Heat Sources

Abstract

Heat sources can be homogenous or concentrated. The latter can be also divided into point sources, linear sources and surface sources. Sources can be instantaneous or perpetually active in time. The basic solutions that account for the presence of point, linear and surface heat sources in an infinite space are presented in references [2, 4, 5, 8, 14, 23, 25]. The analysis of transient temperature fields during the welding process is the object of a discussion in references [7, 10, 17, 20, 21, 24], while the analysis of temperature fields, which are formed during material processing tasks, such as grinding or machine cutting, is discussed in references [3, 6, 9, 13, 18, 26, 29]. When analyzing temperature fields created by instantenous (impulselike) heat sources, one can make use of the Dirac function [11, 31], which satisfies the following conditions:

$$ \delta (t) = 0 dla t \ne 0, $$

(1)

$$ \int\limits_{ - \infty }^\infty {\delta (t)dt = 1} . $$

(2)

Dirac function, therefore, equals zero for all values of t with an exception of t=0, when t is infinite. Definition of this function differs from the classical definition of a function. It can be interpreted graphically (Fig. 25.1).