Related papers: An optimal insulation problem
In this paper we study the following problems: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects…
An accurate and comprehensive numerical solution to the parabolic free boundary problem arising from thin film flow with both velocity and temperature distribution at large Reynolds numbers is obtained using a modified Keller box method. A…
I propose a design strategy to enhance the performance of heat engine via absorption of thermal energy from the channel region. The absorption of thermal energy can be actuated by inelastic processes and may be accomplished by an energy…
Graphene was recently proposed as a material for heat removal owing to its extremely high thermal conductivity. We simulated heat propagation in silicon-on-insulator circuits with and without graphene lateral heat spreaders. Numerical…
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
Thermoelectric conductance of an edge mode is investigated. The edge modes of a $2D $ and $3D$ two band model with parabolic dispersion is considered. For the the one dimensional non interacting fermions the thermal conductivity computed…
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…
Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous $\kappa$ and $\rho c_p$ is known…
This paper explores the concept of near-cloaking in the context of time-dependent heat propagation. We show that after the lapse of a certain threshold time instance, the boundary measurements for the homogeneous heat equation are close to…
A low density binary mixture of granular gases is considered within the Boltzmann kinetic theory. One component, the intruders, is taken to be dilute with respect to the other, and thermal segregation of the two species is described for a…
In contrast to established work that use diffuse surface scattering as the mechanism to lower the thermal conductivities, we show that the largest reduction of heat conduction in thin films is achieved via specular scattering. Our results…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
Based on transformation optics theory, we present a new carpet device that can be used to thermally protect a region from the invasion of external heat flux. The designed device is termed 'thermal carpet', which provides considerable…
We consider the heat equation defined by a generalized measure theoretic Laplacian on $[0,1]$. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure…
The method of simulated annealing is adapted to the temperature-emissivity separation (TES) problem. A patch of surface at the bottom of the atmosphere is assumed to be a greybody emitter with spectral emissivity $\epsilon(k)$ describable…
This paper is devoted to the diffusive limit of the nonlinear radiative heat transfer system with curved boundary domain (\textit{two dimensional disk}). The solution constructed in \cite{ghattassi2022convergence} by the leading order…
Tuning interfacial thermal conductance has been a key task for the thermal management of nanoelectronic devices. Here, it is studied how the interfacial thermal conductance is great influenced by modulating the mass distribution of the…
The radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime is investigated based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions prove that…
This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined. The connection that these paradigms…
We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis-Marchioro-Presutti (KMP) model, the finite…