Heat transport single-phase

Heat transport with phase change such as in boiling or condensation is an efficient method to transfer heat because latent heat per unit mass is very large compared to the sensible heat. For single component fluid, the interface temperature difference involved for heat transfer in evaporation and condensation is relatively small. However, when more than one component is present in a system the temperature difference can be higher. An example is condensation of vapors in the presence of noncondensable gases. The two-phase heat transfer relevant to reactors includes pool boiling, evaporation in a vertical channels, and condensation inside or outside the tubes. 

Weekman and Myers (W3) measured wall-to-bed heat-transfer coefficients for downward cocurrent flow of air and water in the column used in the experiments referred to in Section V,A,4. The transition from homogeneous to pulsing flow corresponds to an increase of several hundred percent of the radial heat-transfer rate. The heat-transfer coefficients are much higher than those observed for single-phase liquid flow. Correlations were developed on the basis of a radial-transport model, and the penetration theory could be applied for the pulsing-flow pattern. 

Between the single phases, molecules and, in most cases, thermal energy are exchanged. The driving force for this molecular and heat transport is a thermodynamic imbalance between the two phases. 

Comparing the mass transport expressions in (115) with their heat-transfer analogues in (114), there is a good deal of similarity — especially in the one-phase relations. For a single phase, the... 

The basic discretization of the two-fluid model equations is similar to the approximations of the corresponding transport equations for single phase flow. A minor difference is that the two-fluid model equations contain the novel phase fraction variables that have to be approximated in an appropriate manner. More important, to design robust, stable and accurate solution procedures with appropriate convergence properties for the two-fluid model equations, emphasis must be placed on the treatment of the interface transfer terms in the phasic momentum, heat and mass transport equations. Because of these extra terms, the coupling between the different equations is even more severe for multiphase flows than for single phase flows. 

For all of the flows that can be classified as unidirectional, the analysis of Section A shows that the governing equations reduce to solving a single heat equation for the magnitude of the scalar velocity component in the flow direction. For heat transfer applications, mathematically analogous problems involve heat transport by pure conduction. As noted earlier, there are excellent comprehensive books devoted exclusively to the solution of this class of problems.4 Here, we consider a related problem, which is chosen because it addresses the physically important coupling of heat transfer in the presence of phase change and also because it is another ID problem that exhibits a self-similar solution. 

Current experimentation on micro-channel two-phase flows has provided some evidence of the heat transfer mechanisms that govern the micro-scale flow boiling process (i) at low vapor qualities, when bubbly flow is the dominant flow pattern, thermal transport is primarily associated to nucleate boiling, (ii) at intermediate vapor qualities, with the intermittent passage of elongated bubbles and slugs of liquid, heat is transferred by single phase... 

Dohle et al. presented a one-dimensional model for the vapor-feed DMFC, including a description of the methanol crossover [158]. The effects of methanol concentration on the cell performance were studied. Scott et al. also developed several simplified single-phase models to study transport and electrochemical processes in liquid-feed DMFC and showed that the cell performance is limited by the slow diffusion of methanol in the liquid [13, 159-171]. Siebke et al. presented a ID mathematical model and a numerical simulation to explore the influence of different physical and electrochemical phenomena in the MEA of the liquid feed DMFC [162]. Dohle et al. presented a model to describe the heat and the power management of a DMFC system [163]. 

Heat transfer to a digitized flow in a microchannel is similar in many ways to single-phase forced convection in microchannels. The thermal boundary conditions that exist are the same however, due to the unique rolling-type flow, DHT behaves in a significantly different fashion. In Fig. 3, the temperature field shows that heat is convected by the vortices and circulates within the droplet. As a droplet rolls down a heated microchannel, cool fluid from the center of the droplet is continually transported to the outer edges of the droplet while hot fluid at the wall is convected inward. Heat gradually diffuses... 

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