Noether, partial Noether operators and first integrals for a linear system

Naeem, Imran; Mahomed, F. M.

doi:10.1016/j.jmaa.2007.11.041

Cited by 11 publications

(15 citation statements)

References 29 publications

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“….. (27) Again, following Kara et al [31] and Naeem and Mahamed [32,34,36], consider the partial Langragian of Eq.…”

Section: Exact Solution By Partial Noether Methodsmentioning

confidence: 99%

Thermal Performance Analysis of Convective-Radiative Fin With Temperature-Dependent Thermal Conductivity in the Presence of Uniform Magnetic Field Using Partial Noether Method

Sobamowo¹

2018

Journal of Thermal Engineering

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In this paper, thermal performance of convective-radiative straight fin with temperature-dependent thermal conductivity in the presence of uniform magnetic field is analyzed using partial Noether method. The exact analytical solution is used to investigate the effects of magnetic field, convective, radiative, thermo-geometric and thermal conductivity (non-linear) parameters on the thermal performance of the fin. The results reveal that as the magnetic, convective and radiative parameters increase, the temperature of the fin decreases rapidly and by implication, the rate of heat transfer through the fin increases. The study provides a platform for comparison of results of any other method of analysis of the problem with the results of the exact analytical solutions in this paper. Also, such an analytical tool is valuable as a design and optimization approach for large scale (not necessarily in size) finned heat exchangers where each fin/row are analytically analyzed and where the surrounding fluid is influenced by a magnetic field.

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“….. (27) Again, following Kara et al [31] and Naeem and Mahamed [32,34,36], consider the partial Langragian of Eq.…”

Section: Exact Solution By Partial Noether Methodsmentioning

confidence: 99%

Thermal Performance Analysis of Convective-Radiative Fin With Temperature-Dependent Thermal Conductivity in the Presence of Uniform Magnetic Field Using Partial Noether Method

Sobamowo¹

2018

Journal of Thermal Engineering

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“…Theorem [15,16]. If the Lie operator (11) is a partial Noether operator corresponding to a partial Lagrangian ‫ܮ‬ of Eq.…”

Section: Partial Noether Methodsmentioning

confidence: 99%

Exact solution of fin problem with linear temperature-dependent thermal conductivity

Kader¹,

Latif²,

Nour³

2016

J. Appl. Math. Comput. Mech.

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In this paper, we obtain the general exact solution of a nonlinear fin equation which governs heat transfer in a rectangular fin with linear temperature-dependent thermal conductivity using the partial Noether method. The relationship between the fin efficiency and the thermo-geometric fin parameter is obtained. Additionally, we obtained the relationship among the fin effectiveness, the thermo-geometric fin parameter and the Biot number.

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“…They only form a Lie algebra if these partial Noethertype symmetries coincide with the Noether symmetries, in which case the condition is stated in the beginning of the third paragraph of the first section. Analogously to the Noether theorem one can state a Partial Noether, or Noether-like, theorem [16]:…”

Section: Preliminariesmentioning

confidence: 99%

“…If a DE or system of DEs admits a Lagrangian formulation then the Noether symmetries and partial Noether-type symmetries are always the same and can be different only when the δL/δx µ term appearing in the equations for calculating the partial Noethertype symmetries (given in the next section) involve the derivative which appears in the corresponding DEs [16]; this statement is also true for the approximate case [17]. We construct a partial Lagrangian for the Minkowski spacetime regarded as exact.…”

Section: Introductionmentioning

confidence: 99%

Approximate Partial Noether Operators of the Schwarzschild Spacetime

Hussain¹,

Mahomed²,

Qadir³

2021

JNMP

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The objective of this paper is twofold: (a) to find a natural example of a perturbed Lagrangian that has different partial Noether operators with symmetries different from those of the underlying Lagrangian. First we regard the Schwarzschild spacetime as a perturbation of the Minkowski spacetime and investigate the approximate partial Noether operators for this perturbed spacetime. It is shown that the Minkowski spacetime has 12 partial Noether operators, 10 of which are different from the 17 Noether symmetries for this spacetime. It is found that for the perturbed Schwarzschild spacetime we recover the exact partial Noether operators as trivial first-order approximate partial Noether operators and there is no non-trivial approximate partial Noether operator as for the Noether case. As a consequence we state a conjecture. (b) Then we prove a conjecture that the approximate symmetries of a perturbed Lagrangian form a subalgebra of the approximate symmetries of the corresponding perturbed Euler-Lagrange equations and illustrate it by our examples. This is in contrast to approximate partial Noether operators.

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Noether, partial Noether operators and first integrals for a linear system

Cited by 11 publications

References 29 publications

Thermal Performance Analysis of Convective-Radiative Fin With Temperature-Dependent Thermal Conductivity in the Presence of Uniform Magnetic Field Using Partial Noether Method

Thermal Performance Analysis of Convective-Radiative Fin With Temperature-Dependent Thermal Conductivity in the Presence of Uniform Magnetic Field Using Partial Noether Method

Exact solution of fin problem with linear temperature-dependent thermal conductivity

Approximate Partial Noether Operators of the Schwarzschild Spacetime

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