1919
DOI: 10.1103/physrev.14.99
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Temperature Distribution in Solids During Heating or Cooling

Abstract: Temperature distribution in solids; surface heated at uniform rate. Equations are derived for the following typical shapes: (i) Rectangular parallelopiped. (ia) Long rectangular rod. (ib) Very thin slab. (2) Cylinder. (2a) Long cylindrical rod. (3) Sphere. (4a) Cylindrical tube heated only outside. (4b) Cylindrical tube heated both inside and outside. (5) Spherical shell heated only outside. Results calculated from these equations are tabulated and in some cases shown graphically. These numerical results may b… Show more

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Cited by 80 publications
(19 citation statements)
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“…Where the relative depth affected by diffusion is not too great, the system may frequently be dealt with by the approximate method already described in section 10 f, but with cylinders of small diameter, or with long times, or both, this simplification is not permissible, and equations for diffusion in one dimension no longer suffice. The most general case of diffusion into a cylinder is a problem of diffusion in three dimensions; this case has been treated by WILLIAMSON and ADAMS (1919). It usually happens, however, in structures of physiological importance such as nerves, individual muscle cells, etc., that the cylinder in question is so long in comparison to its diameter that diffusion into its ends is insignificant and may be neglected.…”
Section: Diffusion In Cylindersmentioning
confidence: 99%
“…Where the relative depth affected by diffusion is not too great, the system may frequently be dealt with by the approximate method already described in section 10 f, but with cylinders of small diameter, or with long times, or both, this simplification is not permissible, and equations for diffusion in one dimension no longer suffice. The most general case of diffusion into a cylinder is a problem of diffusion in three dimensions; this case has been treated by WILLIAMSON and ADAMS (1919). It usually happens, however, in structures of physiological importance such as nerves, individual muscle cells, etc., that the cylinder in question is so long in comparison to its diameter that diffusion into its ends is insignificant and may be neglected.…”
Section: Diffusion In Cylindersmentioning
confidence: 99%
“…The center changes most slowly and even after 20 years the fraction of CFCl3 in the center cells is still 0.12 giving K = 0. 19 there.…”
Section: Spatial Distribution Of Thermal Conductivity In a Foam Slabmentioning
confidence: 93%
“…Heat loss from a sphere is given by [ Carslaw and Jaeger , 1959]: where T 0 is initial temperature; T is temperature after an elapsed time, t ; k is the characteristic thermal diffusivity of the material; r is the sphere radius; and x is the distance from the sphere center. For an object located at the center of a sphere, the sine term disappears and the equation simplifies [ Williamson and Adams , 1919]. We used and to calculate values of sphere radius as a function of elapsed time for the two cases that T / T 0 = 0.9 and 0.7.…”
Section: Thermal History Of Dho 378mentioning
confidence: 99%