TEMPERATURE DISTRIBUTION IN SOLID BODIES DURING HEATING OR COOLING

摘要

Most treatments of the problem of temperature distribution in a solid body during heating or cooling assume that the change in surface temperature is either instantaneous or linear with time. Experience shows that in many cases of practical importance the increase in surface temperature may be represented by a simple exponential function of the time. Equations for the distribution of temperature within a body when the surface is heated in accordance with this exponential relation have been derived for the following shapes: (1) rectangular parallelopiped (brick); (1a) rectangular rod; (1b) slab; (2) cylinder; (2a) cylindrical rod; (3) sphere. These equations also represent the general case of diffusion under the given boundary conditions and apply, therefore, equally well to problems such as the diffusion of one substance into another, as for instance, one metal into another.