Nonisothermal flow of non-Newtonian fluids in a channel

A study is made of the nonisothermal motion of a rheologically complex fluid in a plane-parallel channel in the case of boundary conditions of the third kind on the outer surfaces of the channel walls and with allowance for the dissipation of mechanical energy and temperature dependence of the coefficients. A qualitative investigation of the problem is made for arbitrary temperature dependence of the yield. Special cases are considered: flow of linear viscoplastic medium and a "power-law" medium with abrupt change with the temperature of the yield point and consistency. It is shown that under certain conditions several different flow regimes can be realized simultaneously in the channel and the change in the flow rate of the medium in a channel with varying temperature of the surrounding medium can exhibit hysteresis.