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We examine the non-equilibrium radiative heat transfer between a plate and finite cylinders and cones, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional…

Classical Physics · Physics 2015-05-28 Alexander P. McCauley , M. T. Homer Reid , Matthias Krüger , Steven G. Johnson

We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…

Analysis of PDEs · Mathematics 2024-10-01 Michael Hinz , Anna Rozanova-Pierrat , Alexander Teplyaev

We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…

Analysis of PDEs · Mathematics 2024-05-01 Michael Eden , Tom Freudenberg

Nonreciprocal thermophotonics, by breaking Lorentz reciprocity, exceeds current theoretical efficiency limits, unlocking opportunities to energy devices and thermal management. However, energy transfer in current systems is highly…

The heat transfer behavior of convection-driven dynamos in a rotating plane layer between two parallel plates, heated from below and cooled from the top, is investigated. At a fixed rotation rate (Ekman Number, $E=10^{-6}$) and fluid…

Fluid Dynamics · Physics 2022-06-08 Souvik Naskar , Anikesh Pal

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…

Numerical Analysis · Mathematics 2013-07-05 Xiaohui Peng , Katsiaryna Niakhai , Bartosz Protas

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…

Condensed Matter · Physics 2009-10-28 G. Gonzalez de la Cruz , Yu. G. Gurevich

We study a shape optimization problem involving a solid $K\subset\mathbb{R}^n$ that is maintained at constant temperature and is enveloped by a layer of insulating material $\Omega$ which obeys a generalized boundary heat transfer law. We…

Analysis of PDEs · Mathematics 2022-06-22 Dorin Bucur , Mickaël Nahon , Carlo Nitsch , Cristina Trombetti

The heat trace of a planar polygon contains corner terms depending only on the opening angles, while the heat trace of a smooth planar domain contains curvature terms along the boundary. We show that, for curvilinear polygons, these two…

Spectral Theory · Mathematics 2026-05-19 Sam Looi , David Sher

We consider the heat transfer problem associated with a periodic array of extended surfaces (fins) subjected to convection heat transfer with a uniform heat transfer coefficient. Our analysis differs from the classical approach as (i) we…

Classical Physics · Physics 2015-03-18 Theodoros Leontiou , Marios M. Fyrillas

Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and…

In this paper, we study optimal control problems on the internal energy for a system governed by a class of elliptic boundary hemivariational inequalities with a parameter. The system has been originated by a steady-state heat conduction…

Optimization and Control · Mathematics 2021-10-04 Claudia M. Gariboldi , Domingo A. Tarzia

Optimized transmission conditions in domain decomposition methods have been the focus of intensive research efforts over the past decade. Traditionally, transmission conditions are optimized for two subdomain model configurations, and then…

Numerical Analysis · Mathematics 2022-04-22 Victorita Dolean , Martin J. Gander , Alexandros Kyriakis

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…

Analysis of PDEs · Mathematics 2022-05-26 Ian Tobasco

The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…

Mathematical Physics · Physics 2016-01-12 A. G. Ramm

In this work, we investigate a novel approach for the simulation of two-dimensional, brittle, quasi-static fracture problems based on a shape optimization approach. In contrast to the commonly-used phase-field approach, this proposed…

Optimization and Control · Mathematics 2025-07-28 Tim Suchan , Winnifried Wollner , Kathrin Welker

We study a Dirichlet problem for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determined by a diffeomorphism $\phi$. We analyze the maps that assign to the…

Analysis of PDEs · Mathematics 2025-06-27 Matteo Dalla Riva , Paolo Luzzini , Paolo Musolino

We investigate the two-dimensional transport of heat through viscous flow between two parallel rough interfaces with a given fractal geometry. The flow and heat transport equations are solved through direct numerical simulations, and for…

Statistical Mechanics · Physics 2009-11-10 J. S. Andrade , E. A. Henrique , M. P. Almeida , M. H. A. S. Costa

Convection-diffusion of heat transfer is one of the important phenomena in fluid flow and industrial problems. The involved parameters, boundary conditions, and material properties are greatly affecting the same. As such, the uncertainness…

General Mathematics · Mathematics 2022-05-23 Sudipta Priyadarshini , Sukanta Nayak , Paresh Kumar Panigrahi

Thermal properties of a two-layered composite conductor are modified in case the interface is damaged. The present paper deals with nondestructive evaluation of perturbations of interface thermal conductance due to the presence of defects.…

Mathematical Physics · Physics 2026-05-13 Gabriele Inglese , Raffaele Inglese