ABSTRACT

A great majority of engineering problems, however, involve time-dependent thermal conditions. The initial temperature distribution may not be in thermal equilibrium with the boundary temperatures. From the knowledge of the temperature distribution at any instant, thermal stress distributions can be evaluated, and from the knowledge of how the temperature at a point varies with time, metallurgical conditions may be predicted. In any heating or cooling problem, the heat transfer process between a body and the fluid surrounding it is influenced by both the internal resistance of the body and the surface resistance. The chapter explores the lumped-heat-capacity systems where the elimination of the spatial variation of temperature considerably simplifies the problems. It considers some representative nonperiodic heating and/or cooling problems and obtain solutions by the method of separation of variables. The chapter also consider a periodic problem and introduce the concept of complex temperature.