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: (1) Rectangular parallelopiped. (1a) Long rectangular rod. (1b) 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 be readily applied to the case of similar solids of any size and diffusivity.Temperature distribution in solids; surface suddenly cooled or heated. Equations are derived for the following shapes: (1) Rectangular parallelopiped. (1a) Long rectangular rod. (1b) Very thin slab. (2) Cylinder. (2a) Long cylindrical rod. (3) Sphere. The distribution inside a sphere at various instants is computed and also the temperature at the center of a slab, square bar, cube, long cylinder, and sphere as a function of the time. These numerical results may be readily applied to the case of similar solids of any size and diffusivity.Thermal diffusivity; method of measurement involving determination of temperature-time relation at the center of a symmetrical solid whose surface is heated either at a uniform rate or very suddenly. The convenience of this method is pointed out, but practical details are not considered. The equations given are in convenient form for such uses.