Heat Conduction - With Engineering And Geological Application

INTERNATIONAL SERIES IN PURE AND APPLIED PHYSICS by G. P. HARNWELL. PREFACE: The present volume is the successor to and, in effect, a revision of the Ingersoll and Zobel text of some years ago. To quote from the earlier preface: . . . the theory of heat con duction is of importance, not only intrinsically ’ but also because its broad bearing and the generality of its methods of analysis make it one of the best introductions to more advanced mathe matical physics. The aim of the authors has been twofold. They have attempted, in the first place, to develop the subject with special reference to the needs of the student who has neither time nor mathematical preparation to pursue the study at great length. To this end, fewer types of problems are handled than in the larger treatises, and less stress has been placed on purely mathe matical derivations such as uniqueness, existence, and con vergence theorems. The second aim has been to point out . . . the many applications of which the results are susceptible .... It is hoped that in this respect the subject matter may be of interest to the engineer, for the authors have attempted to select appli cations with special reference to their technical importance, and in furtherance of this idea have sought and received suggestions from engineers in many lines of work. While many of these applications have doubtless only a small practical bearing and serve chiefly to illustrate the theory, . . . the results in some cases . . . may be found worthy of note. The same may be said of the geological problems. While a number of solutions are here presented for the first time ... no originality can be claimed for the underlying mathematical theory which dates back, of course, to the time of Fourier. Since the above was written there has been a steady increase in interest in the theory of heat conduction, largely along practical lines. The geologist and geographer are interested in a new tool which will help them in explaining many thermal phenomena and in establishing certain time scales. The engi neer, whose use of the theory was formerly limited almost entirely to the steady state, has developed many useful tables and curves for the solution of more general cases and is interested in finding still other methods of attack. The physicist and mathematician have done their part in treating problems which have hitherto resisted solution. The present volume carries out and extends the aims of the earlier one. Most of the old material has been retained, although revised, and almost an equal amount of new has been added. The geologist, geographer, and engineer will find many new applications discussed, while the mathematician, physicist, and chemist will welcome the addition of a little Bessel function and conjugate function theory, as well as the several extended tables in the appendixes. Some of these are new and have had to be specially evaluated.