Basic Thermodynamics 3 Heat Transfer

In this section, we will describe and explain the fundamentals for both, thermodynamic and commercial considerations. We will start looking at the basics of heat transfer in PCM, how the heat flux and time to complete a phase change are calculated. Later we will look at the design of complete storages to supply a warm or cold heat transfer fluid (liquid or gas) and discuss general design strategies. 

This chapter will describe how we can apply an understanding of thermodynamic behavior to the processes associated with polymers. We will begin with a general description of the field, the laws of thermodynamics, the role of intermolecular forces, and the thermodynamics of polymerization reactions. We will then explore how statistical thermodynamics can be used to describe the molecules that make up polymers. Finally, we will learn the basics of heat transfer phenomena, which will allow us to understand the rate of heat movement during processing. 

Before describing advanced cycles and improvements in heat transfer the thermodynamics of the basic cycle and the calculation of COP s must be explained. 

Thermodynamics is concerned with energy and the way energy is transferred. It is a science of the macroscopic world but its effects are applied even at the microscopic scale. The first law introduces the basic thermodynamic concepts of work, heat and energy and can be defined as follows Energy can neither be created or destroyed in a system of constant mass, although it may be converted from one form to another. 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

In addition, cure time is increased five minutes for every 0.25 inches of thickness of a molding [6, 7]. In general, these rules do not apply to most polymeric systems because the phenomena of heat transfer and cure kinetics have been over-simplified. The cure rate depends on the basic polymers, curatives, cure temperature, and filler loading. The prediction of cure rate will be discussed from a new model of cure kinetics which is developed from the concept of a non-equilibrium thermodynamic fluctuation theory of chemical relaxation. 

Heat and mass transfer is a basic science that deals with the rate of transfer of thermal energy. It has a broad application area ranging from biological systems to common household appliances, residential and commercial buildings, industrial processes, electronic devices, and food processing. Students are assumed to have an adequate background in calculus and physics. The completion of first courses in thermodynamics, fluid mechanics, and differential equations prior to taking heat transfer is desirable. However, relevant concepts from these topics are introduced and reviewed as needed. 

However, thermodynamics does not state how the heat transferred depends on this temperature driving force, or how fast or intensive this irreversible process is. It is the task of the science of heat transfer to clarify the laws of this process. Three modes of heat transfer can be distinguished conduction, convection, and radiation. The following sections deal with their basic laws, more in depth information is given in chapter 2 for conduction, 3 and 4 for convection and 5 for radiation. We limit ourselves to a phenomenological description of heat transfer processes, using the thermodynamic concepts of temperature, heat, heat flow and heat flux, fn contrast to thermodynamics, which mainly deals with homogeneous systems, the so-called phases, heat transfer is a continuum theory which deals with fields extended in space and also dependent on time. 

The presence of temperature gradients in a multicomponent system introduces an additional complication in the analysis of the mass transfer process such gradients influence the values of physical, thermodynamic, and transport properties, such as the diffusion coefficients. These property variations may be taken care of by introducing temperature dependent property functions or by using average values of the properties (as is done here). The consequence of this simplification is that the basic mass transfer analysis remains essentially unchanged from those in Chapters 8-10 and we need only consider the effect of mass transfer on the heat transfer process. 

Once the continuum hypothesis has been adopted, the usual macroscopic laws of classical continuum physics are invoked to provide a mathematical description of fluid motion and/or heat transfer in nonisothermal systems - namely, conservation of mass, conservation of linear and angular momentum (the basic principles of Newtonian mechanics), and conservation of energy (the first law of thermodynamics). Although the second law of thermodynamics does not contribute directly to the derivation of the governing equations, we shall see that it does provide constraints on the allowable forms for the so-called constitutive models that relate the velocity gradients in the fluid to the short-range forces that act across surfaces within the fluid. 

COEFFICIENTS FOR FILM-TYPE CONDENSATION. The basic equations for the rate of heat transfer in film-type condensation were first derived by Nusselt. " The Nusselt equations are based on the assumption that the vapor and liquid at the outside boundary of the liquid layer are in thermodynamic equilibrium, so that the only resistance to the flow of heat is that offered by the layer of condensate flowing downward in laminar flow under the action of gravity. It is also assumed that the velocity of the liquid at the wall is zero, that the velocity of the liquid at the outside of the film is not influenced by the velocity of the vapor, and that the temperatures of the wall and the vapor are constant. Superheat in the vapor is neglected, the condensate is assumed to leave the tube at the condensing temperature, and the physical properties of the liquid are taken at the mean film temperature. 

As a state property, the molar (or specific) volume can be determined once as a function of pressure and temperature, and tabulated for future use. Tabulations have been compiled for a large number of pure fluids. In very common use are the steam tables, which contain tabulations of the properties of water. Steam is a basic utility in chemical plants as a heat transfer fluid for cooling or heating, as well as for power generation (pressurized steam), and its properties are needed in many routine calculations. Thermodynamic tables for water are published by the American Society of Mechanical Engineers (ASME) and are available in various forms, printed and electronic. A copy is included in the appendix. We will use them not only because water is involved in many industrial processes but also as a demonstration of how to work with tabulated values in general. 

One optimum requires a uniformly distributed entropy production rate in a heat exchanger, mixer, or separator. Consider the example of countercurrent and cocurrent heat exchangers shown in Figure 4.4. Temperature profiles show that the driving force AP or 1/AP is more uniformly distributed in the counter-current than in the cocurrent flow operation. This is the basic thermodynamic reason why a countercurrent is better than a cocurrent operation. The duty of the exchangers depends on the flow rate and Met and outlet temperatures T and T2 of cold streams. The duty is the amount of heat transferred from the hot fluid to cold... 

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