CHAPTER 4 - ON METHODS OF CALCULATING TEMPERATURE DISTRIBUTIONS IN STRUCTURES

Abstract

This chapter presents the methods of calculating temperature distributions in structures. Temperature distributions in solids are determined by using the equation of heat conduction, which is a partial differential equation of parabolic type in the transient case and of elliptic type in the two- or three-dimensional steady case, together with suitable boundary conditions. In most cases, general laws for the external heat transfer are known from experiments and from theory. Temperature distributions in structures and solids are best found by an approach using singly or in combination: (1) laboratory experiments, (2) analogs, and (3) calculations. In steady heat flow, it is fairly obvious that methods are most suitable in a particular case. For one-dimensional heat flow, the analytical methods are preferable in all cases with linear laws of heat flow and of external heat transfer. In two-dimensional heat flow, the analytical method is only suitable for bodies of the simplest geometrical form. In all other cases numerical methods in particular, the relaxation method or analogs are commonly used. In most cases, the temperatures rather than the rates of heat flow are important for structures at elevated temperatures.