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11 – UNSTEADY-STATE MICROSCOPIC BALANCES WITH GENERATION
Modeling in Transport Phenomena, 2007Co-Authors: Ismail TosunAbstract:Publisher Summary The chapter presents the cases in which all the terms in the Inventory Rate Equation are nonzero. The resulting governing Equations for velocity, temperature, and concentration are nonhomogeneous partial differential Equations. Nonhomogeneity may also be introduced by initial and boundary conditions. At time t = 0, a constant pressure gradient is imposed and the fluid begins to flow. It is required to determine the development of the velocity profile as a function of position and time. The purpose of obtaining the velocity distribution is to establish the relationship between the volumetric flow Rate and the pressure drop to estimate the power required to pump the fluid.
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STEADY MICROSCOPIC BALANCES WITH GENERATION
Modeling in Transport Phenomena, 2007Co-Authors: Ismail TosunAbstract:The chapter discusses steady-state microscopic balances with the addition of the generation term to the Inventory Rate Equation. Once the governing Equations for the velocity, temperature, or concentration are developed, the physical significance of the terms appearing in these Equations is explained and the solutions are provided in detail in the chapter. The chapter describes the way in which macroscopic level design Equations are obtained by integrating the microscopic level Equations over the volume of the system. Momentum is geneRated as a result of the forces—that is, gravitational and pressure forces—acting on the system. The analysis is restricted to the cases that hold the assumptions of incompressible Newtonian fluid, one-dimensional, fully developed laminar flow, and constant physical properties.
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Rate OF GENERATION IN MOMENTUM, ENERGY, AND MASS TRANSPORT
Modeling in Transport Phenomena, 2007Co-Authors: Ismail TosunAbstract:This chapter derives the explicit expressions for the generation Rate per unit volume (R) for the cases of momentum, energy, and mass transport. In the Rate of generation of momentum transport, for a given system the Inventory Rate Equation for momentum can be expressed in terms of the forces acting on a system. These forces include: the pressure force (surface force), and the gravitational force (body force). The chapter focuses on the issue of “Rate of generation in energy transport,” and explains the paradox called: “One of the most important problems that the world faces today is energy shortage.” According to the first law of thermodynamics, energy is converted from one form to another and transferred from one system to another but its total is conserved. If energy is conserved, then there should be no energy shortage”. Rate of generation in mass transport are described with the inclusion of Stoichiometry of a chemical reaction, the law of combining proportions, and Rate of reaction. In the law of combining proportions, the molar extent of the reaction is an extensive property measured in moles and its value can be greater than unity. The Rate constant can be determined by running the same reaction at different temperatures and using the Arrhenius relation.
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Unsteady-State Macroscopic Balances
Modeling in Transport Phenomena, 2007Co-Authors: Ismail TosunAbstract:This chapter presents a systematic treatment of steady-state macroscopic balances for the conservation of chemical species, mass, and energy. The basic steps in the development of steady-state macroscopic balances include: (1) defining the system, (2) drawing a simple sketch if possible, (3) listing the assumptions, (4) writing down the Inventory Rate Equation for each of the basic concepts relevant to the problem at hand, (5) using engineering correlations to evaluate the transfer coefficients, and (6) solving the algebraic Equations. Mathematical formulation and derivation of relations and formulas have been done for the three steady-state macroscopic balances. Conservation of energy is defined from first law of thermodynamics followed by relations between heat and work with sign conventions depending on the energy exchange between system and surroundings. The chapter uses an example of an astronaut on the space shuttle Atlantis, to determine the total energy per unit mass. The use of the energy Equation without chemical reactions requires the enthalpy change to be known or calculated. For some substances— such as steam and ammonia, enthalpy values are either tabulated or given in the form of a graph as a function of temperature and pressure and hence, can be determined easily. If enthalpy values are not tabulated, then the method of calculation of the enthalpy values for a known temperature and pressure in a process are given in the chapter. For energy Equation with chemical reactions, thermochemistry that deals with the changes of energy in chemical reactions is explained.
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Modeling in Transport Phenomena: A Conceptual Approach
2002Co-Authors: Ismail TosunAbstract:Modelling in Transport Phenomena: A Conceptual Approach aims to show students how to translate the Inventory Rate Equation into mathematical terms at both the macroscopic and microscopic levels. The emphasis is on obtaining the Equation representing a physical phenomenon and its interpretation. The book begins with a discussion of basic concepts and their characteristics. It then explains the terms appearing in the Inventory Rate Equation, including ""Rate of input"" and ""Rate of output."" The Rate of generation in transport of mass, momentum, and energy is also described. Subsequent chapters detail the application of Inventory Rate Equations at the macroscopic and microscopic levels. This book is intended as an undergraduate textbook for an introductory Transport Phenomena course in the junior year. It can also be used in unit operations courses in conjunction with standard textbooks. Although it is written for students majoring in chemical engineering, it can also serve as a reference or supplementary text in environmental, mechanical, petroleum, and civil engineering courses.
