Work

Variance-driven mean temperature reduction in nonuniformly heated radiative–conductive systems

Year: 2026

Type: article

Abstract: Radiative-conductive systems are intrinsically nonlinear due to the quartic temperature dependence of thermal radiation. Under fixed total heating power, convexity arguments imply that nonuniform temperature distributions radiate more efficiently and therefore exhibit a lower mean temperature than their isothermal counterparts. However, this conclusion remains qualitative, and an explicit quantitative relation between temperature nonuniformity and mean temperature reduction has been lacking. Here we derive a variance-based analytical expression linking the area-averaged temperature to the corresponding isothermal equilibrium temperature in a nonuniformly heated radiative-conductive system. Within a second-order asymptotic expansion about the ambient temperature, we show that the leading reduction in the area-averaged temperature is proportional to the temperature variance. This result transforms the convexity-based inequality into a quantitative statistical relation within the perturbative regime and provides a physically transparent framework for describing nonlinear radiative averaging in thermally heterogeneous systems.

Source: Scientific Reports

DOI: 10.1038/s41598-026-62403-8

Authors: Xiaoli Huang, Juntao Lu, Zihan Zhang, Yongjian Xiong, Jie Fu

Institution: Ningbo University

Language: English

Topic: Thermal Radiation and Cooling Technologies

Subfield: Civil and Structural Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,690

Funder: Natural Science Foundation of Ningbo Municipality