Characteristic Time Required to Achieve Uniform Temperature in Thermal Conduction of N-Dimensional Sphere Heated from Surface
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The thermal conduction of an n-dimensional sphere heated from its surface at a constant temperature was numerically analyzed using a difference scheme, where the maximum dimension number n is 100. The initial and final states of the n-dimensional shpere have uniform temperature profiles of zero and surface temperature, respectively. The characteristic time required to achieve uniform temperature inside the n-dimensional sphere was defined as the time when the temperature difference between the center and the surface is 1/100 of the surface temperature. A power law was found wherein the characteristic time was proportional to the dimension number n to the power of -1.24, which was supported by the finding that the surface arca-to-volume ratio was proportional to n. By regarding slab, cylindrical and spherical thermal conduction as the heating modes of one-, two- and three-dimensional spheres, respectively, the characteristic times during heating of the one- to three-dimensional spheres, which were analytically obtained, were included in the power law.
- 社団法人応用物理学会の論文
- 2000-10-15
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