Nonisothermal structural regime of motion of a nonlinear viscoplastic medium in a plane channel

Abstract

The motions of Newtonian and non-Newtonian media with consideration of the heat of friction and temperature dependence of the rheological characteristics of the medium have been examined by many authors [1–6]. A detailed bibliography of these works is given in [3, 5], In the dissertation of one of the authors* an attempt was made to investigate heat transfer during movement of a nonlinear viscoplastic medium with consideration of the temperature dependence of plastic viscosity at a constant value of the ultimate shear stress to. The last assumption is not always justified, since more often cases are found when not only plastic viscosity but also the ultimate shear stress changes with change in temperature. In this article we will examine the effect of the heat of internal friction with consideration of the temperature dependence of plastic viscosity and ultimate shear stress on the hydraulic characteristics of a laminar regime of motion in a plane channel of nonlinear viscoplastic media whose rheological behavior is described by the generalized Casson equation [5]. The upper and lower estimates are found for nonlinear differential equations describing the indicated processes.