Related papers: An optimization problem in thermal insulation with…
For a heat equation with Robin's boundary conditions which depends on a parameter $\alpha>0$, we prove that its unique weak solution $\rho^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat…
In heat exchangers, an incompressible fluid is heated initially and cooled at the boundary. The goal is to transfer the heat to the boundary as efficiently as possible. In this paper we study a related steady version of this problem where a…
Let $\Omega \subset \mathbb{R}^N$, $N\ge 2$, be an open, connected, bounded set with $C^2$ boundary. In this paper we consider the torsion problem with Robin boundary conditions and we study the symmetry of the solutions when suitable extra…
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…
It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection…
We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject…
Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of…
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…
We consider the dunking problem: a solid body at uniform temperature $T_\text{i}$ is placed in a environment characterized by farfield temperature $T_\infty$ and time-independent spatially uniform heat transfer coefficient; we permit…
We consider a heat conduction problem $S$ with mixed boundary conditions in a $n$-dimensional domain $\Omega$ with regular boundary and a family of problems $S_{\alpha}$ with also mixed boundary conditions in $\Omega$, where $\alpha>0$ is…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
In this paper, we study optimization of the first eigenvalue of the heat equation with spatially nonuniform conductivity on a bounded domain under several constraints for the conductivity. We consider this problem in various boundary…
We introduce an analytical framework for near-field radiative heat transfer in bulk plasmonic and polar media. Considering material dispersion, we derive a closed-form expression for the radiative thermal conductance, which disentangles the…
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…
We present a quantitative estimate for the radially symmetric configuration concerning a Serrin-type overdetermined problem for the torsional rigidity in a bounded domain $\Omega $, when the equation is known on $\Omega \setminus…
By tailoring the geometry of the upper boundary in turbulent Rayleigh-B\'enard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude…
We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled…
This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze the system under two stochastic…