Abstract
Radiant cooling technology is a sustainable technology for improving built environment. The past research only studied the thermal performance (e.g., radiant heat flux) based on Kirchhoff’s law while the accuracy and its reasons were seldom analyzed. This article points out that it is necessary to analyze the precondition before applying Kirchhoff’s law directly, because emissivity may not be equal to absorptivity on radiant surfaces. The independence of the emissivity and absorptivity is considered in the new model based on the inapplicability of Kirchhoff’s law. The analysis of sensitivity and relative deviation are performed to investigate the reasons for errors. The sensitivity of emissivity is about 20%—40% more sensitive to radiant heat flux than the absorptivity. Furthermore, the deviation of the heat flux can reach up to 20% when the absorptivity is in the range from 0.4 to 0.9. This deviation is close to the error range of 21.8% estimated in the past. Thence, the discussion based on the theoretical analysis, shows that the errors in past studies were highly caused by the oversimplified preconditions for applying Kirchhoff’s law and the impact of surface absorption was ignored. Additionally, the validation in the past experiments was highly coincidence, since the key independent tests of the absorptivity and radiant heat flux were neglected. Comprehensively, the new model is valuable to provide a reliable solution for future design and analysis of radiant heat exchange when a radiant surface is not locally equilibrium.
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The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- A :
-
The area of a surface (m2)
- c :
-
The specific heat of the surface layer (J/kgK)
- E :
-
The emission energy by a surface itself (W)
- E con :
-
The energy released by the surface layer in a unit time (J/s)
- En :
-
The entransy for a thermal process (JK)
- E str :
-
The energy stored in the surface layer in a unit time (J/s)
- Ex :
-
The exergy for a thermal process (J)
- G :
-
The locally incident radiation heat flux (W)
- h :
-
The heat transfer coefficient [W/ (m2K)]
- J :
-
The total radiosity leaving by combined emission and reflection (W)
- k :
-
The thermal conductivity of the thermal layer (W/mK)
- m :
-
The mass of the surface layer (kg)
- Q :
-
The amount of heat flux (W)
- q :
-
The density of heat flux (W/m2)
- R :
-
The reflection energy of
- S :
-
The length for radiation between two surfaces (m)
- S y ,x :
-
The sensitivity of x to y (%)
- T :
-
The temperature of a radiant surface (K)
- x :
-
The uncertain factor in a sensitivity analysis
- X 1 ,2 :
-
The view factor from surface 1 to 2
- y :
-
The target variable of a sensitivity analysis
- α :
-
The absorptivity for a surface
- δ :
-
The penetration depth for thermal radiation (m)
- ΔT :
-
The temperature difference of the surface layer from the surface to the inner (K)
- Δ x :
-
The variation of the uncertain factor
- Δy :
-
The variation of the target variable
- ε :
-
The emissivity of a surface
- η :
-
An efficiency or improvement rate (%)
- θ :
-
The normal angle of thermal radiation on a surface (º)
- λ :
-
The spectrum of thermal radiation (m)
- σ :
-
The Stefan-Boltzmann constant
- Φ 1 ,2 :
-
The quantity of radiant heat flux from surface 1 to 2 (W)
- 1 :
-
Any surface 1
- 2 :
-
Any surface 2
- 1 - 5 :
-
From the specific surface 1 to 5
- a :
-
Air
- b :
-
Blackbody
- c :
-
Convective heat exchange
- ctl :
-
Control group
- diss :
-
Dissipation
- i :
-
Internal heat source
- obs :
-
Observation group
- p :
-
Cooling panel
- r :
-
Radiant heat exchange
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Fan Zhang and Guoqiang Zhang. The first draft of the manuscript was written by Fan Zhang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Zhang, F., Zhang, G. A novel model concerning the independence of emissivity and absorptivity for enhancing the sustainability of radiant cooling technology. Environ Sci Pollut Res 29, 55675–55690 (2022). https://doi.org/10.1007/s11356-022-19110-4
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DOI: https://doi.org/10.1007/s11356-022-19110-4