Prediction of Flux

Chen Y, Vayuhauwan P, Matheson LE (1996) Prediction of flux through polydimethylsiloxane membranes using atomic charge calculations application to an extended data set. Int J Pharm 137 149-158. 

It is interesting to note in Table II that, although theoretical prediction of flux agrees well with experimental values at applied pressures above 1.0 x 10 N/m, at lower pressures experimental flux is substantially over predicted by theory. 

S. Boerlage, M. Kennedy, A. Bonne Paul, G. Galjaard and J. Schippers, Prediction of flux decline in membrane systems due to particulate fouling. Desalination, 113 (1997)231-233. 

Wicke-Kallenbach experiment would incorrectly predict the flux in the second experiment if used in a simple Fick equation of the form (10.31). However, if the isobaric flux measurements had been interpreted in terms of... 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

In addition to material balance, two transport equations can be used to predict the flux of water and solute. For instance, the following simplified model can be used (Dandavati etai, 1975 Evangelista, 1986). 

A lower max response at resonance was noted for poly butadiene-acrylic acid-containing pro-pints compared with polyurethane-containing opaque proplnts. Comparison of the measured response functions with predictions of theoretical models, which were modified to consider radiant-heat flux effects for translucent proplnts rather than pressure perturbations, suggest general agreement between theory and expt. The technique is suggested for study of the effects of proplnt-formulation variations on solid-proplnt combustion dynamics... 

Price (P9) has also investigated the ignition characteristics of JPN, a double-base propellant, in an arc-imaging furnace. Price s data show agreement with the predictions of Eq. (8b) for heat fluxes below 1.5 cal/cm2-sec. Above this flux level, the data deviated from the theoretical predictions. 

L7. Levy, S., Prediction of the critical heat flux in forced convection flow, GEAP-3961... 

The temperature distribution in the flow direction for a fixed flow rate differs for different devices. This suggests that the heat transfer mechanism in these devices is not identical. The non-uniform (of about 20%) heat flux leads to conditions at which the wall temperature increases sharply. Idealizing the heat flux as uniform can result in a significant error in prediction of the temperature distribution. 

Zhao YH, Masuoka T, Tsuruta T (2002) Unified theoretical prediction of fully developed nucleate boiling and critical heat flux based on a dynamic microlayer model. Int J Heat Mass Transfer 45 3189-3197... 

Models for Prediction of Incipient Boiling Heat Flux and Wall Superheat... 

A theoretical model for the prediction of the critical heat flux of refrigerants flowing in heated, round micro-channels has been developed by Revellin and Thome (2008). The model is based on the two-phase conservation equations and includes the effect of the height of the interfacial waves of the annular film. Validation has been carried out by comparing the model with experimental results presented by Wojtan et al. (2006), Qu and Mudawar (2004), Bowers and Mudawar (1994), Lazareck and Black (1982). More than 96% of the data for water and R-113, R-134a, R-245fa were predicted within 20%. 

ReveUin R, Thome J. (2008) A theoretical model for the prediction of the critical hat flux in heated micro-channel. Int. J. Heat and Mass Transfer 51 1216-1225 Roach GM, Abdel-Khahk SI, Ghiaasiaan SM, Dowling MF, Jeter SM (1999) Low-flow critical heat flux in heated microchannels. Nucl Sd Eng 131 411 25 Robinson AJ, Judd RL (2001) Bubble growth in a uniform and spatially distributed temperature field. Int J Heat Mass Transfer 44 2699-2710... 

What are called physiologically based pharmacokinetic (PBPK) and pharmacodynamic (PBPD) models are more mechanistically complex and often include more compartments, more parameters, and more detailed expressions of rates and fluxes and contain more mechanistic representation. This type of model is reviewed in more detail in Section 22.5. Here, we merely classify such models and note several characteristics. PBPK models have more parameters, are more mechanistic, can exploit a wider range of data, often represent the whole body, and can be used both to describe and interpolate as well as to predict and extrapolate. Complexity of such models ranges from moderate to high. They typically contain 10 or more compartments, and can range to hundreds. The increase in the number of flux relationships between compartments and the related parameters is often more than proportional to compartment count. 

The flux, and hence the permeance and permeability, can be defined on the basis of volume, mass or molar flowrates. The accurate prediction of permeabilities is generally not possible and experimental values must be used. Permeability generally increases with increasing temperature. Taking a ratio of two permeabilities defines an ideal separation factor or selectivity awhich is defined as ... 

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