A mathematical and computational view of non-stationary thermal transfer

A mathematical and computational view of non-stationary thermal transfer

Paper in proceedings (conference paper)

Computational modelling of non-stationary thermal transfer, coming from the principle of conservation of energy and Fourier constitutive relation, leads to the analysis of initial and boundary value problem for a partial differential equation of parabolic type with unknown temperature where three material characteristics occur typically: thermal conductivity, thermal capacity and thermal transfer coefficient, all dependent on temperature again in general. We shall present how the solution of such problem can be always constructed using the method of discretization in time, e. g. appropriate types of Rothe sequences. For practical evaluations, to avoid infinite-dimensional function spaces, this method is combined with some finite element or similar technique where the optimal balance between i) rapid and robust inexpensive computations and ii) their stability properties related to the choice of time steps belongs to the recent research priorities, with the development stimulated by the progress both in the theory of numerical algorithms and in the computational hardware and software.

Computational modelling of non-stationary thermal transfer, coming from the principle of conservation of energy and Fourier constitutive relation, leads to the analysis of initial and boundary value problem for a partial differential equation of parabolic type with unknown temperature where three material characteristics occur typically: thermal conductivity, thermal capacity and thermal transfer coefficient, all dependent on temperature again in general. We shall present how the solution of such problem can be always constructed using the method of discretization in time, e. g. appropriate types of Rothe sequences. For practical evaluations, to avoid infinite-dimensional function spaces, this method is combined with some finite element or similar technique where the optimal balance between i) rapid and robust inexpensive computations and ii) their stability properties related to the choice of time steps belongs to the recent research priorities, with the development stimulated by the progress both in the theory of numerical algorithms and in the computational hardware and software.

thermal transfer; mathematical and computational modelling

thermal transfer; mathematical and computational modelling

VALA, J.

2026

04.09.2025

American Institute of Physics

Melville (USA)

Thermophysics 2024

AIP conference proceedings

3355

1

United States of America

020016-1

020016-8

8