Heat and Concentration Waves

Analysis and Application

1st Edition - January 1, 1972
Editor: G Turner
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 8 6 8 - 8

Heat and Concentration Waves: Analysis and Applications describes the behavior of a limited class of waves of temperature or concentration that travels in a continuous medium,… Read more

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Heat and Concentration Waves: Analysis and Applications describes the behavior of a limited class of waves of temperature or concentration that travels in a continuous medium, which itself is moving. This book is organized into nine chapters that discuss wave equations as solutions to linear differential equations. After briefly dealing with the fundamentals of waves and pulsed, this book goes on discussing the effect of introducing either an impulse or a steady source into a stream of uniform velocity or the so-called one-dimensional flow. The following chapters present some simplest basic equations for parameter determination in a flowing medium. These chapters also describe the pulses at an ideal boundary and the behavior of sine waves at such boundary, including the concept of reflections and the ease with which sine waves overcome the problems of incorporating boundary conditions into an experimental determination. This text further examines the behavior of reservoir phases under time-varying temperature or concentration. A chapter focuses on high-precision experimental measurements of sine waves. The concluding chapter outlines the computational processes, with emphasis on the estimation of experimental errors because of their effect on the reliability of parameter determination. Topics covered in the supplementary texts include the transformation of variables; the evaluation of important integrals; the normal distribution curve; aspects of the Laplace transform; some forms of transport equation common to both heat and mass transfer processes; and the interference of waves. This book will be of value to physical chemists, chemical and petroleum reservoir engineers, process metallurgists, physiologists, hydrologists, and soil scientists.

Preface Acknowledgments Nomenclature 1. Introduction and Waves and Pulses 1.1 Waves and Pulses: General 1.2 One-Dimensional Traveling Waves 1.3 The Wave Equation 1.4 Incident and Reflected Waves 1.5 Lossy and Lossless Systems 1.6 Nonsinusoidal Waves 1.7 Standing Waves References2. Sources in One-Dimensional Flow 2.1 Introduction 2.2 Sources 2.3 Some Examples of Sources in a Moving Medium References 3. The Ideal Impulse in One-Dimensional Flow 3.1 The Variation of Concentration with Distance from a Moving Origin 3.2 The Variation of Concentration with Time 3.3 The Use of Concentration Distributions to Measure Mean Velocities 3.4 The Use of Concentration Distributions to Measure the Peclet Number 3.5 Examples of the Use of an Instantaneous Source to Determine Pe (Based on Examples by Levenspiel and Smith) 3.6 The Use of a Step Change References 4. The General Pulse; Properties and Uses of Its Transforms 4.1 Introduction 4.2 The Use of the Moments of the Pulse 4.3 Calculations in the Laplace Domain 4.4 The Use of the Fourier Transform References 5. Behavior at a Longitudinal Discontinuity: Pulses 5.1 Boundary Conditions 5.2 The Moments of a Pulse: Boundaries Not at Infinity 5.3 The General Case: Generalized Impulse or Initial Disturbance, n Boundaries 5.4 The General Case: Steady-State, First-Order Reaction, n Boundaries References 6. Sinusoidal Waves 6.1 Introduction 6.2 The Telegrapher's Equations 6.3 Impedance 6.4 Fluxes 6.5 Reflections and Reflection Coefficients 6.6 Compensation for End Effects 6.7 Special but Frequently Occurring Case 6.8 Worked Examples 6.9 The Infinite Bed 6.10 The "Danckwerts Boundary Condition" References 7. Reservoir Phases 7.1 Introduction 7.2 The Steady Cyclic State 7.3 Moments of a Pulse Wave 7.4 The Shunt Admittance of Some Important Cases 7.5 Reservoirs in Series 7.6 Numerical Examples (Sine Waves) References 8. Experimental Measurements 8.1 Introduction 8.2 General Considerations on the Generation and Measurement of Precise Sine Waves 8.3 Practical Aspects of the Generation of Sine Waves 8.4 The Flow of the Fluid 8.5 Measurements of Waves References 9. Practical Considerations and Examples 9.1 Considerations Governing the Choice of Experimental Method 9.2 Advantages of Sine Waves 9.3 Summary of Parameters Found and Methods Used 9.4 Some General Treatments 9.5 Waves in the Reservoir Phase Additional References References Appendix 1. Change of Variable in Moving Systems: Time Appendix 2. Change of Variable in Moving Systems: Distance Appendix 3. The Evaluation of Some Integrals Appendix 4. Some Properties of the Equation y = y0 exp(—k2z2) and of Its Integral Appendix 5. The Development of a Laplace Transform of a PulseAppendix 6. The Laplace Transform of Equation (2.36) Appendix 7. The Variance of a Distribution Appendix 8. Transport Equations Appendix 9. To Show That (b ± ig)1/2 = [(s + b)/2]1/2 ± i(s - b)/2]l/2 Appendix 10. General Wave Properties. Interference Author Index Subject Index