Three-dimensional model of non-Newtonian fluid flow in the rectangular channel

Introduction. The three-dimensional mathematical model of non-Newtonian fluid flow was introduced, with viscosity that depends of shear velocity in rectangular channels of food equipment. Materials and methods. Applying the method of superposition allows to build a field of longitudinal flow of non-Newtonian fluid in rectangular channel of technological equipment with moving borders and thus to define values of velocity and pressure at any point inside the channel. Results and discussion. We developed a model of longitudinal flow of non-Newtonian fluid in rectangular channels on borders of which different longitudinal velocities are set. The model is based on the solution of one-dimensional problem of the Couette flow in the channel The composition of flows in the slit channels with mutually perpendicular pair of borders allows to receive a flow rate formula which satisfies the principle of limit correspondence between the currents in a rectangular and slit channels We suggest a method of construction of the velocity field which is a subdivision of the final section of the channel into sections with a different dependence on the coordinates so that in some areas the velocity depends only on a single coordinate, while in others - only on the other coordinate. We obtain the equations of lines delimiting these areas, and how to determine the shape of boundaries. Conclusion. The analytical formulas allow defining macrokinetic characteristics of each channel at the boundary with arbitrary distribution of velocities of the flow of non-Newtonian fluid the viscosity of which depends on the shear speed.