ABSTRACT
This chapter focuses on a class of problems which involve "local" sources of internal energy such that heat is released continuously or spontaneously in a region of a system of interest that is infinitesimally small compared to the dimensions of the system. It introduces the Dirac delta function and then uses it in the solution of a number of representative examples involving local sources releasing heat continuously or spontaneously in finite regions. The chapter considers two representative cases involving line and point sources of heat in infinite regions, where demonstrates the use of Laplace transforms as another method of solution. It also considers an example involving a moving heat source, as a model of such engineering applications as welding, grinding, metal cutting, flame or laser hardening. The chapter discusses only those cases that involve heat sources, with the understanding that the study of the cases with heat sinks follows the same solution procedures.
