Absorption to reflection transition in selective solar coatings: errata

Kyle D. Olson; Joseph J. Talghader

doi:10.1364/OE.20.026744

Abstract

We correct an equation, calculating the radiating power from a selective solar absorber, which is missing an extra factor of π. We also correct the results of the affected figures.

In section 3 of article [1] we showed two equations for calculating the power being absorbed and emitted from a selective solar absorber. The P_in term was missing a factor of π for integrating over all solid angles. The following equations should replace Eqs. (4) and (5) in the original article.

\begin{matrix} P_{o u t} = \int_{0}^{2 π} \int_{0}^{\frac{π}{2}} (\int_{0}^{λ_{s}} α u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ) \sin (θ) \cos (θ) d θ d φ \\ P_{o u t} = π (\int_{0}^{λ_{s}} α u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ) \end{matrix}

P_{i n} = π C (\int_{0}^{λ_{s}} α u_{λ}^{s o l a r} (T_{s u n}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{s o l a r} (T_{s u n}) d λ)

The missing factor of π also causes the exact peaks of Figs. 3 , 4 , and 5 to shift to slightly lesser wavelengths and higher temperatures. Because of this shift our claim in the abstract should read “With an emissivity of 5%, solar concentration of 10 times the AM1.5 spectrum the optimum transition wavelength is found to be 1.08µm and have a 1230K equilibrium temperature.” The following figures should replace Figs. 3, 4, and 5 in the original article. We would also like to thank Jacob Jonsson, at Lawrence Berkeley National Lab for pointing out our error.

Fig. 3 (a) The ideal thermal equilibrium temperature between a selective absorber and the sun with no concentration (C=1) as a function of transition wavelength. As the emissivity increases notice that the optimum transition wavelength for a certain operating temperature is shifted to shorter wavelengths. AM0 will have a very similar result to this case.

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Fig. 4 Thermal equilibrium temperature as a function of transition wavelength and emissivity for the AM1.5 solar spectrum with no concentration (C=1)

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Fig. 5 Thermal equilibrium temperature as a function of transition wavelength for a selective absorber with an emissivity of 5% under AM1.5 illumination at different concentrations. The optimal transition wavelength is highly dependent on the concentration of incoming radiation.

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References and links

1. K. D. Olson and J. J. Talghader, “Absorption to reflection transition in selective solar coatings,” Opt. Express 20(S4Suppl 4), A554–A559 (2012). [CrossRef] [PubMed]

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Fig. 3 (a) The ideal thermal equilibrium temperature between a selective absorber and the sun with no concentration (C=1) as a function of transition wavelength. As the emissivity increases notice that the optimum transition wavelength for a certain operating temperature is shifted to shorter wavelengths. AM0 will have a very similar result to this case.

View in Article | Download Full Size | PDF

Fig. 4 Thermal equilibrium temperature as a function of transition wavelength and emissivity for the AM1.5 solar spectrum with no concentration (C=1)

View in Article | Download Full Size | PDF

Fig. 5 Thermal equilibrium temperature as a function of transition wavelength for a selective absorber with an emissivity of 5% under AM1.5 illumination at different concentrations. The optimal transition wavelength is highly dependent on the concentration of incoming radiation.

View in Article | Download Full Size | PDF

Equations (2)

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\begin{matrix} P_{o u t} = \int_{0}^{2 π} \int_{0}^{\frac{π}{2}} (\int_{0}^{λ_{s}} α u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ) \sin (θ) \cos (θ) d θ d φ \\ P_{o u t} = π (\int_{0}^{λ_{s}} α u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ) \end{matrix}

P_{i n} = π C (\int_{0}^{λ_{s}} α u_{λ}^{s o l a r} (T_{s u n}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{s o l a r} (T_{s u n}) d λ)

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