Study of the influence of temperature dependent viscosity on fluid flow in annular channels

Abstract

For all liquids, a change in viscosity depending on temperature is characteristic. In most cases, this dependency is commonly overlooked; however, when studying the flow of liquids under conditions of intense heat exchange, the temperature-dependent viscosity can have a significant impact on mass and heat transfer processes. It should be noted that for some liquids, such as polymer solutions or biological fluids, the temperature dependence of viscosity can be extremely complex and nonlinear. In such cases, ignoring this dependence can lead to inaccurate results and errors. Annular channels find wide applications in various technical systems, including heat exchangers and hydraulic devices. Understanding the factors influencing the fluid flow and discharge in such channels is a key aspect of optimizing their design and operation. One of the main factors influencing the flow process and fluid discharge in annular channels is the temperature-dependent viscosity of the fluid. This work investigates the influence of the thermo-viscous parameter with monotonic and non-monotonic temperature-dependent viscosity, as well as the geometric parameter of the annular channel on the fluid flow process and discharge. The mathematical model includes the continuity equation, Navier-Stokes equations, and the temperature equation. The method of control volume and the SIMPLE algorithm, modified to account for the variable viscosity coefficient, were applied for the numerical solution of these equations. It is shown that in the case of liquid flow in an annular channel with a monotonic dependence of viscosity on temperature, the steady-state discharge closely approaches the discharge at maximum viscosity. However, in the case of a liquid with non-monotonic viscosity dependence on temperature, the discharge significantly depends on the thermo-viscous parameter.