Group Invariance in Engineering Boundary Value Problems

Seshadri, Rajeswari; Na, T. Y.

doi:10.1007/978-1-4612-5102-6

Cited by 69 publications

(43 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be noted that like in the previous case (9), the norming quantities (13) have not only corresponding dimensionalities but can also be interrelated reflecting general physical relationships for the coordinate (displacement) and flow rate (10):…”

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 89%

“…The form of the norming quantities (13) shows that they consist just of the physical properties of the medium under investigation and the intensity of the field of mass forces. For example, typical dimensions are not included into them.…”

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 99%

“…In many cases, the procedures that were considered make it possible to reduce the number of model parameters in comparison with that prescribed by the π-theorem. The best result is obtained by using not the scales selected on the basis of the characteristic dimensions and parameters of the processes under study but by constructing norming quantities of the (9) or (13) type. The use of characteristic scales implies retaining of the measurement system and only a multiple or partial change of dimensionality.…”

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 99%

“…An unbiased view of this question suggests that the goal is precisely to reduce the number of parameters and the deletion of dimensions is just a means enabling achievement of exactly this result in a number of cases". Sometimes this is called "the problem of reducing to a minimally parametric form" [13]. But as noted above, this attitude to deletion of dimensions is determined by the standard approach used.…”

Section: Introductionmentioning

confidence: 99%

“…But as noted above, this attitude to deletion of dimensions is determined by the standard approach used. In the literature [13], it was not possible to find examples of combination of special methods for deletion of dimensions that ensure achievement of self-similarity in terms of parameters (similarity criteria) and the ideas of the group methods for solution.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example

Brunetkin

Maksymov

Maksymova

et al. 2017

EEJET

View full text Add to dashboard Cite

4thermophysical properties, etc. In turn, this causes variation in a wide range of the process parameters subject to control. In such a situation, application of the results obtained by analysis of linear models is very problematic and even unfeasible in most cases.The search for new approaches to analysis of nonlinear models is an important element in solution of the problem of optimal control of power equipment using non-certified fuel of a variable composition. Literature review and problem statementAn effective way to simplify the study of complex models is to make them dimensionless. Reduction of dimensionality of the modeling space makes it possible both to reduce number of experimental (full-scale and numerical) studies by IntroductionWhen studying behavior of control systems, dynamic conditions require special consideration. Apparatus of ordinary differential equations is most often used as a mathematical tool for studying such systems. General methods of solution have only their linear forms. For this reason, linear (linearized) approaches are used to construct models of object and controller. However more exact models are represented by nonlinear differential equations. This situation leads to the fact that the results obtained can only be used within the range of small variation of parameters of the controlled processes nearby the linearization point.The use of fuel of a variable composition [1,2] in power equipment instead of certified fuel with a constant composition brings about a continuous variation of the fuel calorific value, amount of combustion products, their temperature, MATHEMATICS AND CYBERNETICS -APPLIED ASPECTS DEVELOPMENT OF

show abstract

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 89%

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 99%

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example

Brunetkin

Maksymov

Maksymova

et al. 2017

EEJET

View full text Add to dashboard Cite

show abstract

Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation

Aziz

Khan

2012

Heat Trans. Asian Res.

View full text Add to dashboard Cite

The paper presents an entropy generation analysis for steady conduction in a slab with temperature-dependent volumetric internal heat generation. The slab experiences asymmetric convective cooling on its two faces. The exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy generation rates in the slab. The total entropy generation rate depends on five dimensionless parameters: reference heat generation temperature Q, the heat generation-temperature variation parameter a, the temperature asymmetry parameter λ, and Biot numbers Bi 1 and Bi 2 . Graphs illustrating the effect of these five parameters on the local and total entropy generation rates are presented and discussed. It is found that the total entropy generation in the slab can be minimized with a suitable choice of the cooling parameters. The paper corrects the flawed entropy results published recently. The present results for the special case of uniform internal heat generation confirm the results presented in a 2003 paper.

show abstract

Lie Group Analysis and Numerical Solutions for Magnetoconvective Slip Flow along a Moving Chemically Reacting Radiating Plate in Porous Media with Variable Mass Diffusivity

Uddin

Khan²,

Ismail

2014

Heat Trans. Asian Res.

View full text Add to dashboard Cite

A numerical investigation of magnetoconvective boundary layer slip flow along a nonisothermal continuously moving permeable nonlinear radiating plate in Darcian porous media is reported. The concentration dependent mass diffusivity, viscous dissipation, Joule heating, and chemical reaction are taken into account. A Lie group of transformation is applied to the governing transport equations and boundary condition to find the corresponding similarity equations. Furthermore, the similarity equations with the relevant boundary conditions are solved numerically using the Runge‐Kutta‐Fehlberg fourth‐fifth order numerical method. Numerical results for the dimensionless velocity, temperature, and concentration distributions as well as friction factor, local Nusselt, and local Sherwood numbers are discussed for various controlling parameters. It is found that that the dimensionless concentration increases whilst the rate of mass transfer decreases with the mass diffusivity parameter. An excellent correlation is found between the present results and published results. The study finds applications in the polymer industry and metallurgy.

show abstract

Group Invariance in Engineering Boundary Value Problems

Cited by 69 publications

References 0 publications

Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example

Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example

Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation

Lie Group Analysis and Numerical Solutions for Magnetoconvective Slip Flow along a Moving Chemically Reacting Radiating Plate in Porous Media with Variable Mass Diffusivity

Contact Info

Product

Resources

About