The problem of developing of highly digestible compound feeds with protected protein for cattle is due to the specifics of the gastric tract of cows and the peculiarities of protein assimilation. Due to the importance of preliminary moisture-heat treatment of grain for the subsequent course of the extrusion process, it was carried out by steam at a pressure of 0.6 МРа before moistening the feed to a humidity of 17–20% and heating to a temperature of 70–80° C. It is established that heat treatment has a significant effect on the carbohydrate complex of grain: heating it at high temperatures causes the destruction of starch, accompanied by the formation of easily soluble carbohydrates, which has a positive effect on the digestibility of feed. The kinetic regularities of the processes of moisture-heat treatment, grinding and extrusion of grain in the production of highly digestible feed with protected protein for cattle were studied. The degree of dextrinization and the digestibility of starch increased with the heating temperature of corn and its mixtures with wheat up to 100–110° C, when the performance of the extruder was 300–320 kg/h, the digestibility of starch extruded corn and grain mixture is increased to 85 and 68 mg of glucose per 1 g of the product (hereinafter mg/g), respectively. For wheat, this indicator is lower and, accordingly, is 50 mg/g. When heated during the extrusion of corn to a temperature of up to 120–140° C, the digestibility of starch was 100–110 mg/g, and for the grain mixture – 80–83 mg/g. At this temperature, the digestibility of the starch of extruded wheat corresponded to 60–65 mg/g. The optimal moisture content of feed in the process of extrusion for the purpose of forming pellets is 18%. Studies of the extrusion effect on the carbohydrate complex of processed feed have shown that the destruction of starch in the extruded product increases. Thus, the content of soluble carbohydrates increases by 27–32%, and the digestibility of starch increases twice in extruded feed compared to unprocessed.

The equations of motion, the equation of continuity, the equation of energy (heat balance), the rheological equation were chosen to describe the non-isothermal flow of the cereals melt in the extruder as the initial equations. The following assumptions were made to solve the model: the flow of a moving viscous medium is assumed to be laminar and steady; the forces of inertia and gravity are so small compared to the forces of friction and pressure that they can be neglected; a viscous medium (melt) is an incompressible liquid characterized by constant thermal conductivity and thermal diffusivity; the change in thermal conductivity in the longitudinal direction was neglected due to the fact that convective heat transfer in the flow direction is higher than the heat transfer by thermal conductivity; heat transfer in the direction perpendicular to the flow of the melt occurs only due to thermal conductivity. The numerical finite difference method was used to solve a system of equations taking into account convective heat transfer. Its essence of use lies in the fact that the considered area (extruder channel) is divided into calculated cells using a grid. The grid consisted of rectangular cells with a constant step between nodes, which exactly lie on the boundaries of the integration region. In this case, the differential equations were transformed into difference equations by replacing the derivatives at a point with finite differences along the cell boundaries. The mathematical model of non-isothermal melt flow in the extruder channel was obtained as a result of the solution. To solve a mathematical model of the process of grain crops extrusion with a non-isothermal flow of their melts, a program in the algorithmic language C ++ was compiled. A non-isothermal mathematical model of the process of extrusion of grain crops at temperatures of the beginning of the Maillard reaction, i.e., up to 120–125 ?, was obtained. It allows us to identify the nature of the temperature change along the length of the extruder. Comparative analysis of the results of the numerical solution and experimental data showed good convergence: the standard deviation did not exceed 12.7%.