Heat transfer basic theory

Consider a vessel containing an agitated liquid. Heat transfer occurs mainly through forced convection in the liquid, conduction through the vessel wall, and forced convection in the jacket media. The heat flow may be based on the basic film theory equation and can be expressed by... 

Chapter 3 of Volume 1 discusses many of the basic properties of gas and methods presented for calculating them. Chapter 6 of Volume 1 contains a brief discussion of heat transfer and an equation to estimate the heat required to change the temperature of a liquid. This chapter discusses heat transfer theory in more detail. The concepts discussed in this chapter can be used to predict more accurately the required heat duty for oil treating, as well as to size heat exchangers for oil and water. 

In our analysis, we discuss experimental results of heat transfer obtained by previous investigators and related to incompressible fluid flow in micro-channels of different geometry. The basic characteristics of experimental conditions are given in Table 4.1. The studies considered herein were selected to reveal the physical basis of scale effect on convective heat transfer and are confined mainly to consideration of laminar flows that are important for comparison with conventional theory. 

In this section, the basic theory required for the analysis and interpretation of adsorption and ion-exchange kinetics in batch systems is presented. For this analysis, we consider the transient adsorption of a single solute from a dilute solution in a constant volume, well-mixed batch system, or equivalently, adsorption of a pure gas. Moreover, uniform spherical particles and isothermal conditions are assumed. Finally, diffusion coefficients are considered to be constant. Heat transfer has not been taken into account in the following analysis, since adsorption and ion exchange are not chemical reactions and occur principally with little evolution or uptake of heat. Furthermore, in environmental applications,... 

In the second paper (17a), by taking into account the heat transfer to the vessel walls, a stable reaction regime is discovered which cannot be obtained by continuous variation of the external conditions. These features of the equations of combustion theory and the basic patterns of exothermic reaction in a jet studied by Ya.B. have recently been used widely in, for example, the modern theory of chemical reactors. 

What problems face the theory of combustion The theory of combustion must be transformed into a chapter of physical chemistry. Basic questions must be answered will a compound of a given composition be combustible, what will be the rate of combustion of an explosive mixture, what peculiarities and shapes of flames should we expect We shall not be satisfied with an answer based on analogy with other known cases of combustion. The phenomena must be reduced to their original causes. Such original causes for combustion are chemical reaction, heat transfer, transport of matter by diffusion, and gas motion. A direct calculation of flame velocity using data on elementary chemical reaction events and thermal constants was first carried out for the reaction of hydrogen with bromine in 1942. The problem of the possibility of combustion (the concentration limit) was reduced for the first time to thermal calculations for mixtures of carbon monoxide with air. Peculiar forms of propagation near boundaries which arise when normal combustion is precluded or unstable were explained in terms of the physical characteristics of mixtures. 

The ratio (10) that we obtain is so small that there is no need to attempt to establish more exactly the relation between the heat transfer and heat of reaction in the various theories of normal combustion [3, 4, 15-18], or the accuracy of the temperature differences in the detonation wave, or to undertake other similar operations which can in no way change the basic results the smallness of the heat flux in the direction of propagation of detonation the adiabatic character (which holds with great accuracy as long as we do not consider heat losses to the walls of the tube) of the chemical reaction in the detonation wave the impossibility of any noticeable role of heat transfer from the heated combustion products in ignition of the fresh, unreacted gas. 

The basic point of the preceding illustration is that there is a great amount of repetitive information flow in the design process. As a result, what is perceived to be an extremely creative process is actually very repetitive in nature. The types of analytical problems that are encountered in the mold/die design process generally fall into the sciences of fluid mechanics and heat-transfer theory. 

Intelligent selection of heat-transfer equipment requires an understanding of the basic theories of heat transfer and the methods for design calculation. In addition, the problems connected with mechanical design, fabrication, and operation must not be overlooked. An outline of heat-transfer theory and design-calculation methods is presented in this chapter, together with an analysis of the general factors that must be considered in the selection of heat-transfer equipment. 

This section draws heavily from the excellent book Chemical Reaction Engineering by Levenspiel [1]. Extensions of this basic theory to heat transfer have been made by the author. For more detail on the effects of heat transfer on the reaction kinetics, please see Wen et al. [9-13]. 

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. 

As stated in Preface, the basic concept of the thermal explosion theory is that whether the thermal explosion or the spontaneous ignition of a chemical of the TD type, including every gas-permeable oxidatively-heating substance, having an arbitrary shape and an arbitrary size, placed in the atmosphere under isothermal conditions, occurs or not is decided, based on the balance between the rate of heat generation in the chemical and the rate of heat transfer from the chemical to the atmosphere at the critical state for the thermal explosion which exists at the end of the early stages of the self-heating process. 

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. 

Some basic terms and definitions from two-phase flow theory are required for the description of heat transfer in boiling. For this we will consider the section of a channel shown in Fig. 4.48, in which the gas and liquid are flowing. An annular flow is shown in the picture for the sake of simplicity, but the following terms are... 

Plate evaporators may be constructed of flat plates or corrugated plates, the latter providing an extended heat transfer surface and improved structural rigidity. Two basic types of heat exchangers are used for evaporation systems plate-and-frame and spiral-plate evaporators. Plate units are sometimes used because of the theory that scale will flake off such surfaces, which can flex more readily than curved tubular surfaces. In some plate evaporators, flat surfaces are used, each side of which can serve alternately as the liquor side and the steam side. Scale deposited while in contact with the liquor can then be dissolved while in contact with the steam condensate. There are still potential scaling problems, however. Scale may form in the valves needed for cycling the fluids and the steam condensate simply does not easily dissolve the seale produced. 

A standard idealization of the basic heat exchanger theory is that the fluid flow rate is distributed uniformly through the exchanger on each side of the heat transfer surface. However, in practice, flow maldistribution is more common and can reduce the idealized performance significantly. 

General Considerations. The importance of fouling phenomena stems from the fact that the fouling deposits increase thermal resistance to heat flow. According to the basic theory, the heat transfer rate in the exchanger depends on the sum of thermal resistances between the two fluids, Eq. 17.5. Fouling on one or both fluid sides adds the thermal resistance R, to the overall thermal resistance and, in turn, reduces the heat transfer rate (Eq. 17.4). Simultaneously, hydraulic resistance increases because of a decrease in the free flow area. Consequently, the pressure drops and the pumping powers increase (Eq. 17.63). 

This model is obviously an extension of the well-known theory of heat transferred by radial conduction. Solution of the basic differential equations depends on the boundary conditions stipulated, the boundary layer and velocity profiles of the continuous phase. 

Dehydration is basically a simultaneous heat and mass transfer operation as explained by Van Arsdel (1963). In applications where rates of drying are low, such as in IM meats, consideration of heat transfer alone is a quite satisfactory approach, and often a preferred one. However, in order to obtain a true understanding of drying and to develop a sound fundamental theory, one must better understand the mass transfer process, both internally and externally (Lubuza, 1976). In addition, one must develop a better... 

No theory is available for estimating the heat and mass transfer coefficients using basic thermophysical properties. The analogy of heat and mass transfer can be used to obtain mass transfer data from heat transfer data and vice versa. For this purpose, the Chilton-Colburn analogies can be used [129]... 

A much larger set of basic parameters is required for description of the thermal force than is necessary for the drag force. Transfer of heat to a particle by the host gas is central to the phenomenon. In the case of a polyatomic host gas, one must work from the more difficult kinetic theory of polyatomic gases [2.123]. Heat transfer at the particle-gas interface presents the problem of specifying the energy accommodation coefficients which often differ substantially from perfect accommodation. Additional complexity will appear in the discussion which follows. 

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