Comparison of the Temperatures in a Solid and Its Scaled Model

摘要

If a solid is constructed of the same material and to scale with a body of any shape and subjected to initial and surface temperature conditions of the same character, properties can be derived to compare or contrast the temperatures at corresponding points in these solids. Seven properties are given in this paper, covering the cases of variable and steady temperatures of solids with and without radiation or convection at any part of the boundary, and with any fixed temperature distribution on the rest of the surface. The law used for the transfer of heat by radiation and convection is a very general one. The thermal coefficients are functions of the temperature. These properties are derived by substitutions of new variables into the heat equation and the boundary conditions. Some of the properties give important information about the effect of the size of a solid upon its rate of cooling or heating. All of the properties are useful in the determination of temperatures in any solid by measuring the temperatures in a large or small scale model.