Fourier's heat conduction equation: History, influence, and connections

Reviews of Geophysics

Volumn 37, Issue 1, 1999, Pages 151-172

  Narasimhan, T N ^a  

^a Lawrence Berkeley National Laboratory   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT TRANSFER; THERMODYNAMICS;

HEAT FLOW; THERMAL CONDUCTIVITY; THERMODYNAMICS;

EID: 0032966943     PISSN: 87551209     EISSN: None     Source Type: Journal    
DOI: 10.1029/1998RG900006     Document Type: Article

References (63)

1. Anderson, H. L., and E. Fermi, Production and absorption of slow neutrons by carbon, Rep. 136, U.S. At. Energy Comm., Washington, D. C., 1940.
2. Archibald, T., Tension and potential: From Ohm to Kirchhoff, Centaurus, 31, 141-163, 1988.
3. Bachelier, E., Théorie de la spéculation, in Ann. de l'Ecole Normale Supérieure, vol. 3, Gauthier-Villars, Paris, 1900. (English translation, in The Random Character of Stock Market Prices, edited by P. H. Cootner, pp. 17-78, MIT Press, Cambridge, Mass., 1964. )
4. Bachelier, E., Théorie de la spéculation, in Ann. de l'Ecole Normale Supérieure, vol. 3, Gauthier-Villars, Paris, 1900. (English translation, in The Random Character of Stock Market Prices, edited by P. H. Cootner, pp. 17-78, MIT Press, Cambridge, Mass., 1964. )
5. Barr, L. W., The origin of quantitative diffusion measurements in solids: A centenary view, in Defects and Diffusion Forum, vols. 143-147, pp. 3-10, Trans Tech, Zürich, Switzerland, 1997.
6. Berthollet, C. L., Essai de Statique Chimique, F. Didot, Paris, 1803.
7. Biot, J. B., Mémoire sur la chaleur, Bibl. Br. Sci. Arts, 27, 310-329, 1804.
8. Buckingham, E., Contributions to our knowledge of the aeration of soils, Bull. 25, 50 pp., U.S. Dep. of Agric., Washington, D. C., 1904.
9. Buckingham, E., Studies on the movement of soil moisture, Bull. 38, Bureau of Soils, U.S. Dep. of Agric., 61 pp., Washington, D. C., 1907.
10. Bullard, E. C., A. E. Maxwell, and R. Revelle, Heat flow through the deep sea floor, Adv. Geophys., 3, 153-181, 1956.
11. Carslaw, H. S., Introduction to Mathematical Theory of Conduction of Heat in Solids, 2nd ed., Macmillan, New York, 1945.
12. Darcy, H., Détermination des lois d'écoulement de l'eau à travers le sable, in Les Fontaines Publiques de la Ville de Dijon, pp. 590-594, Victor Dalmont, Paris, 1856.
13. Dupuit, J. J., Etudes Théoriques et Pratiques sur le Mouvement des Eaux Dans les Canaux Découverts et à Travers les Terrains Perméables, 2nd ed., Dunot, Paris, 1863.
14. Dutrochet, R. J. H., New observations on endosmosis and exosmosis, and on the cause of this dual phenomenon, Ann. Chim. Phys., 35, 393-400, 1827.
15. Edgeworth, F. Y., The law of error, Philos. Mag., Fifth Ser., 16, 300-309, 1883.
16. Einstein, A., Über die von der molekularkinetischen Flüssigkeiten suspendierten Teilchen, Ann. Phys., 17, 549-560, 1905. (English translation, in Investigations on the Theory of Brownian Movement by Albert Einstein, edited with notes by R. Fürth, pp. 1-35, Methuen, London, 1926.)
17. Einstein, A., Über die von der molekularkinetischen Flüssigkeiten suspendierten Teilchen, Ann. Phys., 17, 549-560, 1905. (English translation, in Investigations on the Theory of Brownian Movement by Albert Einstein, edited with notes by R. Fürth, pp. 1-35, Methuen, London, 1926.)
18. Fermi, E., Sul moto dei neutroni nelle sostanze idrogenate, Ric. Sci., 7(2), 13-52, 1936.
19. Fick, A., Ueber diffusion, Poggendorffs Ann. Phys. Chem., 59-86, 1855a.
20. Fick, A., On liquid diffusion, Philos. Mag. J. Sci., 10, 31-39, 1855b.
21. Forchheimer, D. H., Über die Ergiebigkeit von Brunnen-Anlagen und Sickerschlitzen, Z. Architekt. Ing.-Ver., Hannover, 32(7), 539-564, 1886.
22. Fourier, J. B. J., Théorie Analytique de la Chaleur, F. Didot, Paris, 1822.
23. Gardner, W., O. W. Israelsen, N. E. Edlefsen, and H. Clyde, The capillary potential function and its relation to irrigation practice (abstract), Phys. Rev. Ser. II, 20, 199, 1922.
24. Gillispie, C. C. (Ed. in Chief), Dictionary of Scientific Biography, Scribner, New York, 1981.
25. Graham, T. H., On the law of diffusion of gases, Philos. Mag. J. Sci., 2, 175-191, 269-276, 351-358, 1833.
26. Graham, T. H., On the diffusion of liquids, Philos. Trans. R. Soc. London, Part I, 1-46, 1850.
27. Grattan-Guinness, I., and J. R. Ravetz, Joseph Fourier, 1768-1830, 516 pp., MIT Press, Cambridge, Mass., 1972.
28. Green, G., An essay on the application of mathematical analysis to the theories of Electricity and Magnetism, Published by subscription at Nottingham, 1828.
29. Guerlac, H., English Translation and Notes of Memoire on Heat of Lavoisier and Laplace, Neale Watson Academic, New York, 1982.
30. Hagen, G., The flow of water in narrow cylindrical tubes, Poggendorffs Ann. Phys. Chem., 46, 423, 1839.
31. Hallam, A., Great Geological Controversies, Oxford Univ. Press, 1983.
32. Herivel, J., Joseph Fourier, The Man and the Physicist, Clarendon, Oxford, England, 1975.
33. Kirchhoff, G. R., Ueber eine Ableitung der Ohm'schen Gesetze, nach welche sich an die Theorie der Elecktrostatic anschliesst, Ann. Phys., 78, 1849.
34. Lambert, J. H., Pyrométrie, Haude und Spener, Berlin, 1779.
35. Langevin, P., Sur la théorie du movement Brownien, C. R. Acad. Sci. Paris, 146, 530-533, 1908.
36. Laplace, P. S., Memoire sur la théorie de l'annaeau de Saturne, Mem. Acad. R. Sci. Paris, 1787/1789, 249-267, 1789.
37. Lavoisier, M., and P. S. Laplace, Mémoire sur la Chaleur, paper presented at Académie Royale des Sciences, Paris, June 28, 1783. (English translation, H. Guerlac, Neale Watson Academic, New York, 1982.)
38. Lavoisier, M., and P. S. Laplace, Mémoire sur la Chaleur, paper presented at Académie Royale des Sciences, Paris, June 28, 1783. (English translation, H. Guerlac, Neale Watson Academic, New York, 1982.)
39. Maxwell, J. C., On the dynamical theory of gases, Philos. Trans. R. Soc. London, 157, 49-88, 1867.
40. Maxwell, J. C., Scientific worthies, I. Faraday, Nature, 8, 397-399, 1873.
41. Maxwell, J. C., Treatise on Electricity and Magnetism, vol. 1, 2nd ed., Oxford at the Clarendon Press, 1881.
42. Maxwell, J. C., An Elementary Treatise on Electricity, 2nd ed., Oxford at the Clarendon Press, London, 1888.
43. McKenzie, D. P., Some remarks on heat flow and gravity anomalies, J. Geophys. Res., 72(24), 6261-6273, 1967.
44. Middleton, W. E. K., A History of the Thermometer and Its Use in Meterology, Johns Hopkins Press, Baltimore, Md., 1966.
45. Nernst, W. H., Zur kinetik der in Lösung befindlichen Körper, Z. Phys. Chem., 2, 613-622, 634-637, 1888.
46. Nollet, J. A., Investigations on the causes for the ebullition of liquids, in Histoire de l'Académie Royale des Sciences, Paris, pp. 57-104, 1752.
47. Ohm, G. S., Die galvanische Kette, mathematisch Bearbeitet, T. H. Riemann, Berlin, 1827. (English translation, W. Francis, The Galvanic Circuit Investigated Mathematically, 269 pp., Van Nostrand, New York, 1891.)
48. Ohm, G. S., Die galvanische Kette, mathematisch Bearbeitet, T. H. Riemann, Berlin, 1827. (English translation, W. Francis, The Galvanic Circuit Investigated Mathematically, 269 pp., Van Nostrand, New York, 1891.)
49. Pearson, K., The problem of the random walk, Nature, 72, 294, 342, 1905.
50. Pfeffer, W., Osmotische Untersuchungen, Studien zur Zellmechanik, W. Engelmann, Leipzig, Germany, 1877. (English translation, G. R. Kepner and E. J. Stadelmann, Van Nostrand Reinhold, New York, 1940.)
51. Pfeffer, W., Osmotische Untersuchungen, Studien zur Zellmechanik, W. Engelmann, Leipzig, Germany, 1877. (English translation, G. R. Kepner and E. J. Stadelmann, Van Nostrand Reinhold, New York, 1940.)
52. Poiseuille, J. L. M., Recherches experimentales sur le mouvement des liquides dans les tubes de très petits diamètres, Mem. Présentés Divers Savants Acad. R. Sci. Inst. France, 9, 1846.
53. (English translation, W. H. Herschel, Rheol. Mem., 1(1), 1940.)
54. Rayleigh, Lord (J. W. Strutt), On the resultant of a large number of vibrations of the same pitch and of arbitrary phase, Philos. Mag., 10, 73-78, 1880.
55. Rayleigh, Lord (J. W. Strutt), The Theory of Sound, vol. 1, 2nd ed., Macmillan, London, 1894.
56. Richards, L. A., Capillary conduction of liquids through porous mediums, Physics, 1, 318-333, 1931.
57. Roberts-Austen, W. C., On the diffusion of metals, Philos. Trans. R. Soc. London, 187, 383-413, 1896.
58. Samuelson, P. A., Rational theory of Warrant pricing, Ind. Manage. Rev., 6(spring), 13-31, 1965.
59. Stigler, S. M., Francis Ysidro Edgeworth, statistician, Proc. R. Stat. Soc., A, part 3, 287-322, 1978.
60. Taylor, G., Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London, Ser. A., 219, 186-203, 1953.
61. Terzaghi, K., Die Theorie der hydrodynamischen Spannungserscheinungen und ihr erdbautechnisches Anwendungsgebiet, in Proceedings of First International Conference on Applied Mechanics, edited by C. B. Bienzeno and J. M. Burgers, pp. 288-294, J. Waltman Jr., Delft, Netherlands, 1925.
62. Thomson, W., On the uniform motion of heat in homogeneous solid bodies and its connection with the mathematical theory of electricity, Cambridge Math. J., 3, 71-84, 1842.
63. van't Hoff, J. H., Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen, Z. Phys. Chem., 1, 481-493, 1887.