Related papers: Computational Shape Derivatives in Heat Conduction…
A density-based topology optimization framework is developed to manipulate characteristic modes of conducting surfaces. The adjoint sensitivity analysis provides an efficient computation of the material gradient utilized by the local…
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…
This paper addresses the problem of determining the optimum shape for a beer glass that minimizes the heat transfer while the liquid is consumed, thereby keeping it cold for as long as possible. The proposed solution avoids the use of…
Heat dissipation is a very critical problem for designing nano-functional devices, including MoS2/Graphene heterojunctions. In this paper we investigate thermal transport in MoS2/Graphene hybrid nanosheets under various heating conditions,…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
We consider a heat transmission problem across an irregular interface -- that is, non-Lipschitz or fractal -- between two media (a hot one and a cold one). The interface is modelled as the support of a d-upper regular measure. We introduce…
With the rapid advance of high-performance computing and electronic technologies, understanding thermal conductivity in materials has become increasingly important. This study presents a novel method: the Site-projected Thermal Conductivity…
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…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is…
We present a model to show that heat propagation away from a local source depends strongly on dimensionality, leading to dramatic localization in low-dimensional systems. An example of such a system is a carbon nanotube array. We further…
Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…
We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…
The co-optimization of geometry and physical parameters remains challenging in transient multiphysics systems involving moving boundaries, nonlinear material response, phase transitions, and competing objectives. Existing methods often…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
In this article we discuss in detail the effective approaches to enhance the thermal conductivity in polymer composites. It is shown from numerical simulations that maximizing interfacial area between filler and polymer enhances very…
This paper addresses the problem of determining the optimum shape for a beer glass that minimizes the heat transfer while the liquid is consumed, thereby keeping it cold for as long as possible. The proposed solution avoids the use of…
This report describes a mathematical model of heat conduction. The differential equation for heat conduction in one dimensional rod has been derived. The explicit finite difference numerical method is used to solve this differential…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…