Fluid process correlation

For non-Newtonian fluids the correlations in Figure 35 can be used with generally acceptable accuracy when the process fluid viscosity is replaced by the apparent viscosity. For non-Newtonian fluids having power law behavior, the apparent viscosity can be obtained from shear rate estimated by... 

Note that Equation (c) has two variables D and Ap. However, they are related through a fluid flow correlation as follows (part of the process model) ... 

This is a fruitful approach, and much of what follows concerns the development and use of such flow models. The parameters of these models are correlatable with physical properties of the fluid, vessel geometry, and flow rate once such correlations are found for all types of fluid processing, performance predictions can be obtained without resort to experimentation. 

There are three main approaches to model compartment fires [2,3]. The simplest is to use the basic expressions and experimental correlations of the thermochemical and fluid processes occurring to produce an analytical model of the fire development. Analytical fire models are fast to set up and easy to use, because of the few mechanisms involved [2] however, the results are only correct in the order of magnitude, because coupling of the different fire phenomena is difficult in these models. Nevertheless, they can serve as a baseline for more sophisticated computer modeling. 

Darcy s law describes the filtration processes, correlating variables of interest according to equation 2.1. The velocity of the fluid that passes through the filter medium can be determined by equation 2.2. ... 

Slurry Viscosity. Viscosities of magnesium hydroxide slurries are determined by the Brookfield Viscometer in which viscosity is measured using various combinations of spindles and spindle speeds, or other common methods of viscometry. Viscosity decreases with increasing rate of shear. Fluids, such as magnesium hydroxide slurry, that exhibit this type of rheological behavior are termed pseudoplastic. The viscosities obtained can be correlated with product or process parameters. Details of viscosity deterrnination for slurries are well covered in the Hterature (85,86). 

Additional complications can occur if the mode of deformation of the material in the process differs from that of the measurement method. Most fluid rheology measurements are made under shear. If the material is extended, broken into droplets, or drawn into filaments, the extensional viscosity may be a more appropriate quantity for correlation with performance. This is the case in the parting nip of a roUer in which filamenting paint can cause roUer spatter if the extensional viscosity exceeds certain limits (109). In a number of cases shear stress is the key factor rather than shear rate, and controlled stress measurements are necessary. 

Minimum Fluidizing Velocity U,nj, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one of the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen audYu [A.l.Ch.E.j., 610-612 (1966)] given below can then be used to back calculate d. This gives a particle size that takes into account effects of size distribution and sphericity. The correlation can then be used to estimate U, at process conditions, if U,nj cannot be determined experimentally, use the expression below directly. 

Heating or cooling of process fluids in a batch-operated vessel is common in the chemical process industries. The process is unsteady state in nature because the heat flow and/or the temperature vary with time at a fixed point. The time required for the heat transfer can be modified, by increasing the agitation of the batch fluid, the rate of circulation of the heat transfer medium in a jacket and/or coil, or the heat transfer area. Bondy and Lippa [45] and Dream [46] have compiled a collection of correlations of heat transfer coefficients in agitated vessels. Batch processes are sometimes disadvantageous because ... 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

The flow of compressible and non-compressible liquids, gases, vapors, suspensions, slurries and many other fluid systems has received sufficient study to allow definite evaluation of conditions for a variety of process situations for Newtonian fluids. For the non-Newtonian fluids, considerable data is available. However, its correlation is not as broad in application, due to the significant influence of physical and rheological properties. This presentation is limited to Newtonian systems, except where noted. 

Since the process is more complex, the proposed method may not be valid for scale-up calculation. The combination of power and Reynolds number was the next step for correlating power and fluid-flow dimensionless number, which was to define power number as a function of the Reynolds number. In fact, the study by Rushton summarised various geometries of impellers, as his findings were plotted as dimensionless power input versus impeller... 

Celata GP (ed) (2004) Heat transfer and fluid flow in micro-channels. Bergel, New York Chen JC (1966) Correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Process Des Dev 5 322-329... 

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... 

Esterbauer et al. (1991) have demonstrated that /3-carotene becomes an effective antioxidant after the depletion of vitamin E. Our studies of LDL isolated from matched rheumatoid serum and synovial fluid demonstrate a depletion of /8-carotene (Section 2.2.2.2). Oncley et al. (1952) stated that the progressive changes in the absorption spectra of LDL were correlated with the autooxidation of constituent fatty acids, the auto-oxidation being the most likely cause of carotenoid degradation. The observation that /3-carotene levels in synovial fluid LDL are lower than those of matched plasma LDL (Section 2.2.2) is interesting in that /3-carotene functions as the most effective antioxidant under conditions of low fOi (Burton and Traber, 1990). As discussed above (Section 2.1.3), the rheumatoid joint is both hypoxic and acidotic. We have also found that the concentration of vitamin E is markedly diminished in synovial fluid from inflamed joints when compared to matched plasma samples (Fairburn etal., 1992). This difference could not be accounted for by the lower concentrations of lipids and lipoproteins within synovial fluid. The low levels of both vitamin E and /3-carotene in rheumatoid synovial fluid are consistent with the consumption of lipid-soluble antioxidants within the arthritic joint due to their role in terminating the process of lipid peroxidation (Fairburn et al., 1992). 

Chen, J. C., 1966, A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow, Ind Eng. Chem., Process Design and Dev. 5 322. (4)... 

From this discussion of parameter evaluation, it can be seen that more research must be done on the prediction of the flow patterns in liquid-liquid systems and on the development of methods for calculating the resulting holdups, pressure drop, interfacial area, and drop size. Future heat-transfer studies must be based on an understanding of the fluid mechanics so that more accurate correlations can be formulated for evaluating the interfacial and wall heat-transfer coefficients and the Peclet numbers. Equations (30) should provide a basis for analyzing the heat-transfer processes in Regime IV. 

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