Work

Entropy Correctors in Homogenization of Microheterogeneous Rigid Bodies

Year: 2026

Type: article

Abstract: . We propose an effective heat equation for an enhanced heat conduction problem that can account for thermal scale-size effects in miniaturized or nanofabricated metamaterials. The derivation of the proposed enhanced heat conduction problem is based on contributions to the global energy balance in the form of Gurtin’s microforce balance introduced in [M. E. Gurtin, Phys. D, 92 (1996), pp. 178–192] and was first proposed by S. Forest and M. Amestoy [ C. R. Méc., 336 (2008), pp. 347–353]. The resulting effective heat equation retains its classical form with temperature as the macroscopic variable; however, the effective conductivity tensor is constructed using the local entropy and the local gradient of entropy instead of the local temperature.

Source: SIAM Journal on Applied Mathematics

DOI: 10.1137/25m1778420

Author: Grigor Nika

Institution: Karlstad University

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Knowledge Foundation, Svenska Forskningsrådet Formas

Awards: G697468639, G8618756154