The results of the study of fluid flows with viscosities varying considerably as a function of the temperature are presented in the report. The analysis of similarity criteria in the problem of thermoviscous fluid laminar flow in the area with a non-uniform distribution of temperature field is carried out. The hierarchy of mathematical models for the characteristic limiting values of the dimensionless parameters is constructed. The class of problems with non-monotonic dependence of viscosity on temperature is marked out particularly. The media with the abovementioned property are named «abnormally thermoviscous liquids». Examples of numerical analysis of some problems of abnormally thermoviscous liquid flows in channels with heat exchange, porous media, as well as natural convection are given.
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