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.

Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
The Other ◽  
Brinkman Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Properties ◽  
Effects Of Temperature ◽  
Dependent Viscosity

A parametric investigation is carried out on the effects of temperature dependent viscosity and thermal conductivity and of viscous dissipation in simultaneously developing laminar flows of liquids in straight microchannels of constant cross sections. Uniform heat flux boundary conditions are specified at the heated walls. A superposition method is proved to be applicable in order to predict the value of the Nusselt number by considering separately the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity. In addition, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the viscosity and thermal conductivity Pearson numbers and of the Brinkman number.

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.

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.

Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

2012 ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
The Other ◽  
Superposition Method ◽  
Brinkman Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Properties ◽  
Dependent Viscosity

A parametric investigation is carried out on the effects of viscous dissipation and temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Brinkman number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain the correct value of the Nusselt number by considering separately the effects of temperature dependent viscosity and viscous dissipation and those of temperature dependent thermal conductivity. In fact, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant.

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