作者：
Xiong, Pei-Ying;Chu, Yu-Ming;Khan, M. Ijaz;Khan, Sohail A.;Abbas, S. Z.
期刊：
Computational and Theoretical Chemistry,2021年1200:113222 ISSN：2210-271X
通讯作者：
Yu-Ming Chu
作者机构：
[Xiong, Pei-Ying] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Chu, Yu-Ming] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.;[Chu, Yu-Ming] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China.;[Khan, M. Ijaz] Riphah Int Univ I14, Dept Math & Stat, Islamabad 44000, Pakistan.;[Khan, Sohail A.] Quaid I Azam Univ, Dept Math, Islamabad 44000, Pakistan.
通讯机构：
[Yu-Ming Chu] D;Department of Mathematics, Huzhou University, Huzhou 313000, PR China<&wdkj&>Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, PR China
关键词：
Chemical reaction;Entropy generation;Heat generation/absorption;Radiative heat flux;Reiner-Philippof fluid;Viscous dissipation
摘要：
Here we simulate flow of Reiner-Philippoff fluid over a stretching sheet. Energy expression in the presence of heat generation, dissipation and thermal radiation is addressed. Entropy generation and energy communication is developed with the help of thermodynamic second and first laws. Thermodynamics second law states that irreversibility can be generated in any processes and not demolished in any system. Entropy generation is used to improve the system efficiency. Convection of a cooled or heated vertical plate/cone is one of the important problems in mass and heat transportation studies in current times. Physical features of first order chemical reaction are examined. Bejan number formulation is developed. Transformation procedure reduces partial differential system into ordinary system. Newton built in shooting method is used to construct computational outcomes. Prominence of influential variables on temperature, velocity, Bejan number, concentration and entropy optimization are graphically studied. Nusselt and Sherwood numbers are numerically computed against pertinent variables through tables. For higher approximation of Bingham number the velocity and temperature are augmented. Velocity is enhanced against Reiner Philippoff fluid parameter whereas opposite response is noticed for temperature. Temperature boosts up against higher estimation of Eckert number. Bejan number and entropy rate are increased for higher Bingham number and radiation parameter.
作者机构：
[Song, Ying-Qing] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Waqas, Hassan; Farooq, Umar] Govt Coll Univ Faisalabad, Dept Math, Layyah Campus, Faisalabad 31200, Pakistan.;[Al-Khaled, Kamel] Jordan Univ Sci & Technol, Dept Math & Stat, POB 3030, Irbid 22110, Jordan.;[Khan, Sami Ullah] COMSATS Univ Islamabad, Dept Math, Sahiwal 57000, Pakistan.;[Khan, M. Ijaz] Riphah Int Univ, Dept Math, I-14, Islamabad 44000, Pakistan.
通讯机构：
[Yu-Ming Chu] D;Department of Mathematics, Huzhou University, Huzhou 313000, PR China<&wdkj&>Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, PR China
关键词：
Sutterby nanofluid;Bioconvection flow;Marangoni and solutal boundaries;Melting phenomenon;Shooting technique
摘要：
This research communicates the thermal assessment of Sutterby nanofluid containing the gyrotactic microorganisms with solutal and Marangoni boundaries. The applications of melting phenomenon and thermal conductivity are also considered. The flow is confined by a stretched cylinder. The prospective of Brownian motion and thermophoresis diffusions are also taken account via Buongiorno nanofluid model. The problem is formulated with help of governing relations and equations which are altered into dimensionless form via appropriate variables. The numerical scheme based on shooting scheme is employed to access the solution. A comparative analysis is performed to verify the approximated solution. The observations reveal that the velocity profile enhanced with the Marangoni number while a declining velocity profile has been observed with Sutterby nanofluid parameter and Darcy resistance parameter. The nanofluid temperature get rise with thermal conductivity parameter and thermal Biot number. An arising profile of nanofluid concentration is observed for concentration conductivity parameter and buoyancy ratio parameter. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
摘要：
The objective of this article is to explore the unsteady natural convection flows of Prabhakar-like non integer Maxwell fluid. Moreover, wall slip condition on temperature and Newtonian effects on heating are also studied. The generalized memory effects are illustrated with fractional time Prabhakar derivative. Dimensionless temperature and velocity are calculated analytically with the help of Laplace transform technique. A comparison among Prabhakar fractional natural convection flows and classical thermal transport which, illustrated by the Fourier's law. As a limiting case, we recovered the solution of ordinary Maxwell and Newtonian fluids from fractional Maxwell fluids with slip and no slip conditions. The results of fractional and important physical parameters are graphically covered. Accordingly, by comparing Maxwell fluids to viscous fluids, we found out that Maxwell fluids are move rapidly than viscous fluids. Moreover, the ordinary fluids moving fast than fractional fluids.
作者机构：
[Wang, Miao-Kun] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.;[Chu, Hong-Hu] Hunan Univ, Coll Civil Engn, Changsha 410082, Hunan, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Yu-Ming Chu] C;College of Science, Hunan City University, Yiyang, China
关键词：
Gaussian hypergeometric function;Ramanujan's cubic transformation;Ramanujan's generalized modular equation;Generalized Grotzsch ring function
摘要：
We study several special functions in Ramanujan’s generalized modular equation with signature 3. Some sharp inequalities for these functions, including the estimates for the solution of Ramanujan’s generalized modular equation with signature 3 and triplication inequality for the generalized Grötzsch ring function with two parameters, are derived.
作者机构：
[Liu, Hean] Hunan City Univ, Coll Sci, Yiyang 413000, Hunan, Peoples R China.;[Liu, Hean; Ki, Kim Yong] Sehan Univ, Grad Sch, Mokpo 58613, South Korea.
通讯机构：
[Liu, Hean] H;Hunan City Univ, Coll Sci, Yiyang 413000, Hunan, Peoples R China.
摘要：
In the article, we prove that the function x -> (1-x)K-P(root x) is logarithmically concave on (0, 1) if and only if p >= 7/32, the function x -> K(root x)/ log(1 + 4/root 1 - x) is convex on (0, 1) and the function x -> d(2)/dx(2) [K(root x) - log (1+ 4/root 1 - x)] is absolutely monotonic on (0,1), where K(x) = integral(pi/2)(0) (1 - x(2) sin(2) t)(-1/2) dt ( 0 < x < 1) is the complete elliptic integral of the first kind.
摘要：
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
摘要：
The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G. A graph G is called a unicyclic graph if it contains exactly one cycle and a fully loaded unicyclic graph is a unicyclic graph that no vertex with degree less than three in its unique cycle. Let U ( n ) and U ( n ) be the set of unicyclic graphs and fully loaded unicyclic graphs of order n, respectively. In this paper, we determine the graphs of U ( n ) with second-largest Resistance-Harary index and determine the graphs of U ( n ) with largest Resistance-Harary index.
作者机构：
[Wang, Miao-Kun] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.
摘要：
In the article, we present several monotonicity theorems and inequalities for the modular equation functions ma(r) and mu a(r), and find the infinite-series formulas for m1/3(r) and m1/4(r) which depend only on r. As applications, we find several precise explicit estimates for the solution of Ramanujan's generalized modular equation.
摘要：
In this paper, we introduce a new class of functions known as coordinate strongly convex functions. We discuss the relation between strongly convex functions and coordinate strongly convex functions. Also, we present some natural properties of coordinate strongly convex functions. We present Slater’s, Jensen’s and converse of the Jensen inequalities in discrete as well as integral versions for coordinate strongly convex functions. Furthermore, we present Hermite–Hadamard’s type inequalities for coordinate strongly convex functions.
摘要：
In the article, we present the best possible bounds for the weighted Holder mean of the complete p-elliptic integrals of the first and second kinds, which are the generalizations of the previously results for the complete elliptic integrals. (C) 2019 Published by Elsevier Inc.
摘要：
This paper investigates the stability of a class of swarm model with nonlinear dynamics and aperiodically intermittent communication. Different from previous works, it assumes that the agents obtain information from the neighbors at a series of aperiodically time intervals. Moreover, nonlinear dynamics and time delay are considered. It finds that all agents in a swarm can reach cohesion within a finite time under discontinuous communication, where the upper bounds of cohesion depend on the parameters of the swarm model and communication time. A numerical example is given to demonstrate the validity of the theoretical results.
作者机构：
[Chen, Shubo] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.;[Chen, Shubo] Cent South Univ, Coll Math, Changsha 410075, Peoples R China.;[Zhou, Houqing] Shaoyang Univ, Dept Math, Shaoyang 422000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;[Chen, Shubo] C;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.;Cent South Univ, Coll Math, Changsha 410075, Peoples R China.
摘要：
The Zagreb indices are topological indices of graphs, which defined as, M-1(G) = Sigma(v is an element of V(G)) (d(v))(2) , M-2(G) = Sigma(uv is an element of E(G)) (d(u)d(v)). In this paper, we determine the upper and lower bounds for the Zagreb indices of unicyclic graphs in terms of their order and girth. In each case, we characterize the extremal graphs.
关键词：
Quasi-arithmetic mean;Harmonic mean;Geometric mean;Arithmetic mean;Contra-harmonic mean
摘要：
In this article, we prove that the double inequalities
$$\begin{aligned} &\alpha_{1} \biggl[\frac{7C(a,b)}{16}+\frac{9H(a,b)}{16} \biggr]+(1- \alpha_{1}) \biggl[\frac{3A(a,b)}{4}+\frac{G(a, b)}{4} \biggr]\\ &\quad< E(a,b) \\ &\quad< \beta_{1} \biggl[\frac{7C(a,b)}{16}+\frac{9H(a,b)}{16} \biggr]+(1- \beta_{1}) \biggl[\frac{3A(a,b)}{4}+\frac{G(a, b)}{4} \biggr], \\ &\biggl[\frac{7C(a,b)}{16}+\frac{9H(a,b)}{16} \biggr]^{\alpha _{2}} \biggl[ \frac{3A(a,b)}{4}+\frac{G(a, b)}{4} \biggr]^{1-\alpha_{2}}\\ &\quad< E(a,b) \\ &\quad< \biggl[\frac{7C(a,b)}{16}+\frac{9H(a,b)}{16} \biggr]^{\beta _{2}} \biggl[ \frac{3A(a,b)}{4}+\frac{G(a, b)}{4} \biggr]^{1-\beta_{2}} \end{aligned}$$
hold for all
$a, b>0$
with
$a\neq b$
if and only if
$\alpha_{1}\leq 3/16=0.1875$
,
$\beta_{1}\geq64/\pi^{2}-6= 0.484555\dots$
,
$\alpha_{2}\leq3/16=0.1875$
and
$\beta_{2}\geq(5\log2-\log3-2\log \pi)/(\log7-\log6)= 0.503817\dots$
, where
$E(a,b)= (\frac{2}{\pi}\int^{\pi/2}_{0}\sqrt{a\cos^{2}\theta +b\sin^{2}\theta}\,d\theta )^{2}$
,
$H(a,b)=2ab/(a+b)$
,
$G(a,b)=\sqrt{ab}$
,
$A(a,b)=(a+b)/2$
and
$C(a,b)=(a^{2}+b^{2})/(a+b)$
are the quasi-arithmetic, harmonic, geometric, arithmetic and contra-harmonic means of a and b, respectively.
