Related papers: Two optimization problems in thermal insulation
We study several variations of the question of minimum-error discrimination of thermal states. Besides of providing the optimal values for the probability of error, we also characterize the optimal measurements. For the case of a fixed…
We study bi-segment thermal rectifiers whose forward heat fluxes are greater than reverse counterparts. Presently, a shortcoming of thermal rectifiers is that the rectification ratio, namely the forward flux divided by the reverse flux,…
The thermal conductivity of Functionally Graded Materials (FGMs) can be efficiently designed through topology optimization to obtain thermal meta-structures that actively steer the heat flow. Compared to conventional analytical design…
Many efforts have been dedicated to improve the solar steam generation by using a bi-layer structure. In this paper, a two-dimensional mathematical model describing the water evaporation in a bi-layer structure is firstly established and…
This mini-review addresses a bedrock problem for the advance of phononics: the building of feasible and efficient thermal diodes. We revisit investigations in classical and quantum systems. For the classical anharmonic chains of…
We use a gap function in order to compare the torsional performances of different reinforced plates under the action of external forces. Then, we address a shape optimization problem, whose target is to minimize the torsional displacements…
In this paper, we describe ongoing work to investigate the properties of the heat spreader, and its implication on architecture research. In specific, we conduct two experiments to quantify the heat distribution across the surface of a…
We consider two steady-state heat conduction systems called, $S$ and $S_\alpha$, in a multidimensional bounded domain $D$ for the Poisson equation with source energy $g$. In one system, we impose mixed boundary conditions (temperature $b$…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
Unsteady heat transfer in a harmonic chain is analyzed. Two types of thermal perturbations are considered: 1) initial instant temperature perturbation, 2) external heat supply. Closed equations describing the heat propagation are obtained…
Thermal rectification can occur when heat is transferred asymmetrically. We consider in this work, the case of a composite wall with one conductive and radiative layer. Both Rosseland and surface radiation approximations are used for taking…
This paper studies planning problems for a group of heating systems which supply the hot water demand for domestic use in houses. These systems (e.g. gas or electric boilers, heat pumps or microCHPs) use an external energy source to heat up…
A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the deformation gradient and…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
Turbulent convection plays a crucial role in many natural environments, ranging from Earth ocean, mantle and outer core, to various astrophysical systems. For such flows with extremely strong thermal driving, an ultimate scaling was…
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 discuss the initial boundary value problem for a heat equation in a domain surrounded by a layer. The main features of this problem are twofold: on one hand, the layer is thin compared to the scale of the domain, and on the other hand,…
This paper develops a mathematical framework that aims to control the temperature and rotational speed in the activation process of a gas turbine in an optimal way. These controls influence the deformation and the stress in the component…
Refrigerators use a thermodynamic cycle to move thermal energy from a cold reservoir to a hot one. Implementing this operation principle with mesoscopic components has recently emerged as a promising strategy to control heat currents in…
Mimicking vascular systems in living beings, designers have realized microvascular composites to achieve thermal regulation and other functionalities, such as electromagnetic modulation, sensing, and healing. Such material systems avail…