Analytical and Approximate Methods in Transport Phenomena
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Summary
On the job or in the field, when facing a problem with differential equations and boundary conditions, most likely you don’t have time to read through several publications in search of a method that may or may not solve your problem. Organized for quick and easy access to practical solutions, Analytical and Approximate Methods in Transport Phenomena is a reference for the day-to-day problems encountered when working with variables in heat, mass, or momentum transfer.
This text is organized differently from usual resources on applied mathematics for engineers. First, it introduces a new classification system of the problem based on just three numbers, so locating the appropriate solution method is quick and easy. Second, the author presents mathematical methods with applications in mind, introducing examples, as well as common or possible solutions, before presenting any mathematical theory or method. This allows you to identify the issue you need to resolve, then apply the appropriate method to the problem at hand. The book also includes practical discussions of the consequences and applications of various solutions.
The book highlights mathematical methods as tools for solving practical problems, not as a primary objective. Its structure and focus on application, with just the right amount of mathematical rigor, makes it the most effective manual available for easily finding the analytical methods needed to solve transport problems.
Table of Contents
Problems 111; One Variable, 1st Order, 1st Kind Boundary Condition
Introduction
Heating of a Solid
Flow between Two Drums
Heating of a Fluid in a Stirring Tank
Heated Batch Reactor
Reactor with a Time-Controlled Rate
Pressure in a Resting Fluid
Pressure in Fluid under Rotational Movement
Plug-Flow Reactor
Heat Conduction in an Indefinite Wall
Plate-and-Cone Viscometer
Thermocouple
Exercises
References
Problems 112; One Variable, 1st Order, 2nd Kind Boundary Condition
Introduction
Heating of a Solid
Heat Conduction in a Spherical Shell
Batch Reactor
Plug-Flow Reactor
Exercises
Reference
Problems 113; One Variable, 1st Order, 3rd Kind Boundary Condition
Introduction
Heating of a Solid with Controlled Heat Transfer Rate
Temperature-Controlled Batch Reactor
Batch Reactor
Exercises
Problems 121; One Variable, 2nd Order, 1st Kind Boundary Condition
Introduction
Mass Transfer through a Cylindrical Rod
Mass Transfer in a Rod with Variable Diffusivity
Conduction through a Pipe Wall
Electrically Heated Pipe Wall
Heat Transfer in a Spherical Shell
Absorption without Reaction
Diffusion through a Spherical Shell with Zero-Order Reaction
Absorption with Homogeneous Reaction
Reacting Particle
Heat Transfer through a Reacting Plate
Exercises
References
Problems 122; One Variable, 2nd Order, 2nd Kind Boundary Condition
Introduction
Flow on an Inclined Plate
Flow in an Inclined Tube
Rectangular Fin
Circular Fin
Film Condensation
Heat Transfer through a Reacting Plate
Exercises
References
Problems 123; One Variable, 2nd Order, 3rd Kind Boundary Condition
Introduction
Heat Transfer between a Plate and Fluids
Heat Transfer in a Spherical Shell
Reacting Particle
Heat Transfer between a Reacting Plate and a Fluid
Exercises
References
Problems 211; Two Variables, 1st Order, 1st Kind Boundary
Condition
Introduction
Pressure in Fluid Under Rotational Movement
Heating a Flowing Liquid
Plug-Flow Reactor
Exercises
Problems 212; Two Variables, 1st Order, 2nd Kind Boundary Condition
Introduction
Heating of Flowing Liquid
Plug-Flow Reactor
Exercises
Problems 213; Two Variables, 1st Order, 3rd Kind Boundary Condition
Introduction
Heating of Flowing Liquid
Dynamic Plug-Flow Reactor
Exercises
Problems 221; Two Variables, 2nd Order, 1st Kind Boundary Condition
Introduction
Heating an Insulated Rod or a Semi-Infinite Body
Sudden Motion of a Plate
Heating a Flowing Liquid
Plug-Flow Reactor
Temperature Profile in a Rectangular Plate
Heating a Liquid Film
Absorbing Flowing Film
Exercises
Reference
Problems 222; Two variables, 2nd Order, 2nd Kind Boundary Condition
Introduction
Heating an Insulated Rod or Semi-Infinite Body
Drying of a Spherical Particle
Heating a Cylinder
Insulated Rod with Prescribed Initial Temperature Profile
Plate-and-Cone Viscometer
Heating a Rectangular Plate
Exercises
References
Problems 223; Two Variables, 2nd Order, 3rd Kind Boundary Condition
Introduction
Convective Heating of an Insulated Rod or Semi-Infinite Body
Drying of a Spherical Particle
Convective Heating of a Cylinder
Convective Heating of Insulated Rod with Prescribed Temperature at One End
Convective Heating of a Plate
Convective Heating of a Plate with Prescribed
Temperature Function at One Face
Exercises
References
Problems 311; Three Variables, 1st Order, 1st Kind Boundary Condition
Introduction
Heating a Flowing Liquid
Two-Dimensional Reacting Flow
Exercises
Problems 312; Three Variables, 1st Order, 2nd Kind Boundary Condition
Introduction
Heating a Flowing Liquid
Two-Dimensional Reacting Flow
Exercises
Problems 313; Three Variables, 1st Order, 3rd Kind Boundary Condition
Introduction
Heating a Flowing Liquid
Two-Dimensional Reacting Flow
Exercises
Problems 321; Three Variables, 2nd Order, 1st Kind Boundary Condition
Introduction
Temperatures in a Rectangular Plate
Exercises
Appendix A: Fundamental Equations of Transport Phenomena
Appendix B: Fundamental Aspects of Ordinary Differential Equations
Appendix C: Method of Power Series and Special Functions
Appendix D: Laplace Transform
Appendix E: Method of Weighted Residuals
Appendix F: Method of Similarity
Appendix G: Fourier Series and Method of Separation of Variables
Appendix H: Fourier Transforms
Appendix I: Generalized Representation by Series
Exercises
References
Index
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