Introduction to the Mathematical Theory of the Conduction of Heat in SolidsMacmillan and Company, limited, 1906 - 268 pages Introduction to the Mathematical Theory of the Conduction of Heat in Solids by Horatio Scott Carslaw, first published in 1945, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
Table des matières
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Autres éditions - Tout afficher
Introduction to the Mathematical Theory of the Conduction of Heat in Solids Horatio Scott Carslaw Affichage d'extraits - 1921 |
Introduction to the Mathematical Theory of the Conduction of Heat in Solids Horatio Scott Carslaw Affichage d'extraits - 1945 |
Introduction to the Mathematical Theory of the Conduction of Heat in Solids Horatio Scott Carslaw Affichage d'extraits - 1921 |
Expressions et termes fréquents
a₁ Abel's Theorem arbitrary function axis Bessel's functions boundary conditions C.R. Acad characteristic functions coefficients Conduction of Heat constant temperature continuous function cosh curve Cylinder differential equation of conduction expansion flow of heat follows Fourier's Series gain of heat given Green's function Green's Theorem infinite series infinite solid Initial Temperature f(x Initial Temperature Zero integral being taken integral equation interval isothermal Leipzig line source Linear Flow Math mathematical medium at zero method obtain Paris perature Phil Physik plane x=0 positive number positive roots problem Proc radiation takes place radius Semi-Infinite Solid Sine Series sinh Solid bounded solution sphere Steady Temperature summation Surface r=a surface temperature Theorem thermal Thermal Conductivity uniformly convergent unit v₁ vanishes Variable Temperature Whittaker and Watson zero temperature дх მა მე
Fréquemment cités
Page 59 - F. he recognizedt to be a high estimate for the temperature of molten rock, but he adopted it, as he was most anxious not to underestimate the age of the Earth, and his wish was to give the largest possible limits rather than the smallest. Later experiments upon the behaviour of rocks under high temperatures led him to believe that these temperatures are much higher than those required for a typical basalt of the primitive character, and that 1,200° C. would be a fairer estimate. This change from...
Page 59 - These data enable us to compute how long ago the surface must have had the temperature of meltingrock, and when it must have been too hot for vegetable and animal life. Sir William Thomson, in his celebrated essay on this...
Page 4 - Conduction of Heat that the rate at which heat crosses from the inside to the outside of an isothermal surface per unit area per unit time at a point is equal to 8v *8n...
Page 169 - Oreen's function as the temperature at (x, y, z) at the time t due to an instantaneous point source of strength unity generated at the point...
Page 8 - Since the specific heat c is the ratio of the quantity of heat required to raise unit mass of the substance 1° C. to the quantity required to raise unit mass of water 1° C., it is of zero dimensions in mass, length, and time.
Page 3 - U not quite the same at different temperatures, and in an exact definition of the calory the temperature of the water would need to be specified. It is usual to take for this specified temperature 15° C., and the calory will then be the quantity of heat required to raise 1 gramme of water from 15° C. to 16° C. For this 15° calory...
Page 1 - Definitions. When different parts of a solid body are at different temperatures, heat flows from the hotter to the colder portions by a process of electronic and atomic energy transfer known as "conduction.
Page 171 - P(x', y', z') at the time t due to an initial distribution f(x, y, z) and radiation at the surface into a medium at temperature <f>(x,y,z,t) follows from a discussion...
Page 3 - QJ^—VJ) are then simply [If], since the unit of heat varies jointly as the unit of mass and the value of the degree. It follows that On the cgs systemf the unit of heat is the calory, the quantity which will raise 1 gramme of water 1° CJ If it is desired to measure heat by the work necessary to .produce it, the dynamical unit in this system would be the erg. The relation between the calory and this unit is given to a sufficient approximation...
Page 243 - MO for a given time, after which it is kept at zero. Find the temperature at any time in the second stage.