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The present book treats the science of heat conduction to an extent to which it can be taught in the specialized departments of Mechanical, Chemical or Electrical Engineering at a German Engineering University. No special prerequisites are assumed, and the mathematical methods employed draw, essentially, on the content of a normal curriculum in the depart ments mentioned above. The book is intended for adoption in conjunction with a standard lecture course or as an aid to review before examinations. It should also be found helpful to a practicing engineer in solving problems in heat conduction. As far as the readers are concerned, the book should, above all, show that exact and approximate solutions to answer questions which arise in a very large number of important, practical applications are at their disposal. Further, the book will show that in many cases it is possible to perform first estimates in a very elementary manner before engaging in the derivation of complicated analyticsolutions. It is in this way that we utilize the past results of the great mathematicians of earlier generations who have bequeathed to us a considerable stock of methods and solutions. The application of such methods is illustrated in this book with the aid of examples drawn from various branches of science and technology. In this manner, the wide field of applicability of heat transfer will be made clear.
List of contents
1 Introductory Remarks.- 1.1 Fundamental Concepts.- 1.2 Fourier's Equation.- 1.3 Initial and Boundary Conditions.- 2 Transport Properties.- 2.1 Thermal Conductivity of Metals and Alloys.- 2.2 Transport Processes in Dilute Gases.- 2.3 Heat Conduction through Laminated Bodies.- 2.4 Order of Magnitude of Heat Fluxes and Coefficients.- 3 One-Dimensional, Steady-State Heat Conduction.- 3.1 Introductory Remarks.- 3.2 Péclet's Equations.- 3.3 Quasi-steady Heat Conduction.- 3.4 Extended Surfaces.- 4 Steady-State Conduction in the Presence of Heat Sources.- 5 Steady-State Conduction in Several Dimensions.- 5.1 Shape Factor and Shape Resistance.- 5.2 Kirchhoff's Transformation.- 5.3 Conformal Mapping.- 5.4 Fictitious Heat Sources and Sinks.- 5.5 Graphical Methods.- 5.6 Relaxation Method.- 5.7 Experimental Analogs.- 5.7.2 Soap-film Analogy.- 5.8 Summary of Shape Factors.- 6 Nonsteady One-Dimensional Heat Conduction.- 6.1 Fundamental Solutions of the Fourier Equation.- 6.2 Dimensional Analysis.- 6.3 Semi-infinite Body.- 6.4 Two Semi-infinite Bodies in Thermal Contact.- 6.5 Duhamel's Theorem.- 6.6 Temperature Equalization in Simple Bodies.- 6.7 Approximate Solutions.- 6.8 Method of Finite Differences.- 6.9 Experimental Analogs.- 6.10 The Laplace Transformation.- 6.11 Periodic Temperature Variation.- 7 Thermal Explosions.- 8 Continuously Operating Heat Sources.- 9 Moving Sources.- 10 Nonsteady Heat Conduction in Several Dimensions.- 11 Nonsteady Heat Conduction with Phase Transition.- 11.1 Neumann's Exact Solution.- 11.2 The Quasi-steady Approximations.- References.- Appendix A International System of Units.- Appendix B Conversion of Units.- Appendix C The Universal Constants of Physics.- Appendix D Characteristic Dimensionless Numbers in Heat and Mass Transfer.- Appendix E Thermophysical Properties of Solids, Liquids, and Gases.- Appendix F Thermal Conductivity of Liquids at Moderate Pressures.- Appendix G Tables of Mathematical Functions.
