Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model

2020 ◽  
Vol 135 (6) ◽  
Author(s):  
Subhankar Sil ◽  
T. Raja Sekhar
Keyword(s):  
Exact Solutions ◽  
Production Model ◽  
Nonlocal Symmetry ◽  
One Dimensional ◽  
Symmetry Reductions ◽  
Nonlocally Related Systems

Transport processes between fluids and clouds of suspended particles: some exact solutions

1957 ◽  
Vol 242 (1231) ◽  
pp. 430-443 ◽  
Keyword(s):  
Exact Solutions ◽  
Turbulent Mixing ◽  
Liquid Fuel ◽  
Transport Processes ◽  
Dimensional System ◽  
Unsteady Heat Transfer ◽  
One Dimensional ◽  
Homogeneous Reactor ◽  
Fourier Equation ◽  
Gas Component

The paper relates to processes such as the burning of pulverized solid fuel and of liquid fuel sprays, absorption of a gas component by a solvent spray, etc., and takes account of convection and turbulent mixing of the cloud. The Eulerian equation of conservation for the steady process is shown to be transformable into the Fourier equation for unsteady heat transfer in a flowing medium. Exact solutions are given for a one-dimensional system, an axially symmetrical system, and the steady-flow homogeneous reactor. Numerical methods are indicated for more complex systems, and the possibility of solution by means of an analogue is pointed out.

scholarly journals Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems

2014 ◽  
Vol 21 (4) ◽  
pp. 643-671 ◽  
Author(s):  
H. Baran ◽  
I.S. Krasil'shchik ◽  
O.I. Morozov ◽  
P. Vojčák
Keyword(s):  
Exact Solutions ◽  
3 Dimensional ◽  
Symmetry Reductions
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