Semi-logical Solution to Jeffery-Hamel Condition

Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

Editorial - (2022) Volume 11, Issue 2

Semi-logical Solution to Jeffery-Hamel Condition

Farago Istvan*
*Correspondence: Farago Istvan, Department of Applied Analysis and Computational Mathematics, Eotvos Lorand University, Hungary, Email:
Department of Applied Analysis and Computational Mathematics, Eotvos Lorand University, Hungary

Received: 02-Feb-2022, Manuscript No. jacm-22-58293; Editor assigned: 03-Feb-2022, Pre QC No. P-58293; Reviewed: 07-Feb-2022, QC No. Q-58293; Revised: 08-Feb-2022, Manuscript No. R-58293; Published: 13-Feb-2022 , DOI: 10.37421/jacm.2022.11.458
Citation: Istvan, Farago. “Semi-logical Solution to Jeffery-Hamel Condition.” J Appl Computat Math 11 (2022): 458. DOI: 10.37421/jacm.2022.11.458
Copyright: © 2022 Istvan F. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Another methodology in light of the Adomian deterioration and the Fourier change is presented. The technique recommends an answer for the notable magneto-hydrodynamic (MHD) Jeffery-Hamel condition. Consequences of Adomian deterioration technique joined with Fourier change are contrasted and careful and mathematical strategies. The FTADM as a restrictive and new strategy fulfils all limit and beginning circumstances over the whole spatial and worldly spaces. Besides, utilizing the FTADM prompts fast methodology of estimated outcomes toward the specific arrangements is illustrated. The second subsidiary of Jeffery-Hamel arrangement connected with the comparative number of things of recursive terms under an immense spatial space shows the most extreme blunder in the request for 10-5 contrasting with definite and mathematical arrangements. The outcomes likewise suggest that the FTADM can be considered as an exact estimation for settling the thirdrequest nonlinear Jeffery-Hamel conditions.

he Jeffery-Hamel numerical establishment is the most appropriate approach to displaying the incompressible gooey liquid stream between two slanted plates under an attractive field. For the most part, designing applications, for example, liquid mechanics and natural science use Jeffery- Hamel streams. Due to its critical applications in fluid metals-based cooling frameworks' assignment, magneto hydrodynamic generators, gas pedals, siphons, and stream meters are of significant interest of scientists. For MHD Jeffery-Hamel stream, Jeffery and Hamel figured out a numerical starting point for the issue arrangement exhaustively. Regarding life, what to think about it an outside attractive field applied on the liquid stream prompts very various ways of behaving of a directing liquid streaming. Controlling of the liquid stream by varieties of the outside attractive field power is the fundamental explanation of the meaning of the Jeffery-Hamel issues' review. In addition, the methodology of the issue arrangement should incorporate the non-layered factors (the attractive Reynolds and the Hartmann numbers) as well as the point of the plates. In this way, a wide scope of the arrangements exists contrasting with traditional issue. To this point, to get an inexact answer for traditional Jeffery-Hamel stream condition, a couple of approaches are recommended. An assortment of approaches, for example, the homotopy annoyance, the differential change and homotopy examination are acquainted with acquire scientific answer for the nonlinear issues, due to its solid nonlinearity up to this point.

The point of the current work is to present an exact logical answer for the third-request nonlinear Jeffery-Hamel condition by utilizing FTADM. The selectiveness of the FTADM, as another strategy, is the fulfillment of all limit and starting circumstances over the whole spatial and fleeting spaces. In addition, the notable firmly nonlinear third-request Jeffery-Hamel type conditions are addressed utilizing the FTADM where the pattern of fast methodology of the inexact outcomes toward the specific arrangements is illustrated. We tackle the issue with the Reynolds number equivalent to 10 and the plates with the points and a bunch of the Hartmann numbers incorporates: 0, 200, 400, 800, 1000, 2000. Moreover, we examine the Jeffery-Hamel issue's answers by changing the upsides of the successful actual variables [1-5].

FTADM application on Jeffery-Hamel issue

Exhibition of the benefits and approval of FTADM technique are analyzed by settling the one-aspect, third-request and nonlinear Jeffery-Hamel issue in all through of the space. A precise arrangement exists between the arrangement of the Navier-Stokes conditions, in the case of two-layered stream inside a channel with shifted sheets having a vertex and presence a source or sink, and the Jeffery Hamel issue. Another change of the ADM, the Fourier change Adomian decay strategy (FTADM), is proposed to tackle the nonlinear MHD Jeffery-Hamel condition. The examination of our outcomes at different Hartmann numbers got by means of the FTADM with the specific and mathematical information show phenomenal arrangement. The correlation of speed acquired involving the FTADM for Re=10 and at various Hartmann numbers with those got by the mathematical Runge-Kutta strategy show astounding arrangements and the greatest mistake is on the request for 10-5 We presume that the new FTADM is a skilled and exact surmised semiscientific methodology for settling the nonlinear MHD Jeffery-Hamel condition.

Conflict of Interest



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