Creation of mathematical model of extraction by cheese whey from a lupine in the form of a plate

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Prerequisites for creation of model are stated. At a problem definition consideration of a particle of a lupine as unlimited plate is proved. The main assumptions are formulated, regional conditions are written out. Partial solutions of the differential equation, and also the common decision for the current value of a concentration pressure С'( x,у ). Distribution of concentration is symmetric concerning ordinate axis. Final expression for a field of concentration at extraction of a flat plate in a dimensionless look is written out. It is shown that distribution of concentration is rather precisely described by the first member of a row. The conclusion is drawn that for any timepoint under the set boundary conditions the field of concentration has an appearance of a symmetric curve with a maximum on a plate axis (Х=0). For each subsequent timepoint there will be the curve which is monotonously decreasing to a plate surface. It is proved that it is possible to define nature of change of concentration in a body at a preset value the case when strives for infinity at the set physical parameters, thickness of a plate and the organization of high intensity of branch of extractive substances from a surface Is considered. For this case the equations of rather dimensionless concentration and Fourier's number are received. Also the equation for definition of final time of extraction is written out. It is shown that the received solutions of the equations of model are found in a good consent with experimental data.


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