Heat transfer in homogeneous systems

The fundamental mechanism behind heat exchange in microchannels does not differ from the well-established equations in macroscale applications. However, effects which are negligible and assumptions made in larger systems have to be reevaluated and carefully considered on a smaller scale. A main concern with heat transfer in microchannel centers on the question of whether the conventional assumptions and theory can be applied. 

This chapter gives an overview of recent literature concerning homogeneous heat transfer in microchannels d 1 mm). The influences of different effects on heat transfer which are more pronounced in microchannels compared with macroscale systems are discussed. Criteria are given when these different effects have to be considered. Conventional approaches to solve heat transfer problems in macroscale 

Micro Process Engineering, Vol.l Fundamentals, Operations and Catalysts Edited by V. Hessel, A. Renken, J.C. Schouten, and J.-I. Yoshida Copyright 2009 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-31550-5 

In the current literature on heat transfer in microchannels in homogeneous systems, large deviations between the different correlations and measurements can be seen. So far, no general conclusion can be drawn and the available heat transfer coefficient correlations are often restricted to the experimental setup and device used in a particular study. Therefore, there is still a need for precise experimental and numerical work in heat transfer analysis in microchannels to gain a better understanding. 

This chapter focuses on single-phase flow heat transfer in microchannels. For heat transfer of boiling and condensation in microchannels, the interested reader is referred to reviews by Kandlikar [2] and Thome [3]. 

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There is a large amount of literature concerning heat transfer in homogeneous microfiuidic systems, with several recent reviews 7-12]. 

Two other crucial factors are mass transfer and heat transfer. In Chapter 3 we assumed that the reactions were homogeneous and well stirred, so that every substrate molecule had an equal chance of getting to the catalytic intermediates. Here the situation is different. When a molecule reaches the macroscopic catalyst particle, there is no guarantee that it will react further. In porous materials, the reactant must first diffuse into the pores. Once adsorbed, the molecule may need to travel on the surface, in order to reach the active site. The same holds for the exit of the product molecule, as well as for the transfer of heat to and from the reaction site. In many gas/solid systems, the product is hot as it leaves the catalyst, and carries the excess energy out with it. This energy must dissipate through the catalyst particles and the reactor wall. Uneven heat transfer can lead to hotspots, sintering, and runaway reactions. 

The rate at which a chemical reaction occurs in homogeneous systems (single-phase) depends primarily on temperature and the concentrations of reactants and products. Other variables, such as catalyst concentration, initiator concentration, inhibitor concentration, or pH, also can affect reaction rates. In heterogeneous systems (multiple phases), chemical reaction rates can become more complex because they may not be governed solely by chemical kinetics but also by the rate of mass and/or heat transfer, which often play significant roles. 

For the production of chemicals, the rate of the reaction is a key parameter for the productivity defined in Equation (5) as the number of molecules produced per time. In homogeneous systems, the reaction rate depends on temperature, pressure, and composition [1]. In the case of solarthermal cycles, a metal oxide is used for the C02-splitting reaction rendering the reaction medium a heterogeneous two-phase system consisting of a solid (metal, metal oxide) and a fluid (CO2, CO, or carrier gas with O2). Therefore, the reaction kinetics becomes much more complex. Whereas microscopic kinetics only deals with time-dependent progress of the reaction, macroscopic kinetics additionally takes the heat- and mass-transport phenomena in heterogeneous systems into account. The transfer of species from one phase to the other must be considered in the overall mass balance [1]. The reaction of a gas with a porous solid consists of seven steps ... 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

Although they are termed homogeneous, most industrial gas-phase reactions take place in contact with solids, either the vessel wall or particles as heat carriers or catalysts. With catalysts, mass diffusional resistances are present with inert solids, the only complication is with heat transfer. A few of the reactions in Table 23-1 are gas-phase type, mostly catalytic. Usually a system of industrial interest is liquefiea to take advantage of the higher rates of liquid reactions, or to utihze liquid homogeneous cat ysts, or simply to keep equipment size down. In this section, some important noncatalytic gas reactions are described. 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

Micro reaction systems may help to overcome or at least reduce some of the above-mentioned limitations [69]. Electrochemical micro reactors with miniature flow cells where electrodes approach to micrometer distances should have much improved field homogeneity. As a second result of confined space processing, the addition of a conducting salt may be substantially reduced. In addition, benefits from a uniform flow distribution and efficient heat transfer may be utilized. 

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