Group analysis of nonlinear fin equations

Vaneeva, Olena; Johnpillai, A. G.; Popovych, Roman O.; Sophocleous, Christodoulos

doi:10.1016/j.aml.2007.02.023

Cited by 26 publications

(25 citation statements)

References 12 publications

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“…Subsequently, symmetry analysts considered the problem in [12] to determine all forms of thermal conductivity and heat transfer coefficients for which the governing equation admits extra symmetries [13][14][15][16]. However, only general solutions were constructed.…”

Section: Introductionmentioning

confidence: 99%

Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient

Moitsheki

Harley

2011

Pramana - J Phys

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Transient heat transfer through a longitudinal fin of various profiles is studied. The thermal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions are performed. Since the governing boundary value problem is not invariant under any Lie point symmetry, we solve the original partial differential equation numerically. The effects of realistic fin parameters such as the thermogeometric fin parameter and the exponent of the heat transfer coefficient on the temperature distribution are studied.

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Section: Introductionmentioning

confidence: 99%

Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient

Moitsheki

Harley

2011

Pramana - J Phys

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“…In this paper, our research is mainly concentrated on rigorous and exhaustive group classification of the whole class (1) with a detailed proof and Lie symmetry reduction of some truly nonlinear 'variable-coefficient' wave equation (equation with H u k x = 0) from this class. The method used here is a combination of the Lie-Ovsiannikov method [1,49], additional equivalent transformation and furcate split method which was present in recent paper [43,52] and had been applied to investigating a number of different group classification problem [13,28,34,35,51,58,59]. Nonclassical symmetries of the class of generalized quasi-linear wave equations (1) are also investigated.…”

Section: Introductionmentioning

confidence: 99%

Group properties of generalized quasi-linear wave equations

Huang

Zhou

2010

Journal of Mathematical Analysis and Applications

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In this paper, complete group classification of a class of (1 + 1)-dimensional generalized quasi-linear wave equations is performed by using the Lie-Ovsiannikov method, additional equivalent transformation and furcate split method. Lie reductions of some truly 'variable coefficient' wave equations which are singled out from the classification results are investigated. Some classes of exact solutions of these 'variable coefficient' wave equations are constructed by means of both the reductions and the additional equivalent transformations. The nonclassical symmetries to the generalized quasi-linear wave equation are also studied. This enabled to obtain some exact solutions of the wave equations which are invariant under certain conditional symmetries.

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“…has been presented in [38,40], [39] and [19,20], respectively. Although all of the equations mentioned above are particular cases of the more general class,…”

Section: Introductionmentioning

confidence: 99%

Group classification of a class of equations arising in financial mathematics

Иванова

Sophocleous

2010

Journal of Mathematical Analysis and Applications

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We provide a group classification of a class of nonlinearisable evolution partial differential equations which arise in Financial Mathematics. Sixteen different cases are identified for the general problem and another seven for a restricted version. In the cases for which the algebra is suitable we determine the solution to the problem u(0, x) = U , where U is a constant. In addition we provide a number of solutions based upon reduction using inequivalent subalgebras.

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Group analysis of nonlinear fin equations

Cited by 26 publications

References 12 publications

Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient

Transient heat transfer in longitudinal fins of various profiles with temperature-dependent thermal conductivity and heat transfer coefficient

Group properties of generalized quasi-linear wave equations

Group classification of a class of equations arising in financial mathematics

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