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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Catalogue of existence of the multiple physical solutions of hydromagnetic flow over a stretching/shrinking sheet for viscoelastic second-grade and Walter's B fluids
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Catalogue of existence of the multiple physical solutions of hydromagnetic flow over a stretching/shrinking sheet for viscoelastic second-grade and Walter's B fluids

机译：用于粘弹性二级和沃尔特B流体的拉伸/收缩纸张湿法流量的多物理溶液的存在目录

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In this work, the author restudied a fourth-order nonlinear ordinary differential equation that commonly appears in investigating the hydromagnetic flow of two types of viscoelastic fluids over a stretching/shrinking sheet. In this type of problem, vital question arises: what are the parameters values needed to obtain regions and numbers of the physical solutions? To answer this question, the researchers worked on suggesting/estimating the initial values, or even chose them randomly. This usually leads to wasting a lot of time, effort and maybe to untrustworthy results. Towards avoiding this rugged road, the present work answered this question decisively and definitively. In particular, an explicit and direct catalogue of existence multiple real positive solutions was in detail introduced. MATHEMATICA code was programmed and, therefore, many tables and figures of the critical values and regions were produced at different values of the controlled parameters. In addition, and maybe for the first time, the mathematical expressions of these critical values were secured. Hence, remarkable differences were detected between the existing results and those obtained in the literature, therefore, spurious physical sights were gained. In conclusion, this research determined the whole values of the parameters that are required to control the number of solutions or even not to obtain solutions at all. Therefore, the current catalogue aims to help the researchers to avoid guessing the parameters' values on solving the current type of problem.
机译：在这项工作中，作者根据拉伸/收缩片来改造通常出现在研究两种类型的粘弹性流体的水磁性流动的四阶非线性常微分方程。在此类问题中，生命值出现了：获取物理解决方案的区域和数量所需的参数值是什么？为了回答这个问题，研究人员正在建议/估计初始值，甚至随机选择它们。这通常会导致浪费很多时间，努力，也许可能与不值得信任的结果。为了避免这种崎岖的道路，目前的工作果断和明确地回答了这个问题。特别地，介绍了存在多种实际正面解决方案的明确和直接目录。因此，Mathematica代码被编程，因此，在受控参数的不同值下产生许多表和临界值和区域的图。此外，也许是第一次，确保了这些关键值的数学表达式。因此，在现有的结果和文献中获得的人之间检测到显着差异，因此获得了杂散的物理景点。总之，这项研究确定了控制解决方案数量的参数的整个值，甚至根本不获得解决方案。因此，目前的目录旨在帮助研究人员避免猜测解决当前问题类型的参数值。

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