scholarly journals Viscous heating effects in fluids with temperature-dependent viscosity: triggering of secondary flows

2005 ◽  
Vol 540 (-1) ◽  
pp. 21 ◽  
Author(s):  
A. COSTA ◽  
G. MACEDONIO
Keyword(s):  
Secondary Flows ◽  
Viscous Heating ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Heating Effects ◽  
Dependent Viscosity

scholarly journals Viscous heating in fluids with temperature-dependent viscosity: implications for magma flows

2003 ◽  
Vol 10 (6) ◽  
pp. 545-555 ◽  
Author(s):  
A. Costa ◽  
G. Macedonio
Keyword(s):  
Plug Flow ◽  
Practical Interest ◽  
Viscous Friction ◽  
Secondary Flows ◽  
Viscous Heating ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Magma Flow ◽  
Energy And Momentum ◽  
Dependent Viscosity

Abstract. Viscous heating plays an important role in the dynamics of fluids with strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction produces a local temperature increase near the tube walls with a consequent decrease of the viscosity which may dramatically change the temperature and velocity profiles. These processes are mainly controlled by the Peclét number, the Nahme number, the flow rate and the thermal boundary conditions. The problem of viscous heating in fluids was investigated in the past for its practical interest in the polymer industry, and was invoked to explain some rheological behaviours of silicate melts, but was not completely applied to study magma flows. In this paper we focus on the thermal and mechanical effects caused by viscous heating in tubes of finite lengths. We find that in magma flows at high Nahme number and typical flow rates, viscous heating is responsible for the evolution from Poiseuille flow, with a uniform temperature distribution at the inlet, to a plug flow with a hotter layer near the walls. When the temperature gradients  induced by viscous heating are very pronounced, local instabilities may occur and the triggering of secondary flows is possible. For completeness, this paper also describes magma flow in infinitely long tubes both at steady state and in transient phase.

Extensional flows with viscous heating

2007 ◽  
Vol 571 ◽  
pp. 359-370 ◽  
Author(s):  
JONATHAN J. WYLIE ◽  
HUAXIONG HUANG
Keyword(s):  
Critical Value ◽  
The Other ◽  
Viscous Heating ◽  
Constant Force ◽  
Temperature Dependent ◽  
Downstream Location ◽  
Temperature Dependent Viscosity ◽  
Pulling Forces ◽  
Extensional Flows ◽  
Dependent Viscosity

In this paper we investigate the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. We show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We first consider steady drawing of a thread that is fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling forces above a critical value, we show that inertialess solutions cannot exist and inertia is crucial in controlling the dynamics. We also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension at pinching.

A numerical study of solidification and viscous dissipation effects on polymer melt flow in plane channels

2013 ◽  
Vol 33 (2) ◽  
pp. 95-110
Author(s):  
Mustafa Tutar ◽  
Ali Karakus
Keyword(s):  
Shear Rate ◽  
Phase Change ◽  
Viscous Dissipation ◽  
Polymer Melt ◽  
Viscous Heating ◽  
Transient Phase ◽  
Melt Flow ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Abstract The combined effects of solidification and viscous dissipation on the hydrodynamic and thermal behavior of polymer melt flow during the injection process in a straight plane channel of constant cross section are numerically studied by considering the shear-rate and temperature-dependent viscosity and transient-phase change behavior. A numerical finite volume method, in conjunction with a modified form of the Cross constitutive equation to account for shear rate, temperature-dependent viscosity changes and a slightly modified form of the method proposed by Voller and Prakash to account for solidification of the liquid phase, is used and a validation with an analytical solution is presented for viscous heating effects. The hydrodynamic and solidified layers growth under the influence of a transient phase-change process and viscous dissipation, are analyzed for a commercial polymer melt flow, polypropylene (PP) for different parametric conditions namely, inflow velocity, polymer injection (inflow) temperature, the channel wall temperature, and the channel height. The results demonstrate that the proposed numerical formulations, including conjugate effects of viscous heating and transient-solidification on the present thermal transport process, can provide an accurate and realistic representation of polymer melt flow behavior during the injection molding process in plane channels with less simplifying assumptions.

STATIONARY SOLUTIONS TO A QUASI-NEWTONIAN FLOW WITH VISCOUS HEATING

1995 ◽  
Vol 05 (06) ◽  
pp. 725-738 ◽  
Author(s):  
JACQUES BARANGER ◽  
ANDRO MIKELIĆ
Keyword(s):  
Negative Temperature ◽  
Stationary Flow ◽  
Finite Energy ◽  
Stationary Solutions ◽  
Viscous Heating ◽  
System Of Equations ◽  
Temperature Dependent ◽  
Newtonian Flow ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

System of equations describing the stationary flow of a quasi-Newtonian fluid, with temperature-dependent viscosity and with a viscous heating, is considered. Existence of at least one appropriate weak solution is proved, i.e. we get existence of at least one velocity field having finite energy and existence of a non-negative temperature field. Its regularity is a consequence of the L1-forcing term generated by the viscous heating.

Nonlinear equilibrium solutions for the channel flow of fluid with temperature-dependent viscosity

2000 ◽  
Vol 406 ◽  
pp. 1-26 ◽  
Author(s):  
D. P. WALL ◽  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Critical Reynolds Number ◽  
Isothermal Flow ◽  
Basic Flow ◽  
Secondary Flows ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Viscosity Models ◽  
Dependent Viscosity

The nonlinear stability of the channel flow of fluid with temperature-dependent viscosity is considered for the case of vanishing Péclet number for two viscosity models, μ(T), which vary monotonically with temperature, T. In each case the basic state is found to lose stability from the linear critical point in a subcritical Hopf bifurcation. We find two-dimensional nonlinear time-periodic flows that arise from these bifurcations. The disturbance to the basic flow has wavy streamlines meandering between a sequence of triangular-shaped vortices, with this pattern skewing towards the channel wall which the basic flow skews towards. For each of these secondary flows we identify a nonlinear critical Reynolds number (based on half-channel width and viscosity at one of the fixed wall temperatures) which represents the minimum Reynolds number at which a secondary flow may exist. In contrast to the results for the linear critical Reynolds number, the precise form of μ(T) is not found to be qualitatively important in determining the stability of the thermal flow relative to the isothermal flow. For the viscosity models considered here, we find that the secondary flow is destabilized relative to the corresponding isothermal flow when μ(T) decreases and vice versa. However, if we remove the bulk effect of the non-uniform change in viscosity by introducing a Reynolds number based on average viscosity, it is found that the form of μ(T) is important in determining whether the thermal secondary flow is stabilized or destabilized relative to the corresponding isothermal flow. We also consider the linear stability of the secondary flows and find that the most unstable modes are either superharmonic or subharmonic. All secondary disturbance modes are ultimately damped as the Floquet parameter in the spanwise direction increases, and the last mode to be damped is always a phase-locked subharmonic mode. None of the secondary flows is found to be stable to all secondary disturbance modes. Possible bifurcation points for tertiary flows are also identified.

Sign in / Sign up

Export Citation Format

Share Document