Effect of a radial temperature gradient on the stability of the flow of a second-order fluid between two co-axial cylinders

1976 ◽  
Vol 27 (1) ◽  
pp. 115-118
Author(s):  
C. F. Chan Man Fong
Keyword(s):  
Temperature Gradient ◽  
Second Order ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
The Stability

The Effect of Thermal Diffusion on Flow Stability Between Two Rotating Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 318-322 ◽  
Author(s):  
Chin-Hsiu Li
Keyword(s):  
Temperature Gradient ◽  
Prandtl Number ◽  
Outer Cylinder ◽  
Variable Density ◽  
Radial Temperature Gradient ◽  
Rotating Cylinders ◽  
Radial Temperature ◽  
Stabilizing Effect ◽  
The Stability ◽  
Very High

The influence of variable density on the stability of the flow between two rotating cylinders is re-examined. The instability is shown to set in as an oscillatory secondary flow which was overlooked by previous investigators. Results indicate that the radial temperature gradient destabilizes the flow if the outer cylinder is hotter than the inner one, and the destabilizing effect is enhanced if the Prandtl number is high. For the case where the inner cylinder is hotter than the outer one, the stabilizing effect due to the temperature gradient is shown to be weak for any Prandtl number. This modifies previous results which predicted a very high stabilizing effect due to the temperature gradient. The bifurcating structure of the stability curve is shown.

Stability of Flow Between Arbitrarily Spaced Concentric Cylindrical Surfaces Including the Effect of a Radial Temperature Gradient

1964 ◽  
Vol 31 (4) ◽  
pp. 585-593 ◽  
Author(s):  
J. Walowit ◽  
S. Tsao ◽  
R. C. DiPrima
Keyword(s):  
Temperature Gradient ◽  
Couette Flow ◽  
Simple Formula ◽  
Negative Temperature ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Simple Set ◽  
Wide Range ◽  
The Stability ◽  
The Galerkin Method

The stability of Couette flow and flow due to an azimuthal pressure gradient between arbitrarily spaced concentric cylindrical surfaces is investigated. The stability problems are solved by using the Galerkin method in conjunction with a simple set of polynomial expansion functions. Results are given for a wide range of spacings. For Couette flow, in the case that the cylinders rotate in the same direction, a simple formula for predicting the critical speed is derived. The effect of a radial temperature gradient on the stability of Couette flow is also considered. It is found that positive and negative temperature gradients are destabilizing and stabilizing, respectively.

scholarly journals STABILITY OF VISCOUS FLOW IN A CURVED CHANNEL WITH RADIAL TEMPERATURE GRADIENT

2016 ◽  
Vol 15 (8) ◽  
pp. 6957-6966
Author(s):  
Sadhana Pandey ◽  
Neelabh Rai
Keyword(s):  
Temperature Gradient ◽  
Outer Cylinder ◽  
Critical Values ◽  
Wave Number ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Eigen Value ◽  
Cell Patterns ◽  
The Difference ◽  
The Stability

In this paper, the stability of Dean’s problem in the presence of a radial temperature gradient is studied for narrow gap case. The analytical solution of the eigen value problem is obtained by using the Galerkin’s method. The critical values of parameters and Λ are computed, where  is wave number and Λ is a parameter determining the onset of stability from the obtained analytical expressions for the first, second and third approximations. It is found that the difference between the numerical values of critical Λ corresponding to the second and third approximations is very small as compared to the difference between first and second approximations. The critical values of Λ obtained by the third approximation agree very well with the earlier results computed numerically by using the finite difference method. This clearly indicates that for the better result one should obtain the numerical values by taking more terms in approximation. Also, the amplitude of the radial velocity and the cell-patterns are shown on the graphs for different values of the parameter M, which depends on difference of temperatures of outer cylinder to the inner one i.e. on (), where is the temperature of inner cylinder and  is the temperature of outer cylinder.

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