Variance-driven mean temperature reduction in nonuniformly heated radiative–conductive systems
- 1School of Physical Science and Technology, Ningbo University
- 2Zhenhai High School of Zhejiang
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.
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BibTeX
@article{huang2026variancedriven,
title = {{Variance-driven mean temperature reduction in nonuniformly heated radiative–conductive systems}},
author = {Xiaoli Huang and Juntao Lu and Zihan Zhang and Yongjian Xiong and Jie Fu},
journal = {Scientific Reports},
year = {2026},
month = jul,
doi = {10.1038/s41598-026-62403-8},
url = {https://doi.org/10.1038/s41598-026-62403-8},
note = {CC BY},
}
RIS
TY - JOUR
TI - Variance-driven mean temperature reduction in nonuniformly heated radiative–conductive systems
AU - Xiaoli Huang
AU - Juntao Lu
AU - Zihan Zhang
AU - Yongjian Xiong
AU - Jie Fu
PY - 2026
DA - 2026/07/01
JO - Scientific Reports
DO - 10.1038/s41598-026-62403-8
UR - https://doi.org/10.1038/s41598-026-62403-8
AB - 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.
SN - 2045-2322
ER -