Group-Theoretic Properties of the Equations of Motion for a Viscous Heat Conducting Liquid

1998 ◽  
pp. 241-270
Author(s):  
V. K. Andreev ◽  
O. V. Kaptsov ◽  
V. V. Pukhnachov ◽  
A. A. Rodionov
Keyword(s):  
Equations Of Motion ◽  
Heat Conducting ◽  
Conducting Liquid ◽  
Viscous Heat

Unsteady, viscous, circular flow

1961 ◽  
Vol 11 (2) ◽  
pp. 291-308 ◽  
Author(s):  
Merwin Sibulkin
Keyword(s):  
Energy Transfer ◽  
Equations Of Motion ◽  
Heat Conducting ◽  
Low Mach Number ◽  
Energy Field ◽  
Transfer Processes ◽  
Low Mach Number Limit ◽  
Viscous Heat ◽  
Temperature Waves ◽  
Velocity Pressure

In this paper a study of the energy-transfer processes associated with the motion of a viscous, heat-conducting fluid is begun. The class of motions considered are unsteady, two-dimensional, vortical flows. After developing simplified equations of motion and energy appropriate to this type of flow in the low Mach-number limit, general solutions of the momentum equations are presented.The concept of a line impulse of angular momentum is introduced as an example of this class of motions for which a solution of the energy field is obtainable in closed form. The solution for the line impulse can be viewed as a combination of velocity, pressure, and temperature waves concurrently radiating from the origin of the impulse and decaying with time. Particular examples of the development of the energy field of the impulse in both liquids and gases are presented for selected values of Prandtl number. The energy-transfer processes are discussed in some detail, and the resulting differences in the energy fields for liquid gases are emphasized.

Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

1969 ◽  
Vol 37 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Takeo Sakurai
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Boussinesq Approximation ◽  
Circular Cylinders ◽  
Heat Conducting ◽  
Quasi Steady State ◽  
Homogeneous Fluid ◽  
Time Duration ◽  
Viscous Heat ◽  
Final Approach

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

scholarly journals MATHEMATICAL MODELING AND CALCULATION OF GAS DYNAMIC CHARACTERISTICS OF FREE THERMAL AIR VORTEX

2017 ◽  
pp. 93-98
Author(s):  
D. D. Barannikova ◽  
A. G. Obukhov
Keyword(s):  
Gas Flow ◽  
Local Heating ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Point Of View ◽  
Underlying Surface ◽  
Heat Conducting ◽  
Gas Dynamics Equations ◽  
Viscous Heat ◽  
Flow Formation

The article analyzes experimental and analytical studies of ascending swirling air flows. In experimental works such flows are considered from the point of view of the direction of twist, the thermal regimes of heating the underlying surface, the estimation of integral parameters, the method of influence on them, and various methods of visualization. In analytical papers, by constructing solutions of the system of gas dynamics equations, the emergence of a twist of the corresponding direction is proven when there is a gas flow into a vertical cylinder of nonzero radius. In addition, in the numerical modeling of thermal ascending swirling flows, a feature was observed in the behavior of a moving gas at the initial moments of flow formation when the underlying surface was heated locally. This feature consists in the appearance on the boundary of the heating region of counter propagating gas flows with opposite directions of twist. The paper presents the results of numerical simulation of three-dimensional unsteady flows of a compressible viscous heat-conducting gas in thermal swirled vortices with local heating of the underlying surface, taking into account the action of gravity and Coriolis forces.

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