Convection two-phase

No and Kazimi (1982) derived the wall heat transfer coefficient for the forced-convective two-phase flow of sodium by using the momentum-heat transfer analogy and a logarithmic velocity distribution in the liquid film. The final form of their correlation is expressed in terms of the Nusselt number based on the bulk liquid temperature, Nuft ... 

Single-phase convection Single-phase convection Two-phase convection Combined convection on both sides on one side, two-phase on both sides and radiative heat transfer... 

Influence of Chemical Reactions on Uq and When a chemical reaction occurs, the transfer rate may be influenced by the chemical reac tion as well as by the purely physical processes of diffusion and convection within the two phases. Since this situation is common in gas absorption, gas absorption will be the focus of this discussion. One must consider the impacts of chemical equilibrium and reac tion kinetics on the absorption rate in addition to accounting for the effec ts of gas solubility, diffusivity, and system hydrodynamics. 

When a gas reacts with a solid, heat will be transfened from the solid to the gas when the reaction is exothermic, and from gas to solid during an endothermic reaction. The energy which is generated will be distributed between the gas and solid phases according to the temperature difference between the two phases, and their respective thermal conductivities. If the surface temperature of the solid is T2 at any given instant, and that of the bulk of the gas phase is Ti, the rate of convective heat transfer from the solid to the gas may be represented by the equation... 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

C4. Clerici, G. C., Garriba, S., Sala, R., and Tozzi, A., A catalogue of the commonest burn-out correlations for forced convection in the quality region, paper presented at Symp. Boiling and Two-Phase Flow, EURATOM, ISPRA, June, 1966. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

The important reason for the quasi-steady-state approach arises from the difficulty in obtaining a solution to the transient convection problem for two-phase situations. 

The detail experimental study of flow boiling heat transfer in two-phase heat sinks was performed by Qu and Mudawar (2003b). It was shown that the saturated flow boiling heat transfer coefficient in a micro-channel heat sink is a strong function of mass velocity and depends only weakly on the heat flux. This result, as well as the results by Lee and Lee (2001b), indicates that the dominant mechanism for water micro-channel heat sinks is forced convective boiling but not nucleate boiling. 

Yen T-H, Kasagi N, Suzuki Y (2003) Forced convective boiling heat transfer in micro-tubes at low mass and heat fluxes. Int J Multiphase Flow 29 1771-1792 Yu W, France DM, Wambsganss MW, Hull JR (2002) Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. Int J Multiphase Flow 28 927-941... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Eq. (132) states that the interfacial tension has to be balanced by a pressure difference between the two phases. The terms containing derivatives of crin Eqs. (133) and (134) are non-zero only if there are local variations of the interfacial tension, which might be due to differences in concentration or temperature. The flow induced by such an effect is known as Marangoni convection. 

The convective boiling coefficient lijc can be estimated using the equations for singlephase forced-convection heat transfer modified by a factor fc to account for the effects of two-phase flow ... 

This method uses simple, unsophisticated, methods to estimate the two-phase pressure drop through the exchanger and piping, and the convective boiling heat transfer coefficient. The calculation procedure is set out below and illustrated in Example 12.11... 

Figure 4.11 Regions of two-phase forced-convective heat transfer as a function of quality with increasing heat flux as ordinate. (From Collier and Thome, 1994. Copyright 1994 by Oxford University Press, New York. Reprinted with permission.)...

Borishansky, V. M., and I. I. Paleev, Eds., 1964, Convective Heat Transfer in Two-Phase and One-Phase Flows, transl. from Russian-Israeli Program for Scientific Translation, U.S. Dept, of Commerce, Washington, DC, 1969. (4)... 

Hancox, W. T., and W. B. Nicoll, 1971, A General Technique for the Prediction of Void Distributions in Non-Steady Two-Phase Forced Convection, Int. J. Heat Mass Transfer 14 1377 1394. (3) Haramura, Y., and Y. Katto, 1983, A New Hydrodynamic Model of CHF Applicable Widely to Both Pool and Forced Convection Boiling on Submerged Bodies in Saturated Liquids, Int. J. Heat Mass Transfer 26(3) 387 399. (2)... 

Macbeth, R. V., 1963b, Forced Convection Burnout in Simple, Uniformly Heated Channels A Detailed Analysis of World Data, European Atomic Energy Community Symp. on Two Phase Flow, Steady State Burnout and Hydrodynamic Instability, Stockholm, Sweden. (5)... 

Stenning, A. H., and T. N. Veziroglu, 1967, Oscillations in Two-Component, Two-Phase Flow, Vol. 1, NASA CR-72121 and Flow Oscillations in Forced Convective Boiling, Vol. 2, NASA CR-72122, University of Miami, Coral Gables, FL. (6)... 

Whalley, P. B., P. Hutchinson, and G. F. Hewitt, 1973, The Calculation of Critical Heat Flux in Forced Convective Boiling, Rep. AERE-R-7520, European Two Phase Flow Group Meeting, Brussels. (5) Whalley, P. B., P. Hutchinson, and G. F. Hewitt, 1974, The Calculation of Critical Heat Flux in Forced Convection Boiling, Heat Transfer 1974, vol. IV, pp. 290-294, Int. Heat Transfer Conf., Tokyo. (5) Wichner, R. P, and H. W. Hoffman, 1965, Pressure Drop with Forced Convection Boiling of Potassium, Proc. Conf. on Applications of Heat Transfer Instrumentation to Liquid Metals Experiments, ANL-7100, p. 535, Argonne National Lab., Argonne, IL. (3)... 

The wall heat flux qmi cannot be evaluated as in Section II,B. Numerous experimental studies on heat transfer in this two-phase forced-convection region have been carried out, and the results of these investigations are usually presented in the form of a correlation for the wall heat-transfer coefficient hmi, which is defined as in Eq. (32b). Most of these correlations fit one of two generalized forms. The first is... 

The values of the constants that have been determined by various researchers are given in Table III. In all cases Eq. (76) is based on data from both the nucleate boiling and the two-phase forced-convection regions. 

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