Phase change condensation

Similarly, the source term in the energy equation is sum of the electrical resistance heating, heat of formation of water, electrical work, and heat release due to phase change (condensation of water vapor). 

No phase change (condensation or fusion) occurs in the nozzle. 

Kawahara A, Chung PM, Kawaji M (2002) Investigation of two-phase flow pattern, void fraction and pressure drop in a micro-channel. Int J Multiphase Plow 28 1411-1435 Kawaji M (1999) Fluid mechanics aspects of two-phase flow Flow in other geometries. In Kand-likar SG, Shoji M, Dhir VK (eds) Handbook of phase change boiling and condensation. Taylor and Francis, Washington, DC, pp 205-259... 

Carey van P (1992) Liquid-vapor phase-change phenomena. An introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment. Hemisphere, New York Celata GP, Cumo M, Mariani A (1997) Experimental evaluation of the onset of subcooled flow boiling at high liquid velocity and subcoohng. Int J Heat Mass Transfer 40 2979-2885 Celata GP, Cumo M, Mariani A (1993) Burnout in highly subcooled water flow boiling in small diameter tubes. Int J Heat Mass Transfer 36 1269-1285 Chen JC (1966) Correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Process Des Develop 5 322-329... 

Carey VP (1992) Liquid-vapour phase-change phenomena. Hemisphere, Washington, DC Collier SP (1981) Convective boiling and condensation. McGraw-Hill, New York Ha JM, Peterson GP (1998) Capillary performance of evaporation flow in micro grooves an analytical approach for very small tilt angles. ASME J Heat Transfer 120 452 57 Hetsroni G, Yarin LP, Pogrebnyak E (2004) Onset of flow instability in a heated capillary tube. Int J Multiphase Flow 30 1424-1449... 

Phase changes are characteristic of all substances. The normal phases displayed by the halogens appear in Section II-L where we also show that a gas liquefies or a liquid freezes at low enough temperatures. Vapor pressure, which results from molecules escaping from a condensed phase into the gas phase, is one of the liquid properties described in Section II-I. Phase changes depends on temperature, pressure, and the magnitudes of intermolecular forces. 

Phase changes can go in either direction Steam condenses upon cooling, and liquid water freezes at low temperature. Each of these is exothermic because each is the reverse of an endothermic phase change. That is, heat is released as a gas condenses to a liquid and as a liquid freezes to a solid. To make ice cubes, for instance, water... 

Movement across a boundary line corresponds to a phase change. The arrows on the figure show six different phase changes sublimation and its reverse, deposition melting and its reverse, freezing and vaporization and its reverse, condensation. 

Carey, Liquid-Vapor Phase-Change Phenomena An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment... 

In pharmaceutical systems, both heat and mass transfer are involved whenever a phase change occurs. Lyophilization (freeze-drying) depends on the solid-vapor phase transition of water induced by the addition of thermal energy to a frozen sample in a controlled manner. Lyophilization is described in detail in Chapter 16. Similarly, the adsorption of water vapor by pharmaceutical solids liberates the heat of condensation, as discussed in Chapter 17. 

If the no-phase-change restriction does not rigorously apply, a simple design procedure can be formulated based on the results discussed in Section III, where it is shown that thermal equilibrium is quickly achieved in gas-liquid systems because of the large heat effects associated with evaporation or condensation. Although the total mass transfer between the phases may be small, it is not unrealistic to assume that the gas and liquid phases have the same temperature at each axial position. 

By comparing Eqs. (71) and (72) to the non-phase-change equations in Section II,A,2, it can be seen that the only additional parameters to be evaluated are rv and rcl, the absolute rates of vaporization and condensation at the gas-liquid interface. The methods for evaluating all parameters in these model equations are given in Section III,D,2. 

The absolute rates of vaporization and condensation are evaluated by using the rate expressions discussed in Section III,B. The net rate of phase change at the bubble interface or equivalently the rate of bubble growth, has been widely studied for single bubbles in stationary systems. Bankoff (B2) has reviewed the results of these studies. Ruckenstein (R2) has analyzed bubble growth in flowing systems. 

The absolute rates of vaporization and condensation are evaluated from the rate expressions given in Section III,B. In the past, the rate of mass transfer (which is the net rate of phase change) has not been calculated from an understanding of the physics of the phase-change process at the interface. The rate is generally evaluated by applying some simplifying assumptions to the process, rather than from an expression in terms of the dependent variables of the model equations. 

In discussing the phase-change problem in this chapter, the discussion has been limited to the process of vaporizing a liquid. Equally important is the process of condensing a vapor. The equations developed in Section III,C can be applied directly to this process. 

It was shown that in heat transfer with phase change it is necessary to understand the phase-change phenomenon on the molecular level to model effectively the mass- and heat-transfer processes. An analytical expression for the rates of vaporization and condensation was developed. It was also shown that the assumption of a saturated vapor phase greatly simplified the calculation without a significant loss in accuracy for given examples. However, experimental verification of this simplified assumption is currently lacking. 

This section describes the phase change process for a single component on a molecular level, with both vaporization and condensation occurring simultaneously. Molecules escape from the liquid surface and enter the bulk vapor phase, whereas other molecules leave the bulk vapor phase by becoming attached to the liquid surface. Analytical expressions are developed for the absolute rates of condensation and vaporization in one-component systems. The net rate of phase change, which is defined as the difference between the absolute rates of vaporization and condensation, represents the rate of mass... 

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