantilevers Optimized for Nanowire Heat Conduction Measurement

2012 ◽  
Author(s):  
Carlo Canetta ◽  
Ning Gu ◽  
Arvind Narayanaswamy
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Silicon Nitride ◽  
Flat Plate ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Near Field ◽  
Aluminum Coating ◽  
Thermal Sensors

We have developed a microcantilever-based technique for measurement of heat conduction through individual nanowires. We fabricated silicon nitride cantilevers with nominal dimensions of length 100 μm, width 2–6 μm, and thickness 130 nm. Cantilever chips are designed with multiple cantilevers spaced at varying distances. With a reflective aluminum coating of optimized thickness, these bimaterial cantilevers can be used as ultrasensitive thermal sensors capable of measuring very small heat flux through a nanostructure fixed between two cantilevers. The ultrasensitive bimaterial cantilevers designed in this work are not limited to heat conduction measurements, but will also be useful for measuring near-field radiative heat transfer between a sphere, attached to the tip of the cantilever, and a flat plate.

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