# Solution of a mathematical model for the concentration of a hexane solution of technical paraffin to obtain its food modification

**DOI: 10.17586/1606-4313-2022-21-2-77-84**

**UDC 665.637.73:531.31:678.049.36:664.31**

## Solution of a mathematical model for the concentration of a hexane solution of technical paraffin to obtain its food modification

**Maryisheva Marina A., Aleksanyan Igor Yu., Nugmanov A.H-H., Maksimenko Yury A., Titova Lyubov M.**

**For citation:**Maryisheva M.A., Alexanyan I.Yu., Nugmanov A.H.-H., Maksimenko Yu.A., Titova L.M. Solution of a mathematical model for the concentration of a hexane solution of technical paraffin to obtain its food modification. Journal of International Academy of Refrigeration. 2022. No 2. p. 77-84. DOI: 10.17586/1606-4313-2022-21-2-77-84

**Abstract**

For pectin-containing film structures, which are used for the production of biodegradable packaging materials and are hydrophilic in nature, their paraffinization, i.e., applying a thin layer of molten food paraffin to the surface of the film for subsequent protection of packaged food products from moisture and sunlight, will reduce the influence of external factors, primarily moisture, To rationalize the convective preconcentration of a hexane solution, it is necessary to select such regime parameters that will allow not only the removal of hexane with toxic components dissolved in it from the object of study in a relatively simple apparatus, but also significantly reduce the time for the process within temperature restrictions. The latter condition, in view of the complexity of the empirical determination of the temperature distribution in a thin layer of the object of concentration, is advisable to implement by solving the system of equations for the transfer of thermal energy and mass in partial derivatives, however, we can restrict ourselves to one equation for the transfer of thermal energy, using empirical kinetic dependences that describe the removal of n-hexane from the composition. The aim of the study was to adapt paraffin to a hexane solution and solve the model of heat and mass transfer during its concentration in order to exclude the possibility of reducing its temperature below the value of possible preliminary crystallization. The model was implemented numerically by the finite difference method. As a result of the solution, the intensity of the temperature front advancement along the height of the film of the hexanoparaffin composition was found with varying the proportion of paraffin in the process of its concentration with convective supply of thermal energy to it, i.e., it was adapted to the resulting solution and a mathematical model of heat and mass transfer was solved during its concentration to eliminate the likelihood of a decrease in its temperature below the value of possible pre-crystallization. The data obtained do not conflict with the known results of other researchers and can be successfully used for operational calculation and design of the designated processes and units.

**Keywords:**hexanoparaffin mixture, convective preconcentration, water-repellent coatings, paraffinization, edible paraffin, mathematical modeling, temperature restrictions.

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