Introduction and Mechanisms of Heat Transfer

The transfer of energy in the form of heat occurs in many chemical and other types of processes. Heat transfer often occurs in combination with other unit operations, such as drying of lumber or foods, alcohol distillation, burning of fuel, and evaporation. The heat transfer occurs because of a temperature difference driving force and heat flows from the high- to the low-temperature region. 

In Section 2.3 we derived an equation for a general property balance of momentum, thermal energy, or mass at unsteady state by writing Eq. (2.3-7). Writing a similar equation but specifically for heat transfer. 

Assumiirg tlile rate of transfer of heat occurs only by conduction, we can rewrite Eq. (2.3-14), which is Fourier s law, as 

Making an unsteady-state heat balance for the x direction only on the element of volume or control volume in Fig. 4.1-1 by using Eqs. (4.1-1) and (4.1-2) with the cross-sectional area being A m.  

This means the rate of heat input by conduction = the rate of heat output by conduction or q is a constant with time for steady-state heat transfer. 

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Nonisothermal systems are accounted for by the introduction of temperature-control units into the generic reactor unit representation. These units consist of elements associated with the manipulation of temperature changes and constitute temperature profiles (profile-based approach) and heaters/coolers (unit-based approach). The assumption of thermal equilibrium between the contacting phases reduces the need for a single temperature per shadow reactor compartment. The profile-based system (PBS) finds the optimum profiles without considering the details of heat transfer mechanisms. Because the profiles are imposed rather than... 

Sample Introduction and Transfer System. The sample Introduction and sample transfer system is a lengthened version of the PHI Model 15-720B Introduction system which consists of a polymer bellows-covered heating and cooling probe, a transferable sample holder, an eight-port dual-axis cross, and the mlnlreactor Interface port and transfer probe (Figure 2). There Is also a transfer vessel port with the necessary transfer probe for Introduction of air sensitive samples. They are not part of the reactor/surface analysis system. The dual cross and attached hardware are supported by the probe drive mechanism which floats on a block driven vertically and transversely by two micrometers. These micrometers plus the probe drive mechanism allow X-Y-2... 

The topics of heat, mass and momentum transfer, known collectively as transport processes, are fully examined in the books by Welty et al. [21] and Bird et al. [22]. There is a useful introduction to fluid mechanics and heat transfer by Kay and Nedderman [23], while mass transfer is fully discussed by Treybal [24] and Sherwood et al. [25]. Coulson and Richardson [26] also give clear introductions to these subjects. 

Denn, Polymer Melt Processing Foundations in Fluid Mechanics and Heat Transfer Duncan and Reimer, Chemical Engineering Design and Analysis An Introduction Fan and Zhu, Principles of Gas-Solid Flows Fox, Computational Models for Turbulent Reacting Flows... 

Carey, V. P. (1992) Liquid-Vapor Phase-Change Phenomena An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment, in Series in Chemical and Mechanical Engineering, G.F. Hewitt and C.L. Tien, Editors, Taylor Francis Series, Hemisphere Pub. Corp., Washington, D.C., p. xvii, 645. 

These heat-transfer mechanisms have been modeled both analytically and numerically for many flow geometries. Most numerical methods require a computer to obtain an analytical answer, and because of the simphflcations and assumptions required to obtain a solution, they are usually more accurate than the empirical methods discussed in this chapter. Good introductions to these methods are provided by Hewitt [1], Patankar [10], and Shah and London [11]. 

Slack [25] and Cahill et al. [26] explored the theoretical limits on k for solids within a phonon model of heat transport. Their work utilized the concept of the minimum thermal conductivity, Kj n- At this minimum value the mean free path for all heat carrying phonons in a material approaches the phonon wavelengths [25]. In this limit, the material behaves as an Einstein solid in which energy transport occurs via a random walk of energy transfer between localized vibrations in the solid. Experimentally, K an is often comparable to the value in the amorphous state of the same composition. In principle jc in can be achieved by the introduction of one or more phonon scattering mechanisms that reduce the phonon mean free path to its minimum value over a broad range of frequencies, and therefore reduces Kl over a broad range of temperatures. In practice, there are relatively few crystalline compounds for which this limit is approached. 

Merzbach, Uta G., and Carl B. Boyer. A History of Mathematics. 3d ed. Hoboken, N.J. John Wiley Sons, 2011. An excellent and highly readable history of the subject that chronicles the earliest principles as well as the latest computer-aided proofs. Schafer, M. Computational Engineering, Introduction to Numerical Methods. New W>rk Springer, 2006. Schafer includes applications in fluid mechanics, structural mechanics, and heat transfer for newer fields such as computational engineering and... 

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