Using a Numerical Model

This way of working is surely the easiest one, but only when the model is perfectly built. 

It is necessary when reading the instructions of the model to find the equation upon which it is based. For example, a model built only by using Equation 1.34 obtained with an infinite value of the coefficient of convection is a very poor model the accuracy of the value determined for the diffusivity can be appreciated by comparing the kinetics curves obtained either by calculation with the model or by plotting the experimental data. Moreover, the kinetics curves would be expressed preferably either in terms of time or by using the square root of time, and be drawn with an expanded scale of time. 

in the valuable model, the kinetics of release of the additives is expressed by Equation (1.52), while the amount of the additive in the liquid is obtained from the value of the concentration measured at any time t in the liquid, by the obvious relationship  

the kinetics of release of the additives should be determined by following the increase in the concentration of this additive in the liquid. 

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DATA ANALYSIS USING A NUMERICAL MODEL AND PARAMETER ESTIMATION TECHNIQUES... 

Meroney and Neff 1984 To calculate the behavior of heavy and cold gas clouds subject to dilution by a water spray curtain, using a numerical model. Work included model validation. Variations in curtain position, spray entrainment velocity, wind speed and source conditions resulted in a wide range of spray-curtain performances. 

For this aim, we use a numerical model which is on the one hand to some degree physical, and on the other hand simple enough that it allows to perform long simulations. The basic version of the model consists of a segmented two-dimensional strike-slip fault in a three-dimensional elastic half space and is inherently discrete, because it does not arise from discretizing a continuous model. 

Milliman et al. (1999) postulated an enormous loss of CaCOj in the upper water column for, to date, unknown reasons. Jansen et al. (2002) used a numerical model in order to investigate and predict, whether such a loss could be attributed to... 

Popovic Z.B., Khot U.N., Novaro G.M., Casas E, Greenberg N.L., Garcia M.J., Francis G.S., and Thomas J.D. 2005. Effects of sodium nitroprusside in aortic stenosis associated with severe heart failure pressure-volume loop analysis using a numerical model. Am. J. Physiol. Heart Circ. Physiol. 288(1) H416-23. Epub 2004 Sep 2. 

During a spill where the travel time is as long as that here, potential for unsteadiness of the river flow exists. If appreciable unsteadiness were expected, e.g., due to heavy rains, the best way to proceed would generally be to use a numerical model, such as the MIT model (75), or similar ones. Of course, a conservative estimate of concentrations can be made by neglecting the expected additional dilution. However, account would have to be taken of the decreased time of travel to downstream locations of interest, for example, fish hatcheries or water intakes. Not only would the material reach those points faster at higher flows, but the decreased time would result in less decay for nonconservative substances. 

This analysis was carried out using a numerical model to calculate the disturbing and restoring forces on each conveyance as it travelled the length of wind, subjected to the specific ventilation conditions within the L7 shaft. The characteristics of the supplied conveyances... 

Using a numerical model, taking into account not only the diffusivity but also the coefficient of convection. 

The results are expressed either in terms of the profiles of temperature developed through the thickness of the PET bottle and of the mould or in terms of mass transfer of the additive through the thickness of the bottle. The following figures are drawn, as they are obtained from calculation using a numerical model ... 

The following figures are obtained from calculation using a numerical model taking all the above facts into account ... 

In order to use a numerical model to predict flow behaviour with real yam packages, which are typically anisotropic, some means of predicting the package permeability distribution is required. In general, this parameter will be a complex... 

The situation is even more complex when viscous dissipation and the release of the crystallization enthalpy are taken into account. For pressure-driven flows, where the shear rate varies from the core to the wall of the flow channel, the flow becomes nonisothermal and a locally increased temperature can reduce the flow effects, since the characteristic relaxation times, and thus the Weissenberg number, will decrease. This might lead to cases where a stronger flow has less effect on the formation of oriented crystalline structures. These cases can only be analyzed by using a numerical model, as for example a finite element code, that includes all physical aspects of the problem [11,72-77]. 

Calculations using a numerical model for the kinetics and mechanism of ammonia synthesis show that the reaction orders and activation energy in this model are not constant but show some dependence on the reaction conditions for the catalyst [396],... 

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