Charts are presented for determining complete temperature histories in spheres, cylinders, and plates. It is shown that for values of the dimensionless time ratio X greater than 0.2 the heating equations reduce to such a simple form that for each shape two charts which give temperatures at any position within the heated or cooled bodies can be plotted. It is also shown that the usual simple heating and cooling charts can also be used for the determination of temperatures and heating times in bodies heated by a constant rate of heat generation at the surface (induction heating). Finally, a two-dimensional chart is given for finding heating times in short cylinders, thereby eliminating the trial-and-error solution that is necessary when heating times are found from the present one-dimensional charts.
The heat flow through insulation containing “through-metal,” or “thermal short-circuits” has been investigated. The heat flow through such a structure (occurring, for example, in the insulation of ship hulls) can be considerably larger than would be found from adding to the heat flow through the insulation that contributed by the “through-metal,” as if the two were independent. Thus the apparent effectiveness of an insulation can be very much smaller than would be calculated from the thermal conductivity alone. From the many different forms of thermal short-circuits, one specific type has been selected for investigation, i.e., that of metal strips or fins extending through insulation which is covered on its surfaces by sheet metal. General curves are developed and their application explained, from which an “increase factor” for any condition (conductivity and thickness of the insulation, conductivity and thickness of the strips, outside film conductance) can be read. The “increase factor” is defined as the ratio of the heat flow through an actual structure, compared with the flow that would occur if the insulation and heat flow through metal strips were independent of each other. The method of developing these general curves and the basis of the experimental technique used are explained in two Appendixes.
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