Non-linear stability for convection with quadratic temperature dependent viscosity

Linear stability of two immiscible liquids driven by a constant pressure gradient through a long vertical annulus in the gravitational field is investigated. If viscosity depends on temperature, it is found that thermal conductivity stratification can induce an interfacial instability, which is different from the instability identified by Yih (1986). The effect of temperature-dependent viscosity on various unstable modes and mode competitions are studied.

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Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-04-2019-0346 ◽

2019 ◽

Vol 29 (12) ◽

pp. 4607-4623 ◽

Cited By ~ 36

Author(s):

Zahid Ahmed ◽

Sohail Nadeem ◽

Salman Saleem ◽

Rahmat Ellahi

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Variable Viscosity ◽

Numerical Study ◽

Temperature Dependent ◽

Temperature Dependent Viscosity ◽

Content Type ◽

Non Linear ◽

Dependent Viscosity ◽

Shrinking Surface

Purpose The purpose of this paper is to present a novel model on the unsteady MHD flow of heat transfer in carbon nanotubes with variable viscosity over a shrinking surface. Design/methodology/approach The temperature-dependent viscosity makes the proposed model non-linear and coupled. Consequently, the resulting non-linear partial differential equations are first reformed into set of ordinary differential equations through appropriate transformations and boundary layer approximation and are then solved numerically by the Keller box method. Findings Graphical and numerical results are executed keeping temperature-dependent viscosity of nanofluid. It is noted that, for diverse critical points, it is found that at one side of these critical values, multiple solutions exist; on the other side, no solution exists. A comparison is also computed for the special case of existing study. The temperature and pressure profiles are also plotted for various effective parameters. Originality/value The work is original.

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A linear stability analysis on the onset of thermal convection of a fluid with strongly temperature-dependent viscosity in a spherical shell

Theoretical and Computational Fluid Dynamics ◽

10.1007/s00162-011-0250-x ◽

2011 ◽

Vol 27 (1-2) ◽

pp. 21-40 ◽

Cited By ~ 12

Author(s):

Masanori Kameyama ◽

Hiroki Ichikawa ◽

Arata Miyauchi

Keyword(s):

Stability Analysis ◽

Spherical Shell ◽

Linear Stability ◽

Linear Stability Analysis ◽

Thermal Convection ◽

Temperature Dependent ◽

Temperature Dependent Viscosity ◽

Dependent Viscosity

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

Journal of Fluid Mechanics ◽

10.1017/s0022112096000869 ◽

1996 ◽

Vol 323 ◽

pp. 107-132 ◽

Cited By ~ 46

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.

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