Effect of Radial Temperature Gradient on the Stability of Magnetohydrodynamic Dean Flow in an Annular Channel at High Magnetic Parameter

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
S. Dholey
Keyword(s):  
Temperature Gradient ◽  
Magnetic Parameter ◽  
Annular Channel ◽  
Axial Direction ◽  
Critical Value ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Dean Flow ◽  
Electrically Conducting ◽  
The Stability

The effect of a radial temperature gradient on the stability of Dean flow of an electrically conducting fluid in an annular channel is investigated. A strong constant magnetic field is imposed in the axial direction. Finite-difference method is used to solve the eigenvalue problem. For given values of gap width d, between the cylinders, and magnetic parameter Q, electrically nonconducting (NC) walls are found to be more destabilizing than perfectly conducting (PC) walls when the temperature parameter N < 0. This trend persists even for small positive values of N but when N (>0) exceeds a critical value depending on Q, PC walls are slightly more destabilizing than NC walls. The critical value of the radii ratio η (0 < η < 1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of N and Q.

scholarly journals Thermal Effect on the Instability of Annular Liquid Jet

Aerospace ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 382
Author(s):  
Xiao Cui ◽  
Boqi Jia
Keyword(s):  
Reynolds Number ◽  
Temperature Gradient ◽  
Thermal Effect ◽  
Weber Number ◽  
Marangoni Effect ◽  
Critical Value ◽  
Liquid Jet ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Annular Liquid Jet

The linear instability of an annular liquid jet with a radial temperature gradient in an inviscid gas steam is investigated theoretically. A physical model of an annular liquid jet with a radial temperature gradient is established, dimensionless governing equations and boundary conditions are given, and numerical solutions are obtained using the spectral collocation method. The correctness of the results is verified to a certain extent. The liquid surface tension coefficient is assumed to be a linear function of temperature. The effects of various dimensionless parameters (including the Marangoni number/Prandtl number, Reynolds number, temperature gradient, Weber number, gas-to-liquid density ratio and velocity ratio) on the instability of the annular liquid jet are discussed. A decreasing Weber number destabilizes the annular liquid jet when the Weber number is lower than a critical value. It is found that the effects of the Marangoni effect are related to the Weber number. The Marangoni effect enhances instability when the Weber number is small, while the Marangoni effect weakens instability when the Weber number is large. In addition, because the thermal effect is considered, a decreasing Reynolds number enhances the instability when the Weber number is lower than a critical value, which is similar to the results of a viscous liquid sheet with a temperature difference between two planar surfaces. Furthermore, the effects of other dimensionless parameters are also investigated.

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.

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