The linear stability of channel flow of fluid with temperature-dependent viscosity

1996 ◽  
Vol 323 ◽  
pp. 107-132 ◽  
Author(s):  
D. P. Wall ◽  
S. K. Wilson
Keyword(s):  
Linear Stability ◽  
Channel Flow ◽  
Finite Difference Methods ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Viscosity Models ◽  
Shape Effects ◽  
The Stability ◽  
Dependent Viscosity

The classical fourth-order Orr-Sommerfeld problem which arises from the study of the linear stability of channel flow of a viscous fluid is generalized to include the effects of a temperature-dependent fluid viscosity and heating of the channel walls. The resulting sixth-order eigenvalue problem is solved numerically using high-order finite-difference methods for four different viscosity models. It is found that temperature effects can have a significant influence on the stability of the flow. For all the viscosity models considered a non-uniform increase of the viscosity in the channel always stabilizes the flow whereas a non-uniform decrease of the viscosity in the channel may either destabilize or, more unexpectedly, stabilize the flow. In all the cases investigated the stability of the flow is found to be only weakly dependent on the value of the Péclet number. We discuss our results in terms of three physical effects, namely bulk effects, velocity-profile shape effects and thin-layer effects.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

scholarly journals A Novel Viscosity-Temperature Model of Glass-Forming Liquids by Modifying the Eyring Viscosity Equation

2020 ◽  
Vol 10 (2) ◽  
pp. 428 ◽  
Author(s):  
Chunyu Chen ◽  
Huidan Zeng ◽  
Yifan Deng ◽  
Jingtao Yan ◽  
Yejia Jiang ◽  
...  
Keyword(s):  
Mathematical Expression ◽  
Impact Factors ◽  
Viscosity Data ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Regression Methods ◽  
Glass Forming ◽  
Viscosity Models ◽  
Polymer Liquids ◽  
Dependent Viscosity

Many models have been created and attempted to describe the temperature-dependent viscosity of glass-forming liquids, which is the foundational feature to lay out the mechanism of obtaining desired glass properties. Most viscosity models were generated along with several impact factors. The complex compositions of commercial glasses raise challenges to settle these parameters. Usually, this issue will lead to unsatisfactory predicted results when fitted to a real viscosity profile. In fact, the introduction of the reliable viscosity-temperature data to viscosity equations is an effective approach to obtain the accurate parameters. In this paper, the Eyring viscosity equation, which is widely adopted for molecular and polymer liquids, was applied in this case to calculate the viscosity of glass materials. On the basis of the linear variation of molar volume with temperature during glass cooling, a modified temperature-dependent Eyring viscosity equation was derived with a distinguished mathematical expression. By means of combining high-temperature viscosity data and the glass transition temperature (Tg), nonlinear regression analysis was employed to obtain the accurate parameters of the equation. In addition, we have demonstrated that the different regression methods exert a great effect on the final prediction results. The viscosity of a series of glasses across a wide temperature range was accurately predicted via the optimal regression method, which was further used to verify the reliability of the modified Eyring equation.

Onset of Thermogravitational Convection in a Ferrofluid Layer With Temperature Dependent Viscosity

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
I. S. Shivakumara ◽  
Jinho Lee ◽  
C. E. Nanjundappa
Keyword(s):  
Perturbation Technique ◽  
Temperature Dependent ◽  
Regular Perturbation ◽  
Temperature Dependent Viscosity ◽  
Stability Parameters ◽  
Thermogravitational Convection ◽  
Different Types ◽  
The Stability ◽  
Dependent Viscosity ◽  
Bounding Surfaces

The onset of thermogravitational convection in a horizontal ferrofluid layer is investigated with viscosity depending exponentially on temperature. The bounding surfaces of the ferrofluid layer are considered to be either stress free or rigid-ferromagnetic and insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also by a regular perturbation technique for different types of velocity boundary conditions, namely free-free, rigid-rigid, and lower rigid- upper free. It is observed that increasing the viscosity parameter, Λ, and the magnetic number, M1, is to hasten the onset of ferroconvection, while the nonlinearity of fluid magnetization, M3, is found to have no influence on the stability of the system. The critical stability parameters are found to be the same in the limiting cases of either no magnetic forces or no buoyancy forces.

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