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This paper presents a multiscale methodology for efficient unsteady conjugate heat transfer simulations. The solid domain is modelled by coupling a global representation of the temperature field, based on the eigenfunctions of the unsteady…

Computational Physics · Physics 2025-07-31 Yann Dreze , Muting Hao , Luca di Mare

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…

Numerical Analysis · Mathematics 2016-12-23 Natalie E. Sheils

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…

Numerical Analysis · Mathematics 2025-03-18 Liang Fang , Xiandong Liu , Lei Zhang

We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well…

Computational Engineering, Finance, and Science · Computer Science 2025-06-27 Y. Navidtehrani , C. Betegón , E. Martínez-Pañeda

In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…

Numerical Analysis · Mathematics 2026-02-23 Sarah Nataj , David C. Del Rey Fernández , David Brown , Rajeev Jaiman

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…

Fluid Dynamics · Physics 2019-10-23 X. Liu , Z. Xie , S. Dong

Frequently, the design of physicochemical processes requires screening of large numbers of alternative designs with complex geometries. These geometries may result in conformal meshes which introduce stability issues, significant…

Computational Physics · Physics 2021-01-19 E. J. Monte , J. Lowman , N. M. Abukhdeir

An uncoupled multi-scale homogenization approach is used to estimate the effective thermal conductivities of plain weave C/C composites with a high degree of porosity. The geometrical complexity of the material system on individual scales…

Materials Science · Physics 2008-07-23 Blanka Tomkova , Michal Sejnoha , Jan Novak , Jan Zeman

The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…

Mathematical Physics · Physics 2026-05-22 Kiprian Berbatov , Pieter D. Boom , Andrew L. Hazel , Andrey P. Jivkov

A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I.…

Applied Physics · Physics 2025-07-10 Gan Fu , Mitrofan Curti , Calina Ciuhu , Elena A. Lomonova

Extended from its electromagnetic counterpart, transformation thermodynamics applied to thermal conduction equations can map a virtual geometry into a physical thermal medium, realizing the manipulation of heat flux with almost arbitrarily…

Classical Physics · Physics 2015-06-19 Yichao Liu , Wei Jiang , Sailing He , Yungui Ma

A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the…

Fluid Dynamics · Physics 2015-09-15 Jian-Jun Shu , I. Pop

Thermal behavior has become a first-order constraint in advanced 2.5D/3D integrated circuits (ICs) and heterogeneous packages. As power densities rise and multiple active dies are vertically integrated, heat removal paths become…

Hardware Architecture · Computer Science 2026-04-07 Baibhari Priya Barua , Md Rahatul Islam Udoy , Ahmedullah Aziz

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

Like any fluid heated from below, the atmosphere is subject to vertical instability which triggers convection. Convection occurs on small time and space scales, which makes it a challenging feature to include in climate models. Usually…

Atmospheric and Oceanic Physics · Physics 2015-06-12 Corentin Herbert , Didier Paillard

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…

Mathematical Physics · Physics 2016-04-11 Bernard Deconinck , Beatrice Pelloni , Natalie Sheils

An innovative and accurate dynamic Compact Thermal Model extraction method is proposed for multi-chip power electronics systems. It accounts for thermal coupling between multiple heat sources. Transient electro-thermal coupling can easily…

General Physics · Physics 2008-01-08 W. Habra , P. Tounsi , F. Madrid , P. Dupuy , C. Barbot , J. -M. Dorkel

Conduction transfer functions (CTF) are commonly used in the building services to quickly estimate hourly conduction heat loads through multilayered walls without resorting to expensive, time-consuming solutions of the heat equation. It is…

Computational Engineering, Finance, and Science · Computer Science 2021-10-26 Khodr Jaber

In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…

Numerical Analysis · Mathematics 2021-08-19 Chao Zhang , Lifeng Wang , Zhijun Shen , Zhiyuan Li , Igor Menshov

The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to…

Computational Physics · Physics 2020-10-19 Ole H. H. Meyer , Karl Yngve Lervåg , Åsmund Ervik
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