Analytical Solutions For Transport Processes

This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field.

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content

Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered. A unique feature of this book is its emphasis on scaling principles and the use of asymptotic methods, both as a means of solution and as a basis for qualitative understanding of the correlations that exist between independent and dependent dimensionless parameters in transport processes. Laminar Flow and Convective Transport Processes is suitable for use as a textbook for graduate courses in fluid mechanics and transport phenomena and also as a reference for researchers in the field.

The subject of this book is to study the porous media and the transport processes occur there. As a first step, the authors discuss several techniques for artificial representation of porous. Afterwards, they describe the single and multi phase flows in simplistic and complex porous structures in terms of macroscopic and microscopic equations as well as of their analytical and numerical solutions. Furthermore, macroscopic quantities such as permeability are introduced and reviewed. The book also discusses with mass transport processes in the porous media which are further strengthen by experimental validation and specific technological applications. This book makes use of state-of-the-art techniques for the modeling of transport processes in porous structures, and considers of realistic sorption mechanisms. It the applies advanced mathematical techniques for upscaling of the major quantities, and presents the experimental investigation and application, namely, experimental methods for the measurement of relevant transport properties. The main benefit of the book is that it discusses all the topics related to transport in porous media (including state-of-the-art applications) and presents some of the most important theoretical, numerical and experimental developments in porous media domain, providing a self-contained major reference that is appealing to both the scientists and the engineers. At the same time, these topics encounter a variety of scientific and engineering disciplines, such as chemical, civil, agricultural, mechanical engineering. The book is divided in several chapters that intend to be a resume of the current state of knowledge for benefit of related professionals and scientists.

Teaches, using simple analytical models how physical, chemical, and biological processes in the subsurface affect contaminant transport Uses simple analytical models to demonstrate the impact of subsurface processes on the fate and transport of groundwater contaminants Includes downloadable modeling tool that provides easily understood graphical output for over thirty models Modeling tool and book are integrated to facilitate reader understanding Collects analytical solutions from many sources into a single volume and, for the interested reader, shows how these solutions are derived from the governing model equations

This book presents a methodology for the development and computer implementation of dynamic models for transport process systems. Rather than developing the general equations of transport phenomena, it develops the equations required specifically for each new example application. These equations are generally of two types: ordinary differential equations (ODEs) and partial differential equations (PDEs) for which time is an independent variable. The computer-based methodology presented is general purpose and can be applied to most applications requiring the numerical integration of initial-value ODEs/PDEs. A set of approximately two hundred applications of ODEs and PDEs developed by the authors are listed in Appendix 8.

This cutting-edge reference clearly explains pharmaceutical transport phenomena, demonstrating applications ranging from drug or nutrient uptake into vesicle or cell suspensions, drug dissolution and absorption across biological membranes, whole body kinetics, and drug release from polymer reservoirs and matrices to heat and mass transport in freeze-drying and hygroscopicity. Focuses on practical applications of drug delivery from a physical and mechanistic perspective, highlighting biological systems. Written by more than 30 international authorities in the field, Transport Processes in Pharmaceutical Systems discusses the crucial relationship between the transport process and thermodynamic factors analyzes the dynamics of diffusion at liquid-liquid, liquid-solid, and liquid-cultured cell interfaces covers prodrug design for improving membrane transport addresses the effects of external stimuli in altering some natural and synthetic polymer matrices examines properties of hydrogels, including synthesis, swelling degree, swelling kinetics, permeability, biocompatibility, and biodegradability presents mass transfer of drugs and pharmacokinetics based on mass balance descriptions and more! Containing over 1000 references and more than 1100 equations, drawings, photographs, micrographs, and tables, Transport Processes in Pharmaceutical Systems is a must-read resource for research pharmacists, pharmaceutical scientists and chemists, chemical engineers, physical chemists, and upper-level undergraduate and graduate students in these disciplines.

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 Pheno