Related papers: Optimal heat transfer and optimal exit times
A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and non-equilibrium…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
In this paper, we study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures $\theta_0$ and $\theta_1$. This problem was studied by Esposito et al [13,14] where…
In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…
We analyze the time-dependent energy and heat flows in a resonant level coupled to a fermionic continuum. The level is periodically forced with an external power source that supplies energy into the system. Based on the tunneling…
In this work we solve approximately the radiative heat transfer problem in one dimension to perform a comparative analysis of the time averaged performance of the partially transparent radiative windows and radiative coolers. Our physical…
We find steady channel flows that are locally optimal for transferring heat from fixed-temperature walls, under the constraint of a fixed rate of viscous dissipation (enstrophy = $Pe^2$), also the power needed to pump the fluid through the…
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also…
The time needed for a particle to exit a confining domain through a small window, called the narrow escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean…
Convective and radiative cooling are the two principle mechanisms by which the Earth's surface transfers heat into the atmosphere and that shape surface temperature. However, this partitioning is not sufficiently constrained by energy and…
In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the steady problem for the Boltzmann equation in a general bounded domain with diffuse reflection boundary conditions corresponding to…
A thermal analogue of the classical brachistochrone problem, which minimizes the connection time between two equilibrium states of harmonically confined Brownian particles, has recently been solved theoretically. Here we report its…
The dynamic heat transfer between two half-spaces separated by a vacuum gap due to coupling of their surface modes is modelled using the theory that describes the dynamic energy transfer between two coupled harmonic oscillators each…
We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
Producing useful electrical work in consuming chemical energy, the fuel cell have to reject heat to its surrounding. However, as it occurs for any other type of engine, this thermal energy cannot be exchanged in an isothermal way in finite…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…