Group classification of the two-dimensional equations of motion of a viscous heat-conducting perfect gas

1996 ◽  
Vol 37 (2) ◽  
pp. 170-176 ◽  
Author(s):  
V. V. Bublik
Keyword(s):  
Equations Of Motion ◽  
Group Classification ◽  
Heat Conducting ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Viscous Heat

The compressible viscous heat-conducting vortex

1960 ◽  
Vol 8 (2) ◽  
pp. 284-292 ◽  
Author(s):  
Leslie M. Mack
Keyword(s):  
Vortex Flow ◽  
Viscosity Coefficient ◽  
Typical Case ◽  
Successive Approximations ◽  
Heat Conducting ◽  
Stagnation Temperature ◽  
Perfect Gas ◽  
Viscous Heat ◽  
Prandtl Numbers ◽  
Steady Laminar

The plane, steady, laminar vortex flow of a viscous, heat-conducting perfect gas is treated. Simple relations are obtained for the flow quantities in the irrotational vortex, for arbitrary Prandtl numbers. When the Prandtl number is ½, the irrotational vortex is also isentropic. When the temperature dependence of the viscosity coefficient is taken into account, the vortex flow is rotational. An exact solution for the rotational vortex is obtained which is suitable for numerical evaluation by successive approximations. Distributions of velocity, temperature, pressure, density, and stagnation temperature through the rotational vortex are given for a typical case.

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.

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