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Keywords
(6)
Boundary Condition
Boundary Layer
Conservation Law
Continuity Equation
Partial Differential Equation
Stream Function
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Conservation laws and conserved quantities for laminar twodimensional and radial jets
Conservation laws and conserved quantities for laminar twodimensional and radial jets,10.1016/j.nonrwa.2008.07.003,Nonlinear Analysisreal World Appl
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Conservation laws and conserved quantities for laminar twodimensional and radial jets
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Citations: 5
)
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R. Naz
,
D. P. Mason
,
F. M. Mahomed
A systematic way to derive the conserved quantities for the liquid jet, free jet and wall jet using conservation laws is presented. Both twodimensional and radial jets are considered. The jet flows are described by Prandtl’s momentum
boundary layer
equation and the continuity equation. The multiplier approach (also know as variational derivative approach) is first applied to construct a basis of conserved vectors for the system. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the liquid jet and the free jet. The multiplier approach is then applied to construct a basis of conserved vectors for the thirdorder
partial differential equation
for the stream function. The basis consists of two local conserved vectors one of which is a nonlocal conserved vector for the system. The conserved quantities for the free jet and the wall jet are derived from the corresponding conservation laws and boundary conditions. The approach gives a unified treatment to the derivation of conserved quantities for jet flows and may lead to a new classification of jets through conserved vectors and their multipliers.
Journal:
Nonlinear Analysisreal World Applications  NONLINEAR ANALREAL WORLD APP
, vol. 10, no. 5, pp. 26412651, 2009
DOI:
10.1016/j.nonrwa.2008.07.003
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Citation Context
(2)
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5
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Rehana Naz
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Conservation laws for laminar axisymmetric jet flows with weak swirl
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5
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6
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Rehana Naz
.
Conservation laws for laminar axisymmetric jet flows with weak swirl
References
(9)
Laminare Strahlausbreitung
(
Citations: 74
)
H. Schlichting
Journal:
Zammzeitschrift Fur Angewandte Mathematik Und Mechanik
, vol. 13, no. 4, pp. 260263, 1933
The radial free jet
(
Citations: 14
)
W Schwarz
Journal:
Chemical Engineering Science  CHEM ENG SCI
, vol. 18, no. 12, pp. 779786, 1963
The wall jet
(
Citations: 202
)
M. B. Glauert
Journal:
Journal of Fluid Mechanics  J FLUID MECH
, vol. 1, no. 06, 1956
The radial spread of a liquid jet over a horizontal plane
(
Citations: 117
)
E. J. Watson
Journal:
Journal of Fluid Mechanics  J FLUID MECH
, vol. 20, no. 03, 1964
Group Invariant Solution and Conservation Law for a Free Laminar TwoDimensional Jet
(
Citations: 5
)
D P MASON
Journal:
Journal of Nonlinear Mathematical Physics  J NONLINEAR MATH PHYS
, vol. 9, no. Supplement, 2002
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Citations
(5)
Conservation laws for laminar axisymmetric jet flows with weak swirl
Rehana Naz
Journal:
Applicable Analysis
, vol. 91, no. 5, pp. 10451052, 2012
Conservation laws for laminar axisymmetric jet flows with weak swirl
Rehana Naz
Journal:
Applicable Analysis
, vol. aheadofp, no. aheadofp, pp. 18, 2011
Conservation laws for a complexly coupled KdV system, coupled Burgers’ system and Drinfeld–Sokolov–Wilson system via multiplier approach
(
Citations: 1
)
R. Naz
Journal:
Communications in Nonlinear Science and Numerical Simulation  COMMUN NONLINEAR SCI NUMER SI
, vol. 15, no. 5, pp. 11771182, 2010
Conservation laws for thirdorder variant Boussinesq system
R. Naz
,
F. M. Mahomed
,
Tasawar Hayat
Journal:
Applied Mathematics Letters
, vol. 23, no. 8, pp. 883886, 2010
Group invariant solution for a free jet on a hemispherical shell
R. Naz
Journal:
Applied Mathematics and Computation  AMC
, vol. 215, no. 9, pp. 32653270, 2010