We address the problem of two-dimensional heat conduction in a solid slab embedded with an isothermal, symmetric pipe of general cross section. Similar formulations have applications in continuum mechanics and electricity. The main objective of this work is to develop a Shape Optimization algorithm that will reveal the optimal shapes of the pipe such that the conduction rate is maximized or min...

Shocks are often simulated using the classical molecular dynamics (MD) method in which the electrons are not included explicitly and the interatomic interaction is described by an effective potential. As a result, the fast electronic heat conduction in metals and the coupling between the lattice vibrations and the electronic degrees of freedom can not be represented. Under conditions of steep t...

We study the behavior in time of solutions to several systems equations for porous-thermo-elastic problems when one variables is considered be quasi-static or, other words, whose second derivative can neglected. analyze three different situations using classical Fourier law and also type II or III Green–Naghdi heat conduction models.

The interaction of thermal radiation with conduction and laminar natural convection in a vertical circular pin, situated at participating gas, is numerically investigated. An absorbing and emitting gas is considered, and treated to be a gray participating media. Under the idealizing of gray gas, the Rosselan4 approximation is employed to describe the radiative heat flux in the energy equation. ...

As a paradigm for heat conduction in 1 dimension, we propose a class of models represented by chains of identical cells, each one of which containing an energy storage device called a “tank”. Energy exchange among tanks is mediated by tracer particles, which are injected at characteristic temperatures and rates from heat baths at the two ends of the chain. For stochastic and Hamiltonian models ...

We investigate the well-posedness, the exponential stability, or the lack thereof, of thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial boundary value problems for different boundary conditions deal with systems of partial differential equations in...

A nanofluid is a dilute liquid suspension of particles with at least one critical dimension smaller than ~100 nm. Research works so far suggest that nanofluids offer excellent heat transfer enhancement over conventional base fluids. The enhancement depends on several factors such as particle shape, particle size distribution, volume fraction of nanoparticles, temperature, pH, and thermal conduc...

The work proposes and studies a model for one-dimensional spatially extended systems, which involve nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation, and the general Kuramoto-Sivashinsky equation represent special cases of the proposed model for limited spatial interaction ranges and for infinite propagation ...

This paper presents an exact analytical solution for two-dimensional conductive heat transfer in spherical composite pressure vessels .The vessels are in spherical shape and fibers are winded in circumferential direction. The analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. The heat transfer equ...

An analytical model by Lefèvre and Lallemand (1) that couples a 2D hydrodynamic model for both the liquid and the vapor phases inside a flat micro heat pipe (FMHP) and a 3D thermal model of heat conduction inside the FMHP wall has been modified. It consists of superposing two independent solutions in order to take into account the impact of evaporation or condensation on the equivalent thermal ...