Heat transfer coefficients phase changes

A manufacturing technology to produce very small encapsulated phase-change materials has been developed (47). These encapsulated phase-change materials were appHed in a convective heat-transfer test section, and a 50—100% higher heat-transfer coefficient was reported. 

Fig. 17. Heat-transfer coefficient comparisons for the same volumetric flow rates for (A) water, 6.29 kW, and a phase-change-material slurry (O), 10% mixture, 12.30 kW and ( ), 10% mixture, 6.21 kW. The Reynolds number was 13,225 to 17,493 for the case of water.

The above equations for heat transfer apply when there is no heat generation or absorption during the reaction, and the temperature difference between the solid and the gas phase can be simply defined tliroughout the reaction by a single value. Normally this is not the case, and due to the heat of the reaction(s) which occur tlrere will be a change in the average temperature with time. Furthermore, in tire case where a chemical reaction, such as the reduction of an oxide, occurs during the ascent of tire gas in the reactor, the heat transfer coefficient of the gas will vary with tire composition of tire gas phase. 

For turbulent flow in single-phase systems, the predicted temperature profile is not changed significantly if the Peclet number is assumed to be infinite. Therefore, in turbulent two-phase systems the second-order terms in Eqs. (9) probably do not have a significant effect on the resulting temperature profiles. In view of the uncertainties in the present state of the art for determining the holdups and the heat-transfer coefficients, the inclusion of these second-order terms is probably not justified, and the resulting first-order equations should adequately model the process. 

In many design problems, the determination of a wall heat-transfer coefficient or the heat flux between the tube wall and the fluid mixture is only part of the required information. The pressure drop within the system, the rate of phase change at the gas-liquid interface, the point at which the tube walls become dry, and the holdup of the fluids at each point in the pipe must all be determined. 

Theorem 1 (Corner Point Theorem). Assume the following (1) constant heat capacities and no phase change, (2) supply and target temperature uncertainties only (no uncertainties in flow rates or heat transfer coefficients), (3) constant stream split fractions (Saboo et al., 1987b), and... 

Heat exchanger network resilience analysis can become nonlinear and nonconvex in the cases of phase change and temperature-dependent heat capacities, varying stream split fractions, or uncertain flow rates or heat transfer coefficients. This section presents resilience tests developed by Saboo et al. (1987a,b) for (1) minimum unit HENs with piecewise constant heat capacities (but no stream splits or flow rate uncertainties), (2) minimum unit HENs with stream splits (but constant heat capacities and no flow rate uncertainties), and (3) minimum unit HENs with flow rate and temperature uncertainties (but constant heat capacities and no stream splits). 

Extend the multiperiod synthesis-analysis-resynthesis algorithm to handle temperature-dependent heat capacities and phase change and uncertain heat transfer coefficients. 

More sophisticated techniques can solve problems with multiphase shell-and-tube exchangers, phase changes of process streams, and varying overall heat transfer coefficients. We may analyze a heat exchanger network as a single heat... 

Heat transfer in bubble column slurry reactors was studied by Kolbel and coworkers (75-77) and Deckwer et al. (13). The addition of solids increases the wall-to--suspension heat transfer coefficient. However, this increase is only due to changes in the physico-chemical properties and represents no independent contribution of the particles. Therefore, the heat transfer model, i.e. eqn. (17), developed by Deckwer (<53) for two-phase BCR also applies to slurry reactors as was proved for particle sizes up to 120 yum. This confirms that solids and liquid in the slurry can be regarded as a pseudo-homogeneous phase provided the gas velocity is large enough to provide for complete fluidization of the particles. 

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