Abstract

This paper deals with radiation’s contribution to thermal insulation. The mechanism by which a stack of absorbers limits radiative heat transfer is examined in detail both for black-body shields and grey-body shields. It shows that radiation energy transfer rates should be much faster than conduction rates. It demonstrates that, for opaque screens, increased reflectivity will dramatically reduce the rate of heat transfer, improving thermal insulation. This simple model is thought to contribute to the understanding of how animal furs, human clothes, rockwool insulators, thermo-protective containers, and many other passive energy-saving devices operate.

© 2014 Optical Society of America

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References

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  1. H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
    [CrossRef]
  2. B.J. Teerink, Hair of West-European Mammals (Cambridge University, 1991).
  3. P. R. Morrison and W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
    [CrossRef]
  4. C. F. Herreid and B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
    [CrossRef] [PubMed]
  5. G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
    [CrossRef]
  6. J. C. McLoughlin, Synapsida: A New Look into the Origin of Mammals (Viking, 1980).
  7. R. J. G. Savage and M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).
  8. P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
    [CrossRef] [PubMed]
  9. C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
    [CrossRef] [PubMed]
  10. C. D. Stahel and S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).
  11. L. B. Davis and R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
    [CrossRef]
  12. G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
    [PubMed]
  13. G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
    [CrossRef] [PubMed]
  14. C. Skowron and M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).
  15. G. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).
  16. K. Stephan and A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
    [CrossRef]
  17. C. M. Soukoulis, Photonic Band Gaps and Localization Nato ASI series B 308(Plenum, 1993).
    [CrossRef]
  18. A. Langendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
    [CrossRef]
  19. R. G. Somes and R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).
  20. S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).
  21. J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
    [CrossRef] [PubMed]
  22. I. M. Weiss and H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
    [CrossRef] [PubMed]
  23. R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
    [CrossRef]
  24. F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
    [CrossRef]
  25. U. Sivert and A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).
  26. T. I. Ward and S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

2012 (1)

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

2010 (1)

I. M. Weiss and H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

2009 (1)

A. Langendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

2003 (1)

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

1999 (1)

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

1996 (1)

R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
[CrossRef]

1993 (1)

R. G. Somes and R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

1991 (1)

G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
[CrossRef]

1988 (2)

G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
[PubMed]

G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
[CrossRef] [PubMed]

1985 (1)

K. Stephan and A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

1982 (1)

C. D. Stahel and S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

1980 (1)

C. Skowron and M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

1967 (1)

C. F. Herreid and B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

1957 (1)

P. R. Morrison and W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

1950 (1)

P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Abney, M.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Bakken, G. S.

G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
[CrossRef]

Bersanelli, M.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Berta, A.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Birkebak, R. C.

L. B. Davis and R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
[CrossRef]

Burger, R. E.

R. G. Somes and R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

Burigana, C.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Butler, R.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Costa, D. P.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Davis, L. B.

L. B. Davis and R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
[CrossRef]

Dawson, C.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Doran, S. M.

T. I. Ward and S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

Forshaw, P.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Fu, R.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Heidi, A.

U. Sivert and A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).

Herreid, C. F.

C. F. Herreid and B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

Hock, R.

P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Hu, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Irving, L.

P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Jeronimidis, G.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Kern, M.

C. Skowron and M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

Kessel, B.

C. F. Herreid and B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

Kinoshita, S.

S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

Kirchner, H. O. K.

I. M. Weiss and H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

Laesecke, A.

K. Stephan and A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

Langendijk, A.

A. Langendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Li, Y.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Lightman, A. P.

G. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).

Liu, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Liwanag, H. E. M.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Long, M. R.

R. J. G. Savage and M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).

Mandolesi, N.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

McLoughlin, J. C.

J. C. McLoughlin, Synapsida: A New Look into the Origin of Mammals (Viking, 1980).

Mennella, A.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Morgante, G.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Morrison, P. R.

P. R. Morrison and W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

Nicol, S. C.

C. D. Stahel and S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

Rice, G.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Rybicki, G.

G. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).

Sandri, M.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Savage, R. J. G.

R. J. G. Savage and M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).

Scholander, P. F.

P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Sivert, U.

U. Sivert and A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).

Skowron, C.

C. Skowron and M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

Somes, R. G.

R. G. Somes and R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

Soukoulis, C. M.

C. M. Soukoulis, Photonic Band Gaps and Localization Nato ASI series B 308(Plenum, 1993).
[CrossRef]

Soulen, R.

R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
[CrossRef]

Stahel, C. D.

C. D. Stahel and S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

Stephan, K.

K. Stephan and A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

Teerink, B.J.

B.J. Teerink, Hair of West-European Mammals (Cambridge University, 1991).

Terenzi, L.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Tietz, W. J.

P. R. Morrison and W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

Valenziano, L.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

van Tiggelen, B.

A. Langendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Villa, F.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Vincent, J. F. V.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Walsberg, G. E.

G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
[PubMed]

G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
[CrossRef] [PubMed]

Walters, V.

P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Wang, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Ward, T. I.

T. I. Ward and S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

Weiss, I. M.

I. M. Weiss and H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

Wiersma, D. S.

A. Langendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Williams, T. M.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Xu, C.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Yoshioka, S.

S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

Yu, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Zi, J.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Auk (1)

C. Skowron and M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

Biol. Bull. (1)

P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Biol. J. Linn. Soc. (1)

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Comp. Biochem. Physiol. (1)

C. F. Herreid and B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

Forma (1)

S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

J. Comp. Physiol. (1)

C. D. Stahel and S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

J. Comp. Physiol. B (1)

G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
[CrossRef] [PubMed]

J. Exp. Biol. (1)

G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
[PubMed]

J. Exp. Zool. A Ecol. Genet. Physiol. (1)

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Figures (6)

Fig. 1
Fig. 1

Warm-blooded animals like mammals and birds have hairs or feathers which serve multiple functions. One of them is camouflage, when the coloration or pattern of coloration matches the background to make the animal less conspicuous. However, a more ancient function must have been thermal insulation. A good example is the polar bear (Ursus maritimus), where the thick white hair clearly needs to serve these functions. Alan D. Wilson, Polar Bear (Sow), Kaktovik, Barter Island, Alaska, with permission.

Fig. 2
Fig. 2

a) A simple model for the “radiative insulator” described in section 3. A hot black body thermostat at temperature Ta faces a cold black body thermostat at temperature Tb. The exchange of energy between these thermostats is only radiative. The insulator is a set of n black or grey sheets interposed between the thermostats. b) Energy exchanges between two neighboring sheets, say sheets i and i + 1, are denoted I i + and I i + 1 , for energy travelling to sheet i + 1 and to sheet i, respectively.

Fig. 3
Fig. 3

a) Distribution of the equilibrium temperatures of 100 black-body sheets, shielding thermostats at 37°C and −40°C. b) Base 10 logarithm of the energy attenuation factor as a function of the number of black-body shielding sheets, for thermostats at 37°C and −40°C. Only radiative energy exchanges are included in the model.

Fig. 4
Fig. 4

a) Distribution of the equilibrium temperatures of 100 grey-body sheets with increasing reflectances: r = 0.0 (black-body result, in blue), 0.2, 0.4, 0.6, 0.8 and 0.99 (magenta), shielding thermostats at 37°C and −40°C. b) Base 10 logarithm of the energy attenuation factor as a function of the number of grey-body shielding sheets, for thermostats at 37°C and −40°C. The shields are assumed opaque to far infrared radiation (t = 0). The upper curve is the black-body shields result and simply repeats the results shown in Fig. 3. The lower ones, from top down, correspond to increasing reflectances: r = 0.2, 0.4, 0.6, 0.8 and 0.99.

Fig. 5
Fig. 5

a) External shape of blue peacock Pavo cristatus feather’s barbules. b) External shape of white peacock Pavo cristatus mut. alba feather’s barbules. The segments, visible on most birds, are here terminated by long appendages, which add the capacity to diffuse light and thermal radiation.

Fig. 6
Fig. 6

Feather’s barb from the train of a white peacock. a) scanning electron microscopy cross-section. The barbs, by contrast to the uniformly solid barbules, are structured by large polyhedral cells. b) Optical microscope view. The white coloration is identified coming from the barb polyhedral cells. Barbules are seen as transparent with diffusing white at their appendages.

Equations (28)

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d W d t = ( K S L ) ( T a T b ) .
K = { 0.0204 W / mK ( 50 ° C ) 0.0243 W / mK ( 0 ° C ) 0.0257 W / mK ( 20 ° C ) 0.0271 W / mK ( 40 ° C ) 0.0285 W / mK ( 60 ° C )
1 S d W d t 37.4 W / m 2 .
d W d t = σ S ( T a 4 T b 4 ) .
1 S d W d t 356.5 W / m 2 .
R 0 = 1 S d W d t = σ ( T a 4 T b 4 ) .
w i = σ T i 4 .
I i + = I i = w i .
I 0 + = σ T a 4 = w a .
I n + 1 = σ T b 4 = w b .
I i + I i + = I i 1 + + I i + 1 .
I i + I i + 1 = I i 1 + I i ,
w i 1 2 w i + w i + 1 = 0
2 w 1 + w 2 = w a
w n 1 2 w n = w b .
η ( n ) = I i + I i + 1 R 0 = I 0 + I 1 R 0 .
I i + = 1 1 r 2 j = 0 i 1 ( t 1 r 2 ) j w i j + r 1 r 2 j = 1 n i ( t 1 r 2 ) j 1 w i + j + ( t 1 r 2 ) i w a + r ( t 1 r 2 ) n i w b
I i = r 1 r 2 j = 1 i 1 ( t 1 r 2 ) j 1 w i j + 1 1 r 2 j = 0 n i ( t 1 r 2 ) j w i + j + r ( t 1 r 2 ) i 1 w a + r ( t 1 r 2 ) n i + 1 w b .
I 0 + = w a
I 1 = j = 1 n ( t 1 r 2 ) j 1 w j + r w a + t ( t 1 r 2 ) n 1 w b
I n + 1 = w b
I n + = j = 1 n ( t 1 r 2 ) j 1 w n + 1 j + r w b + t ( t 1 r 2 ) n 1 w a .
I 0 + = w a
I n + = w n + r w b
I i + = 1 1 r 2 w i + r 1 r 2 w i + 1
I 1 = w 1 + r w a
I n + 1 = w b
I i = r 1 r 2 w i 1 + 1 1 r 2 w i .

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