Viscous heating of high Prandtl number fluids with temperature-dependent viscosity

1986 ◽  
Vol 29 (8) ◽  
pp. 1177-1183 ◽  
Author(s):  
E.R.G. Eckert ◽  
M. Faghri
Keyword(s):  
Prandtl Number ◽  
Viscous Heating ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
High Prandtl Number ◽  
Dependent Viscosity

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.

scholarly journals Analytical shock solutions at large and small Prandtl number

2013 ◽  
Vol 726 ◽  
Author(s):  
B. M. Johnson
Keyword(s):  
Prandtl Number ◽  
Maximum Error ◽  
System Of Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
One Dimensional ◽  
Ideal Gases ◽  
Constant Viscosity ◽  
Dependent Viscosity ◽  
Shock Fronts

AbstractExact one-dimensional solutions to the equations of fluid dynamics are derived in the $\mathit{Pr}\rightarrow \infty $ and $\mathit{Pr}\rightarrow 0$ limits (where $\mathit{Pr}$ is the Prandtl number). The solutions are analogous to the $\mathit{Pr}= 3/ 4$ solution discovered by Becker and analytically capture the profile of shock fronts in ideal gases. The large-$\mathit{Pr}$ solution is very similar to Becker’s solution, differing only by a scale factor. The small-$\mathit{Pr}$ solution is qualitatively different, with an embedded isothermal shock occurring above a critical Mach number. Solutions are derived for constant viscosity and conductivity as well as for the case in which conduction is provided by a radiation field. For a completely general density- and temperature-dependent viscosity and conductivity, the system of equations in all three limits can be reduced to quadrature. The maximum error in the analytical solutions when compared to a numerical integration of the finite-$\mathit{Pr}$ equations is $\mathit{O}({\mathit{Pr}}^{- 1} )$ as $\mathit{Pr}\rightarrow \infty $ and $\mathit{O}(\mathit{Pr})$ as $\mathit{Pr}\rightarrow 0$.

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