Integrable cases of gravitating static isothermal fluid spheres

The propagation properties of linear wave motions in magnetic and/or velocity shears which vary in one coordinate z (say) are usually governed by a second order linear ordinary differential equation in the independent variable z. It is proved that associated with any such differential equation there always exists a quantity A which is independent of z. By employing A a measure of the intensity of the wave, this result is used to investigate the general propagation properties of hydromagnetic-gravity waves (e.g. critical level absorption, valve effects and wave amplification) in magnetic and/or velocity shears, using a full wave treatment. When variations in the basic state are included, the governing differential equation usually has more singularities than it has in the W.K.B.J. approximation, which neglects all variations in the background state. The study of a wide variety of models shows that critical level behaviour occurs only at the singularities predicted by the W.K.B.J. approximation. Although the solutions of the differential equation are necessarily singular at the irregularities whose presence is solely due to the inclusion of variations in the basic state, the intensity of the wave (as measured by A) is continuous there. Also the valve effect is found to persist whatever the relation between the wavelength of the wave and the scale of variations of the background state. In addition, it is shown that a hydromagnetic-gravity wave incident upon a finite magnetic and/or velocity shear can be amplified (or over-reflected) in the absence of any critical levels within the shear layer. In a Boussinesq fluid rotating uniformly about the vertical, wave amplification can occur if the horizontal vertically sheared flow and magnetic field are perpendicular. In a compressible isothermal fluid, on the other hand, wave amplification not only occurs in both magnetic-velocity and velocity shears but also in a magnetic shear acting alone.

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Class of solutions of Einstein's field equations for static fluid spheres

Physical Review D ◽

10.1103/physrevd.26.1254 ◽

1982 ◽

Vol 26 (6) ◽

pp. 1254-1261 ◽

Cited By ~ 18

Author(s):

D. N. Pant ◽

A. Sah

Keyword(s):

Einstein’S Field Equations ◽

Field Equations ◽

Einstein's Field Equations ◽

Static Fluid ◽

Fluid Spheres

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General relativistic fluid spheres with nonzero vacuum energy density

Journal of Mathematical Physics ◽

10.1063/1.528202 ◽

1988 ◽

Vol 29 (2) ◽

pp. 443-445 ◽

Cited By ~ 8

Author(s):

William A. Hiscock

Keyword(s):

Energy Density ◽

Vacuum Energy ◽

Vacuum Energy Density ◽

Relativistic Fluid ◽

General Relativistic ◽

Fluid Spheres

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Second Law Analysis of Laminar Flow in a Circular Pipe Immersed in an Isothermal Fluid

Journal of Thermodynamics ◽

10.1155/2013/234264 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Vishal Anand ◽

Krishna Nelanti

Keyword(s):

Laminar Flow ◽

Entropy Generation ◽

Circular Tube ◽

Dimensionless Temperature ◽

Bejan Number ◽

Uniform Wall Temperature ◽

Thermal Boundary Conditions ◽

Fluid Properties ◽

Isothermal Fluid ◽

Uniform Wall

Entropy generation and pumping power to heat transfer ratio (PPR) of a laminar flow, for a circular tube immersed in an isothermal fluid, are studied analytically in this paper. Two different fluids, namely, water and ethylene glycol, are chosen to study the influence of fluid properties on entropy generation and PPR. The expressions for dimensionless entropy generation, Bejan number and PPR are derived in a detailed way and their variations with Reynolds number, external Biot number, and the dimensionless temperature difference are illustrated. The results of the analysis are compared with those for a laminar flow in a circular tube with uniform wall temperature boundary condition. Finally, a criterion is established to determine which type of thermal boundary conditions is more suitable for a particular fluid, with respect to its influence on entropy generation.

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