An Initial Value Method for the Solution of a Class of Nonlinear Equations in Fluid Mechanics

Na, T. Y.

doi:10.1115/1.3425046

Cited by 31 publications

(24 citation statements)

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“…In order to check the accuracy of our analyses, we have compared the surface the shear stress of f �� (0) for S = 0 with that of Garg and Rajagopal [154]. Also, we have compared our results (f �� (0), g � (0)) for K = β = 0 with those of Glauert [147] and Na [151]. The heat transfer parameter (−θ � (0) for β = K = Ec = 0) is compared with that of Tan and Wang [150].…”

Section: Resultsmentioning

confidence: 99%

“…A detailed discussion on the history of this model, and some of the controversy that surrounds it, are presented by Dunn and Fosdick [141]. The steady incompressible and two-dimensional flow of an electrically conducting fluid past a semi-infinite plate with or without a magnetodynamic pressure gradient has been studied by Greenspan and Carrier [146], Glauert [147], Davies [148], Gribben [149], Tan and Wang [150], Na [151], and Nath [152]. In the present study, it is assumed that this model models the fluid exactly.…”

Section: Discussionmentioning

confidence: 99%

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Chapter 6. Application of the Keller-box Method to More Advanced Problems

Vajravelu¹,

Prasad²

2014

Keller-Box Method and Its Application

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In this chapter, we discuss the application of the Keller-box method to solve more advanced coupled nonlinear boundary value problems of one or more independent variables. In Sections 6.1 and 6.3, the effects of variable fluid properties on the boundary layer flow and heat transfer of a fluid over a flat sheet are studied; whereas in Section 6.2, we study dusty fluid flow over a stretching sheet. The hydromagnetic mixed convection boundary layer flow of an electrically conducting fluid over a non-isothermal wedge and sphere under different physical situations are analyzed in Sections 6.4 and 6.5. In Section 6.6, we study the flow and heat transfer of an electrically conducting viscoelastic fluid past a semi-infinite plate.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Chapter 6. Application of the Keller-box Method to More Advanced Problems

Vajravelu¹,

Prasad²

2014

Keller-Box Method and Its Application

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“…The reader can compare the top frame of Figure 3 with its bottom frame, the bottom frame was obtained by plotting the numerical results of a second computation with the parameters in (9). In this case, the computation, using the same adaptive criteria as in the first one, required 1520 steps with 32 rejections with t 2 OE0, 5 10 3 ; the used limits for the step size were t min 5.82 10 15 and t max D 10 4 .…”

Section: Numerical Resultsmentioning

confidence: 99%

Extended scaling invariance of one‐dimensional models of liquid dynamics in a horizontal capillary

Fazio

Iacono

Jannelli

et al. 2012

Math Methods in App Sciences

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In this paper, we consider the adaptive numerical solution of one‐dimensional models of liquid dynamics in a horizontal capillary. The bulk liquid is assumed to be initially at rest and is put into motion by capillarity: the smaller is the capillary radius, the steeper becomes the initial transitory of the meniscus location derivative, and as a consequence, the numerical solution to a prescribed accuracy becomes harder to achieve. Therefore, in order to solve a capillary problem effectively, it would be advisable to apply an adaptive numerical method. Here, we show how an extended scaling invariance that can be used to define a family of solutions from a computed one. In the viscous case, the similarity transformation involves solutions of liquids with different density, surface tension, viscosity, and capillary radii, whereas in the inviscid case, we can generate a family of solutions for the same liquid and capillaries with different radii. With our study, we are able to prove that the monitor function, used in the adaptive algorithm, is invariant with respect to the considered scaling group. It follows, from this particular results, that all the solutions within the generated family verify the adaptive criteria used for the computed one. Moreover, all the solutions have the same order of accuracy even if the maximum value of the step size varies under the action of the scaling group. Copyright © 2012 John Wiley & Sons, Ltd.

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“…A review paper was written by Klamkin [22]. Extensions of non-iterative TM, by requiring the invariance of one and of two or more physical parameters when they are involved in the mathematical model, were respectively proposed by Na [23] and by Scott, Rinschler and Na [24]; see also Na [7,Chapters 8 and 9]. A survey book, written by Na [7, Chs 7-9] on the numerical solution of BVP, devoted three chapters to numerical TMs.…”

Section: Introductionmentioning

confidence: 99%