In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scatterin...

Purpose The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear nonlinear behaviour. Design/methodology/approach A series runs were conducted a canonical test problem. These used as databases or “learning sets” both networks. second set was the prediction accuracy approaches. Findings results indicate that outperform in...

Effect of a crystalline-amorphous interface on heat conduction has been studied using atomistic simulations of a silicon system. System with amorphous silicon was created using the bond-switching Monte Carlo simulation method and heat conduction near room temperature was studied by molecular dynamics simulations of this system. INTRODUCTION As the sizes of electronic devices decrease an increas...

Starting from the basic equations of solids we have shown one possible construction of the modification method of the law of heat conduction. Based on this method the steps of development can be outlined, the sequence and role of the tasks can be established. As an additional result we managed to highlight some aspects of the cognitive process, which emerge in the course of natural scientific r...

The hyperbolic heat conduction equation (HHCE), which acknowledges the finite speed of heat propagation, is based on microscopic evidence from the kinetic theory and statistical mechanics. However, it was argued that the HHCE could violate the second law of thermodynamics. This paper shows that a HHCE like equation (RHCE) can be derived directly from the theory of relativity, as a direct conseq...

In the heat conduction problems if the heat flux and/or temperature histories at the surface of a solid body are known as functions of time, then the temperature distribution can be found. This is termed as a direct problem. However in many heat transfer situations, the surface heat flux and temperature histories must be determined from transient temperature measurements at one or more interior...

Non-Fourier models of heat conduction have been increasingly considered in the last years in the modeling of microscale heat transfer in engineering and biomedical problems. Models that incorporate time lags in the heat flux and/or the temperature gradient result in heat conduction modeling equations in the form of partial differential equations with delay, while some approximations may yield p...

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