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Referencias:

• Dusinberre, G.M., (1961) Heat Transfer Calculations by Finite-Difference, , Scranton: International Textbook
• Patankar, S.V., (1980) Numerical Heat Transfer and Fluid Flow, , New York: McGraw-Hill
• Celnikier, L.M., (1980) Am. J. Phys, 48 (3), p. 211
• Milne, W.E., (1957) Numerical Analysis, , New York: McGraw-Hill
• Fourier, J., (1822) Thiorie Analitique De La Chaleur, 4, p. 669. , Fourier used this equation as a fundamental equation in this analytic theory of heat. See, (Paris) (comprising some of his papers since 1807), English translation by Freeman, Cambridge, 1878. However, this equation was introduced by Biot. See BIOT, J. B., 1804, Bibliothéque Britannique 27, 310 and BIOT, J. B., 1816, Traité de Physique, Paris
• Thompson, W., Heat (1880) Encyclopaedia Britannica, 11. , (Lord Kelvin), 9th ed, §82
• Thompson, W., (1884) Mathematical and Physical Papers, 2, p. 41. , (Lord Kelvin), (Cambridge: University Press), Article
• Dusinberre, G.M., (1945) Trans. Am. Soc. Mech. Engrs, 67, p. 703
• Powers, D.L., (1973) Boundary Value Problems, p. 199. , second editionNew York: Academic Press
• Jackob, M., (1962) Heat Transfer, , 8th edition (New York: Wiley), equation (18-15)
• The value B = 2/3 simplifies the algorithm. If we choose B≠2/3, the operation giving the next value of the temperature of a box is not a simple average but is given by equation (8) T(xi)+∆T(xi)=(1-B)T(xi)+B [T(xi-1)+T(xi+1)]/2 It is interesting to note that a value 0<B(Formula Presented)2/3 gives more weight to the temperature of the ith box compared to the temperatures of the [(i – l)th and (i + l)th boxes; one expects this to occur in the case of very small time intervals (a limiting case is B = 0, i.e. ∆T(xi) = 0, which corresponds to ∆t = 0). On the contrary, B(Formula Presented)l would generate oscillations and other undesirable behaviours, corresponding to a choice of ∆t much greater than the characteristic time of the process. The case B= 1 is misleading since, in such a case, the temperature of a box is independent of its previous value; If we are interested just in the steady state, it is not too important if somebody introduces a mistake in the calculation; the method is self-correcting and gives the right solution if subsequently we continue without mistakes for a sufficient number of steps. Errors are not important provided we do not repeat them. Practice with pupils indicates that errors are ordinarily not very large and do not change the thermal evolution very much. Thus, it does not seem worth beginning again when an error is detected; the adiabatic case, the stationary solution lim (Formula Presented)is a linear function of x; Jackob, M., (1962) Heat Transfer, , 8th edition (New York: Wiley), equation (18-15)
• An interesting case is a cross-section that varies linearly with the length of the bar. If the variation is large enough, a transformation can be defined changing the nonuniform section bar into a two-dimensional problem: a disk that transfers heat from its centre to its perimeter; Jackob, M., (1962) Heat Transfer, , 8th edition (New York: Wiley), equation (18-15)

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