HEAT EXCHANGE EQUATION DURING THE FLOW OF NON-NEWTONIAN LIQUIDS IN TECHNOLOGICAL EQUIPMENT CHANNELS

In this article we considered the processes of heat exchange in the channels of technological equipment in the cases that are most common in machines and apparatus of the chemical and food industries. In the first case, the external environment is considered to be an infinite heat tank with a given temperature. In the second case, the role of the external environment is performed by the channel with a moving heat carrier, while the temperature of the heat carrier is not set and varies along the length of the channel. The heat transfer equation includes convective terms and terms with thermal conductivity. We formulated the heat exchange equation for the flow of non-Newtonian (viscoplastic and generalized-shifted) fluids. It is determined that: during the flow of generalized-shifted fluid in a flat channel with set wall temperatures it is necessary to define two heat transfer coefficients; in the flat channel immersed in the heat tank - four heat transfer coefficients; in the flat channel surrounded by a bypass channel eight heat transfer coefficients. When describing heat transfer with a rectangular channel, for all these cases, it is necessary to determine respectively four, eight and sixteen heat transfer coefficients. During the flow of viscoplastic fluid, it is necessary to determine: in the flat channel with the set wall temperatures - four heat transfer coefficients; in the channel immersed in the heat tank - six heat transfer coefficients; in the channel surrounded by a bypass channel - ten heat transfer coefficients. When describing the heat transfer of a flow in a rectangular channel for the same cases, it is necessary to define respectively eight, twelve and twenty heat transfer coefficients. The heat exchange equations are a system of first-order differential equations in finite differences for the temperature of the liquid in the channel. And this is their main difference from the calculations for the cases of fixed temperatures on the walls of the straight channel and the immersion of the straight channel in the heat tank with a fixed temperature. It is shown that the fluid temperature depends on the longitudinal coordinate along the channel. In this case, the dependence of temperature on the geometric characteristics of the channel is determined by the cross-sectional area of the channel and its perimeter, as well as the ratio of geometric dimensions (width, height and length) of the channel. When performing engineering calculations, the obtained expressions allow to determine the corresponding coefficients of convective heat transfer and heat transfer during the flow of non-Newtonian fluids in the channels and with the external environment.