General Concepts of Heat Transfer

Until the beginning of the 19th century, it was thought that heat was an invisible substance called caloric. An object at a high temperature was thought to contain more caloric than one at a low temperature. However, British physicist Benjamin Thompson in 1798 and British chemist Sir Humphry Davy in 1799 presented 

The sensation of warmth or coldness is caused by temperature. Adding heat to a substance not only raises its temperature, but also produces changes in several other qualities. The substance expands or contracts its electric resistance changes and in the gaseous form, its pressure changes. Five different temperature scales are in use today Celsius, Fahrenheit, Kelvin, Rankine, and international thermodynamic. 

The term resistance refers to the property of any object or substance to resist or oppose the flow of an electrical current. The unit of resistance is the ohm. The abbreviation for electric resistance is R and the symbol for ohms is the Greek letter omega, 5. For certain electrical calculations the reciprocal of resistance is used, 1/R, which is termed conductance, G. The unit of conductance is the mho, or ohm spelled backward, and the symbol is an inverted omega. 

Heat is measured in terms of the calorie, defined as the amount of heat necessary to raise the temperature of 1 gram of water at a pressure of 1 atmosphere from 15° to 16 °C. This unit is sometimes called the small calorie, or gram calorie, to distinguish it from the large calorie, or kilocalorie, equal to 1000 small calories, which is used in nutritional studies. In mechanical engineering practice in the United States and the United Kingdom, heat is measured in British thermal units (Btu). One Btu is the quantity of heat required to raise the temperature of 1 pound of water 1 ° F and is equal to 252 calories. 

The term latent heat is also pertinent to our discussions. The process of changing from solid to gas is referred to as sublimation from solid to liquid, as melting and from liquid to vapor, as vaporization. The amount of heat required to produce such a change of phase is called latent heat. If water is boiled in an open container at a pressure of 1 atmosphere, its temperature does not rise above 100° C (212° F), no matter how much heat is added. The heat that is absorbed without changing the temperature is latent heat it is not lost, but is expended in changing the water to steam. 

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In this chapter, we briefly describe fundamental concepts of heat transfer. We begin in Section 20.1 with a description of heat conduction. We base this description on three key points Fourier s law for conduction, energy transport through a thin film, and energy transport in a semi-infinite slab. In Section 20.2, we discuss energy conservation equations that are general forms of the first law of thermodynamics. In Section 20.3, we analyze interfacial heat transfer in terms of heat transfer coefficients, and in Section 20.4, we discuss numerical values of thermal conductivities, thermal diffusivities, and heat transfer coefficients. 

Radiation is frequently associated with that bad nuclear stuff. However, the general scientific meaning of this word is much broader. Back in chapter 4 we discussed the concept of heat, or the process by which energy is transferred from a hotter body to a colder one. What wasn t discussed was how energy gets exchanged between objects. Heat exchange can occur via conduction, convection, and radiation. 

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. 

The formulation of an engineering discipline such as heat transfer is based on definitions of concepts and statements of natural laws in terms of these concepts. The natural laws of heat transfer, like those of other disciplines, can be neither proved nor disproved but are arrived at inductively, on the basis of evidence collected from a wide variety of experiments. As we continue to increase our understanding of the universe, the present statements of natural laws will be refined and generalized. For the time being, however, we shall refer to these statements as the available approximate descriptions of nature and employ them for the solution of current problems of engineering. 

Hence, the ordinate in Fig. 6.22 can also be used in conjunction with Eq. 6.107 or 6.109 to calculate the cross flow skin friction coefficient for cases of very small yaw angles (ts =1). Note that Iaw is equal to unity because the solution of Eq. 6.102 with Pr = 1 and an insulated surface is / = 1. Although the trends exhibited in Figs. 6.21 and 6.22 are generally similar, it must be cautioned that such large variations in the Reynolds analogy factor occur that the latter is no longer a useful concept. The heat transfer parameter for a cooled surface shows a rather small variation with Pp for Pp > Vi, a fact first utilized in Ref. 44 to obtain relatively simple expressions for the local heat flux to blunt bodies in hypersonic flow. 

The concept of an overall heat-transfer coefficient is used in the calculation of the rate of heat transfer in an evaporator. The general equation can be written... 

This work particularly emphasizes the importance of selecting the initiator system for optimum reactor operation and reveals general concepts which specify the desired properties and operational modes of an optimum initiator system. In addition, the effects of the system heat transfer and the CTA (chain transfer agent) level on the conversion-molecular weights relationships are presented. 

The investigations refer to the general capability of micro reactors to perform short-time processing with highy intensified mass and heat transfer. A special focus of most investigations on the oxidation of ammonia was the heat management. The use of new concepts for heat supply and removal opens the door to operation in new process regimes with very different product spectra. 

Cyclohexene hydrogenation is a well-studied process that serves as model reaction to evaluate performance of gas-liquid reactors because it is a fast process causing mass transfer limitations for many reactors [277,278]. Processing at room temperature and atmospheric pressure reduces the technical expenditure for experiments so that the cyclohexene hydrogenation is accepted as a simple and general method for mass transfer evaluation. Flow-pattern maps and kinetics were determined for conventional fixed-bed reactors as well as overall mass transfer coefficients and energy dissipation. In this way, mass transfer can be analyzed quantitatively for new reactor concepts and processing conditions. Besides mass transfer, heat transfer is an issue, as the reaction is exothermic. Hot spot formation should be suppressed as these would decrease selectivity and catalytic activity [277]. 

Up to this point we have shown how conduction problems can be solved by finite-difference approximations to the differential equations. An equation is formulated for each node and the set of equations solved for the temperatures throughout the body. In formulating the equations we could just as well have used a resistance concept for writing the heat transfer between nodes. Designating our node of interest with the subscript i and the adjoining nodes with subscript j, we have the general-conduction-node situation shown in Fig. 3-10. At steady state the net heat input to node i must be zero or... 

We stait this chapter with one-dimensional steady heat conduction in a plane wall, a cylinder, and a sphere, and develop relations for thennal resistances in these geometries. We also develop thermal resistance relations for convection and radiation conditions at the boundaries. Wc apply this concept to heat conduction problems in multilayer plane wails, cylinders, and spheres and generalize it to systems that involve heat transfer in two or three dimensions. We also discuss the thermal contact resislance and the overall heat transfer coefficient and develop relations for the critical radius of insulation for a cylinder and a sphere. Finally, we discuss steady heat transfer from finned surfaces and some complex geometries commonly encountered in practice through the use of conduction shape factors. 

The present section reviews the concepts behind the Generalized Integral Transform Technique (GITT) [35-40] as an example of a hybrid method in convective heat transfer applications. The GITT adds to tiie available simulation tools, either as a companion in co-validation tasks, or as an alternative approach for analytically oriented users. We first illustrate the application of this method in the full transformation of a typical convection-diffusion problem, until an ordinary differential system is obtained for the transformed potentials. Then, the more recently introduced strategy of... 

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