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Annals of Mathematics Volume 3-4

Annals of Mathematics Volume 3-4


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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1887 edition. Excerpt: ...the same dimensions and material as the bar of the previous example, cooling in a medium which produces an emissivity great enough to make c, f, and f exceed unity. Without assigning to these symbols any particular values, it appears that the bar would very quickly assume the temperature of the medium. For we have, as in 11, a = 50,"" b=c--2TM', and = 0.185; the quantities V," Va!" and the derivatives of I7" and V" relatively to yl and l become practically nil soon after the initial epoch. Thus, from (25) and (42), we find the following table of values which show the rapid decrease of those quantities with the time Hence we see that, with such values of, rn and as render equations (26) applicable, the bar in question would have sensibly the same temperature as the surrounding medium in less than two minutes after the initial epoch. Other conditions remaining constant, the rate of cooling of a mass diminishes very rapidly with an increase of its dimensions. In order to strikingly illustrate this fact by means of the analysis, we may contrast the cooling of the bar just considered with the cooling of a cubic meter of the same material. The use of the formulas will be sufficiently indicated by computing the temperatures, corresponding to a few values of the time, at the five points designated by the following values of their co-ordinates: To compute V, V," V" for such values of the time as we have assumed, one may use equations (25) and (42) or equations (32) and (43), the latter being best for the smaller and the former best for the greater times. We have used both sets of formulas as a check on the computed results. The quantities needed in equations (26) are given...


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Product Details
  • ISBN-13: 9781154981575
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1154981576
  • Publisher Date: 12 Oct 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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