Enhancement of Transfer Rates

Let us consider Fourier s law to describe the influence of transfer scales on heat transfer rates. For simplicity, Fourier s law for the flux in one-dimensional space can be written as 

Besides the effect of decreasing linear dimensions on the corresponding gradients, the effective surface area for exchange processes has to be considered. Let us integrate Equation 1.1 for a unit volume of reactor  

The surface to volume ratio for microdevices can be as high as 50 000 m m [4]. For comparison, the specific surface area of typical laboratory and production vessels seldom exceed 100 m m . Moreover, because of the laminar flow regime within microcapillaries, the internal heat transfer coefficient is inversely proportional to the channel diameter. Therefore, overall heat transfer coefficients up to 25000 W m can be obtained, exceeding those of conventional heat exchangers by at least 1 order of magnitude [5]. Indeed, conventional heat exchangers have overall heat transfer coefficients of less than 2000 W m [6]. 

Similar performance enhancement could be realized by the miniaturization for mass transfer leading to efficient mixing. For multiphase systems within microdevices, the interfacial surface to volume ratio between the two fluids is notably Increased. Indeed, the miniaturized systems possess high interfacial area up to 30000m m . The traditional bubble columns do not exceed a few 100 m m- [7]. 

The characteristic time of chemical reactions, which is defined by intrinsic 

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