Related papers: An optimal insulation problem
This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditions. Using the flow approach and Steklov eigenvalue…
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…
We establish a connection between anomalous heat conduction and anomalous diffusion in one dimensional systems. It is shown that if the mean square of the displacement of the particle is $<\Delta x^2> =2Dt^{\alpha} (0<\alpha\le 2)$, then…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…
Technological progress in electronics usually requires their use in increasingly aggressive environments, such as rapid thermal cycling and high power density. Thermal diodes appear as excellent candidates to thermally protect critical…
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed…
We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($\theta\equiv T_c/T_h<1$). The…
In this paper, we will consider an optimal shape problem of heat insulation introduced by Bucur-Buttazzo-Nitsch. We will establish the existence of optimal shapes in the class of $M$-uniform domains. We will also show that balls are stable…
This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($\theta\equiv T_c/T_h<1$). The…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
We study the insulated conductivity problem with closely spaced insulators embedded in a homogeneous matrix where the current-electric field relation is the power law $J = |E|^{p-2}E$. The gradient of solutions may blow up as $\varepsilon$,…
We analyze an optimization problem of the conductivity in a composite material arising in a heat conduction energy storage problem. The model is described by the heat equation that specifies the heat exchange between two types of materials…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
A method for the most efficient removal of heat, through an anisotropic composite, is proposed. It is shown that a rational placement of constituent materials, in the radial and the azimuthal variation, at a given point in the composite…
This paper is concerned with configurations of two-material thermal conductors that minimize the Dirichlet energy for steady-state diffusion equations with nonlinear boundary conditions described mainly by maximal monotone operators. To…
There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for thermoelectric generation of energy, heat…
The nanoparticle packed bed (NPB) as a kind of promising thermal insulation materials has drawn widely concern because of their quite low thermal conductivities (k). In this paper, based on the concept that NPB morphology enable low k, we…