The purpose of this study is to generalize the concept of Q -hesitant fuzzy sets and soft set theory to Q -hesitant fuzzy soft sets. The Q -hesitant fuzzy set is an admirable hybrid property, specially developed by the new generalized hybrid structure of hesitant fuzzy sets. Our goal is to provide a formal structure for the m -polar Q -hesitant fuzzy soft (MQHFS) set. First, by combining m-pole fuzzy sets, soft set models, and Q -hesitant fuzzy sets, we introduce the concept of MQHFS and apply it to deal with multiple theories in B C K / B C I -algebra. We then develop a framework including MQHFS subalgebras, MQHFS ideals, closed MQHFS ideals, and MQHFS exchange ideals in B C K / B C I -algebras. Furthermore, we prove some relevant properties and theorems studied in our work. Finally, the application of MQHFS-based multicriteria decision-making in the Ministry of Health system is illustrated through a recent case study to demonstrate the effectiveness of MQHFS through the use of horizontal soft sets in decision-making.
本研究的目的是将Q -犹豫模糊集和软集理论的概念推广到Q -犹豫模糊软集。Q -犹豫模糊集是一种很好的混合性质，是由犹豫模糊集的一种新的广义混合结构发展起来的。我们的目标是为m极Q犹豫模糊软集(MQHFS)提供一个形式化的结构。首先，结合m-极点模糊集、软集模型和Q -犹豫模糊集，引入MQHFS的概念，并将其应用于B - C - K / B - C - I代数中的多种理论。然后，我们开发了一个框架，包括MQHFS子代数、MQHFS理想、闭MQHFS理想和MQHFS交换理想在B C K / B C I -代数中。此外，我们还证明了工作中研究过的一些相关性质和定理。最后，通过最近的一个案例研究，说明了基于MQHFS的多标准决策在卫生部系统中的应用，以证明MQHFS通过在决策中使用水平软集来证明MQHFS的有效性。
{"title":"Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making","authors":"Maryam Abdullah Alshayea, K. M. Alsager","doi":"10.1155/2023/8163134","DOIUrl":"https://doi.org/10.1155/2023/8163134","url":null,"abstract":"The purpose of this study is to generalize the concept of \u0000 \u0000 Q\u0000 \u0000 -hesitant fuzzy sets and soft set theory to \u0000 \u0000 Q\u0000 \u0000 -hesitant fuzzy soft sets. The \u0000 \u0000 Q\u0000 \u0000 -hesitant fuzzy set is an admirable hybrid property, specially developed by the new generalized hybrid structure of hesitant fuzzy sets. Our goal is to provide a formal structure for the \u0000 \u0000 m\u0000 \u0000 -polar \u0000 \u0000 Q\u0000 \u0000 -hesitant fuzzy soft (MQHFS) set. First, by combining m-pole fuzzy sets, soft set models, and \u0000 \u0000 Q\u0000 \u0000 -hesitant fuzzy sets, we introduce the concept of MQHFS and apply it to deal with multiple theories in \u0000 \u0000 B\u0000 C\u0000 K\u0000 /\u0000 \u0000 B\u0000 C\u0000 I\u0000 \u0000 \u0000 -algebra. We then develop a framework including MQHFS subalgebras, MQHFS ideals, closed MQHFS ideals, and MQHFS exchange ideals in \u0000 \u0000 B\u0000 C\u0000 K\u0000 /\u0000 \u0000 B\u0000 C\u0000 I\u0000 \u0000 \u0000 -algebras. Furthermore, we prove some relevant properties and theorems studied in our work. Finally, the application of MQHFS-based multicriteria decision-making in the Ministry of Health system is illustrated through a recent case study to demonstrate the effectiveness of MQHFS through the use of horizontal soft sets in decision-making.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87802606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiabao Wu, Kezheng Zuo, D. Cvetković-Ilić, Honglin Zou
The paper focuses on the class of the Bott–Duffin inverses. Several original features of the class are identified and new properties are characterized. Some of the results available in the literature are recaptured in a more general form. BD matrices are also introduced and some properties are given.
{"title":"New Characterizations and Representations of the Bott–Duffin Inverse","authors":"Jiabao Wu, Kezheng Zuo, D. Cvetković-Ilić, Honglin Zou","doi":"10.1155/2023/7623837","DOIUrl":"https://doi.org/10.1155/2023/7623837","url":null,"abstract":"The paper focuses on the class of the Bott–Duffin inverses. Several original features of the class are identified and new properties are characterized. Some of the results available in the literature are recaptured in a more general form. BD matrices are also introduced and some properties are given.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83723177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In most fields of applied sciences, inequalities are important in constructing mathematical systems and associated solution functions. Convexity also has a significant impact on an assortment of mathematical topics. By utilizing a comprehensive version of Riemann–Liouville integrals and the functions’ convexity condition, we present and prove novel fractional inequalities. According to the current literature, this work is a novel addition to the literature, and the proposed technique for addressing fractional inequalities issues is straightforward and simple to execute. It is also easy to see that all of the inequalities that have been developed are inclusive and may be reduced to a variety of other inequalities that have been proposed in the literature. Additionally, certain numeric examples with graphs are provided to support the theoretical results.
{"title":"New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals","authors":"Abd-Allah Hyder","doi":"10.1155/2023/9532488","DOIUrl":"https://doi.org/10.1155/2023/9532488","url":null,"abstract":"In most fields of applied sciences, inequalities are important in constructing mathematical systems and associated solution functions. Convexity also has a significant impact on an assortment of mathematical topics. By utilizing a comprehensive version of Riemann–Liouville integrals and the functions’ convexity condition, we present and prove novel fractional inequalities. According to the current literature, this work is a novel addition to the literature, and the proposed technique for addressing fractional inequalities issues is straightforward and simple to execute. It is also easy to see that all of the inequalities that have been developed are inclusive and may be reduced to a variety of other inequalities that have been proposed in the literature. Additionally, certain numeric examples with graphs are provided to support the theoretical results.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"42 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87856000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to study a class of Kirchhoff-type problems with variable exponent. By means of the perturbation technique, the method of invariant sets for the descending flow and necessary estimates and the existence of infinitely many sign-changing solutions to this problem are obtained.
{"title":"Sign-Changing Solutions for Kirchhoff-Type Problems with Variable Exponent","authors":"Changmu Chu, Ying Yu","doi":"10.1155/2023/6210890","DOIUrl":"https://doi.org/10.1155/2023/6210890","url":null,"abstract":"This paper is devoted to study a class of Kirchhoff-type problems with variable exponent. By means of the perturbation technique, the method of invariant sets for the descending flow and necessary estimates and the existence of infinitely many sign-changing solutions to this problem are obtained.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"54 6","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72568902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For s-convex functions, the Hermite–Hadamard inequality is already well-known in convex analysis. In this regard, this work presents new inequalities associated with the left-hand side of the Hermite–Hadamard inequality for s-convexity by utilizing a novel technique based on Green’s function. Also, Hölder, Young, and power-mean inequalities are used to obtain these new inequalities. Finally, some applications to special means of real numbers are provided. In conclusion, we think that the methodology used in this work will encourage more research in this field.
{"title":"Some Further Results Using Green’s Function for <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>s</mi>\u0000 </math>-Convexity","authors":"Çetin Yıldız, Levent Akgün, M. Khan, N. Rehman","doi":"10.1155/2023/3848846","DOIUrl":"https://doi.org/10.1155/2023/3848846","url":null,"abstract":"For s-convex functions, the Hermite–Hadamard inequality is already well-known in convex analysis. In this regard, this work presents new inequalities associated with the left-hand side of the Hermite–Hadamard inequality for s-convexity by utilizing a novel technique based on Green’s function. Also, Hölder, Young, and power-mean inequalities are used to obtain these new inequalities. Finally, some applications to special means of real numbers are provided. In conclusion, we think that the methodology used in this work will encourage more research in this field.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83226939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Soobin Kwak, S. Kang, Seokju Ham, Youngjin Hwang, Gyeonggyu Lee, Junseok Kim
In this article, we develop an unconditionally stable numerical scheme for the modified Fisher–Kolmogorov–Petrovsky–Piscounov (Fisher–KPP) equation modeling population dynamics in two-dimensional space. The Fisher–KPP equation models the process of interaction between reaction and diffusion. The new solution algorithm is based on an alternating direction implicit (ADI) method and an interpolation method so that it is unconditionally stable. The proposed finite difference method is second-order accurate in time and space variables. Therefore, the main purpose of this study is to propose the novel Fisher–KPP equation with a nonlinear growth term and develop an unconditionally stable second-order numerical scheme. The novelty of our method is that it is a numerical method with second-order accuracy using interpolation and ADI methods in two dimensions. We demonstrate the performance of the proposed scheme through computational tests such as convergence and stability tests and the effects of model parameters and initial conditions.
{"title":"An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation","authors":"Soobin Kwak, S. Kang, Seokju Ham, Youngjin Hwang, Gyeonggyu Lee, Junseok Kim","doi":"10.1155/2023/5527728","DOIUrl":"https://doi.org/10.1155/2023/5527728","url":null,"abstract":"In this article, we develop an unconditionally stable numerical scheme for the modified Fisher–Kolmogorov–Petrovsky–Piscounov (Fisher–KPP) equation modeling population dynamics in two-dimensional space. The Fisher–KPP equation models the process of interaction between reaction and diffusion. The new solution algorithm is based on an alternating direction implicit (ADI) method and an interpolation method so that it is unconditionally stable. The proposed finite difference method is second-order accurate in time and space variables. Therefore, the main purpose of this study is to propose the novel Fisher–KPP equation with a nonlinear growth term and develop an unconditionally stable second-order numerical scheme. The novelty of our method is that it is a numerical method with second-order accuracy using interpolation and ADI methods in two dimensions. We demonstrate the performance of the proposed scheme through computational tests such as convergence and stability tests and the effects of model parameters and initial conditions.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79752138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sondos M. Syam, Z. Siri, R. Kasmani, Kenan Yildirim
In this article, we focus on two classes of fractional wave equations in the context of the sequential Caputo derivative. For the first class, we derive the closed-form solution in terms of generalized Mittag–Leffler functions. Subsequently, we consider a more general class of nonhomogeneous fractional wave equations. Due to the complexity of finding exact solutions for these problems, we employ a numerical technique based on the operational matrix method to approximate the solution. We provide several theoretical and numerical examples to validate the effectiveness of this numerical approach. The results demonstrate the accuracy and efficiency of the proposed method.
{"title":"A New Method for Solving Sequential Fractional Wave Equations","authors":"Sondos M. Syam, Z. Siri, R. Kasmani, Kenan Yildirim","doi":"10.1155/2023/5888010","DOIUrl":"https://doi.org/10.1155/2023/5888010","url":null,"abstract":"In this article, we focus on two classes of fractional wave equations in the context of the sequential Caputo derivative. For the first class, we derive the closed-form solution in terms of generalized Mittag–Leffler functions. Subsequently, we consider a more general class of nonhomogeneous fractional wave equations. Due to the complexity of finding exact solutions for these problems, we employ a numerical technique based on the operational matrix method to approximate the solution. We provide several theoretical and numerical examples to validate the effectiveness of this numerical approach. The results demonstrate the accuracy and efficiency of the proposed method.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81717218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Defined on the top of classical L p -spaces, the Besov spaces of periodic functions are good at encoding the smoothness properties of their elements. These spaces are also characterized in terms of summability conditions on the coefficients in trigonometric series expansions of their elements. In this paper, we study the approximation properties of 2 π -periodic functions in a Besov space under a norm involving the seminorm associated with the space. To achieve our results, we use a summability method presented by a lower triangular matrix with monotonic rows.
{"title":"Fourier Series Approximation in Besov Spaces","authors":"Birendra Singh, Uaday Singh","doi":"10.1155/2023/4250869","DOIUrl":"https://doi.org/10.1155/2023/4250869","url":null,"abstract":"Defined on the top of classical \u0000 \u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 p\u0000 \u0000 \u0000 \u0000 -spaces, the Besov spaces of periodic functions are good at encoding the smoothness properties of their elements. These spaces are also characterized in terms of summability conditions on the coefficients in trigonometric series expansions of their elements. In this paper, we study the approximation properties of \u0000 \u0000 2\u0000 π\u0000 \u0000 -periodic functions in a Besov space under a norm involving the seminorm associated with the space. To achieve our results, we use a summability method presented by a lower triangular matrix with monotonic rows.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77540653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
图G = vg的幂正则标记，eg是对射f:1,2，…，V G使得边e = u v被赋标签为1，如果f u= f vN或f v =F - n，对于某个n∈n∪0，否则标记为0，并且满足标记为0的边的个数和标记为1的边的个数相差不超过1。允许幂诚恳标记的图称为幂诚恳图。本文给出了幂诚恳图的一些刻画，并探讨了幂诚恳标记的np完全问题。这项工作也排除了电力亲切标记的禁止子图表征的任何可能性。
{"title":"Some Characterizations and NP-Complete Problems for Power Cordial Graphs","authors":"C. M. Barasara, Y. B. Thakkar","doi":"10.1155/2023/2257492","DOIUrl":"https://doi.org/10.1155/2023/2257492","url":null,"abstract":"<jats:p>A power cordial labeling of a graph <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>G</mi>\u0000 <mo>=</mo>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <mo>,</mo>\u0000 <mi>E</mi>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> is a bijection <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>V</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>⟶</mo>\u0000 <mfenced open=\"{\" close=\"}\" separators=\"|\">\u0000 <mrow>\u0000 <mn>1,2</mn>\u0000 <mo>,</mo>\u0000 <mo>…</mo>\u0000 <mo>,</mo>\u0000 <mrow>\u0000 <mfenced open=\"|\" close=\"|\" separators=\"|\">\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> such that an edge <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>e","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"44 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83023927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article considered the steady two-dimensional boundary layer flow of incompressible viscous Casson nanofluids over a permeable, convectively heated, shrinking/stretching slippery sheet surface. The achievements of this work are extremely relevant, both theoretically with respect to the mathematical modeling of non-Newtonian nanofluid flow with heat transfer in engineering systems and with respect to engineering cooling applications. The combined impacts of suction/injection, viscous dissipation, convective heating, and chemical reactions were considered. The governing modeled partial differential equations with boundary conditions are transformed into nonlinear ordinary differential equations using similarity transformations and finally converted to the first-order initial value problem. Then, the technique of the fourth-fifth order Runge–Kutta–Fehlberg with the shooting method is used to obtain numerical solutions. Moreover, the effects of different involving parameters on the dimensionless temperature, velocity, and concentration, as well as, from an engineering viewpoint, local Nusselt number, the skin friction, and local Sherwood number are illustrated and presented in graphs and tabular forms. For critical shrinking parameter λ c , the existence of a dual solution within the interval λ c < λ < 0 is revealed, and this range escalates with the suction and slipperiness parameters; hence, both control the flow stability. The increment in the values of the porous media, Casson, Forchheimer, slipperiness, and convective heating parameters reduces the local skin friction and intensifies the rates of mass and heat transfer. For the Newtonian flow (that is, as the Casson parameter β gets to infinity ∞ ), the thermal boundary layer thickness, temperature profile, and skin friction diminish, whereas the concentration profile, mass, and heat transfer rates increase compared to the non-Newtonian Casson nanofluid. These results excellently agree with the existing ones.
本文研究了不可压缩粘性卡森纳米流体在可渗透、对流加热、收缩/拉伸滑片表面上的二维边界层稳定流动。这项工作的成果是非常相关的，无论是理论方面的非牛顿纳米流体流动的数学建模与传热工程系统和工程冷却应用。考虑了吸力/喷射、粘性耗散、对流加热和化学反应的综合影响。利用相似变换将具有边界条件的控制模型偏微分方程转化为非线性常微分方程，最后转化为一阶初值问题。然后，利用四五阶龙格-库塔-费伯格技术与射击法求解数值解。此外，不同的涉及参数对无因次温度、速度和浓度的影响，以及从工程的角度来看，局部努塞尔数、表面摩擦和局部舍伍德数都用图表和表格的形式进行了说明和呈现。对于临界收缩参数λ c，揭示了在λ c < λ < 0区间内存在对偶解，且该范围随吸力参数和滑性参数的增大而增大;因此，两者都控制着流动的稳定性。多孔介质、Casson、Forchheimer、滑度和对流加热参数值的增加减少了局部表面摩擦，提高了质量和传热率。与非牛顿卡森纳米流体相比，牛顿流体(即当卡森参数β趋于无穷∞时)的热边界层厚度、温度分布和表面摩擦减小，而浓度分布、质量和换热率增加。这些结果与已有的结果非常吻合。
{"title":"Stability Analysis of Dual Solutions of Convective Flow of Casson Nanofluid past a Shrinking/Stretching Slippery Sheet with Thermophoresis and Brownian Motion in Porous Media","authors":"Kifle Adula Duguma, O. Makinde, L. Enyadene","doi":"10.1155/2023/5954860","DOIUrl":"https://doi.org/10.1155/2023/5954860","url":null,"abstract":"This article considered the steady two-dimensional boundary layer flow of incompressible viscous Casson nanofluids over a permeable, convectively heated, shrinking/stretching slippery sheet surface. The achievements of this work are extremely relevant, both theoretically with respect to the mathematical modeling of non-Newtonian nanofluid flow with heat transfer in engineering systems and with respect to engineering cooling applications. The combined impacts of suction/injection, viscous dissipation, convective heating, and chemical reactions were considered. The governing modeled partial differential equations with boundary conditions are transformed into nonlinear ordinary differential equations using similarity transformations and finally converted to the first-order initial value problem. Then, the technique of the fourth-fifth order Runge–Kutta–Fehlberg with the shooting method is used to obtain numerical solutions. Moreover, the effects of different involving parameters on the dimensionless temperature, velocity, and concentration, as well as, from an engineering viewpoint, local Nusselt number, the skin friction, and local Sherwood number are illustrated and presented in graphs and tabular forms. For critical shrinking parameter \u0000 \u0000 \u0000 \u0000 λ\u0000 \u0000 \u0000 c\u0000 \u0000 \u0000 \u0000 , the existence of a dual solution within the interval \u0000 \u0000 \u0000 \u0000 λ\u0000 \u0000 \u0000 c\u0000 \u0000 \u0000 <\u0000 λ\u0000 <\u0000 0\u0000 \u0000 is revealed, and this range escalates with the suction and slipperiness parameters; hence, both control the flow stability. The increment in the values of the porous media, Casson, Forchheimer, slipperiness, and convective heating parameters reduces the local skin friction and intensifies the rates of mass and heat transfer. For the Newtonian flow (that is, as the Casson parameter \u0000 \u0000 β\u0000 \u0000 gets to infinity \u0000 \u0000 ∞\u0000 \u0000 ), the thermal boundary layer thickness, temperature profile, and skin friction diminish, whereas the concentration profile, mass, and heat transfer rates increase compared to the non-Newtonian Casson nanofluid. These results excellently agree with the existing ones.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75229487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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