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Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

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Chinese Physics B 2024年第2期33卷 108-114页

作者： U.S.Mahabaleshwar G.P.Vanitha L.M.Pérez Emad H.Aly I.Pop Department of Studies in Mathematics Davangere UniversityShivagangothriDavangereIndia Departamento de F´ısica FACIUniversidad de Tarapac´aCasilla 7DAricaChile Department of Mathematics Faculty of EducationAin Shams UniversityRoxyCairoEgypt Department of Mathematics Babes-Bolyai University400084 Cluj-NapocaRomania

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked *** the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is *** resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity *** transformed differential equations are solved *** of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted *** skin friction and Nusselt number were also *** addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching ***,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O ***,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

关键词： magnetohydrodynamic nanofluid stretching/shrinking sheet axisymmetric flow analytical solution suction/injection

axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis

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Applied Mathematics and Mechanics(English Edition) 2016年第7期37卷 919-928页

作者： T.HAYAT S.MAKHDOOM M.AWAIS S.SALEEM M.M.RASHIDI Department of Mathematics Quaid-i-Azam University Department of Mathematics COMSATS Institute of Information Technology Department of Mathematics Statistics and Physics Qatar University Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems Tongji University

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method （OHAM）. The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.

关键词： axisymmetric flow optimal homotopy analysis method (OHAM) analysis,convective boundary condition

axisymmetric Stagnation-Point flow of Nanofluid Over a Stretching Surface

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Advances in Applied Mathematics and Mechanics 2014年第2期6卷 220-232页

作者： M.Nawaz T.Hayat Department of Humanities and Sciences Institute of Space Technology P.O.Box 2750Islamabad 44000Pakistan Department of Mathematics Quaid-i-Azam University 45320 Islamabad 44000Pakistan Department of Mathematics Faculty of SciencesKing Abdulaziz UniversityJeddah 80253Saudi Arabia

This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching *** model exhibiting Brownian motion and thermophoresis is *** solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method(HAM).Comparative study between the HAM solutions and previously published numerical results shows an excellent ***,temperature and mass fraction are displayed for various values of *** local skin friction coefficient,the local Nusselt number and the local Sherwood number are *** is observed that the presence of nanoparticles enhances the thermal conductivity of base *** is found that the convective heat transfer coefficient(Nusselt number)is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.

关键词： Nanofluid axisymmetric flow stagnation point Nusselt number Sherwood number

Numerical simulation of motion and deformation of ring bubble along body surface

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Applied Mathematics and Mechanics(English Edition) 2013年第12期34卷 1495-1512页

作者：倪宝玉张阿漫 G.X.WU College of Shipbuilding Engineering Harbin Engineering University Department of Mechanical Engineering University College London

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.

关键词： bubble dynamics moving boundary axisymmetric flow boundary elementmethod

Unsteady peristaltic transport of Maxwell fluid through finite length tube:application to oesophageal swallowing

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Applied Mathematics and Mechanics(English Edition) 2012年第1期33卷 15-24页

作者： S. K. PANDEY D. TRIPATHI Department of Applied Mathematics Institute of Technology Banaras Hindu University Department of Mathematics Indian Institute of Technology Ropar

This paper analytically investigates the unsteady peristaltic transport of the Maxwell fluid in a finite tube. The walls of the tube are subjected to the contraction waves that do not cross the stationary boundaries. The analysis is carried out by a long wavelength approximation in the non-dimensional form. The expressions for the axial and radial velocities are derived. The pressures across the wavelength and the tubelength are also estimated. The reflux phenomenon is discussed, which culminates into the determination of the reflux limit. Mathematical formulations are physically interpreted for the flow of masticated food materials such as bread and white eggs in the oesophagus. It is revealed that the Maxwell fluids are favorable to flow in the oesophagus as compared with the Newtonian fluids. This endorses the experimental finding of Takahashi et al. （Takahashi, T., Ogoshi, H., Miyamoto, K., and Yao, M. L. Viscoelastic properties of commercial plain yoghurts and trial foods for swallowing disorders. Rheology, 27, 169- 172 （1999））. It is further revealed that the relaxation time does not affect the shear stress and the reflux limit. It is found that the pressure peaks are identical in the integral case while different in the non-integral case.

关键词： peristaltic transport Maxwell fluid oesophagus axisymmetric flow reflux

Investigation of the Surface Vortex in a Spillway Tunnel Intake

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Tsinghua Science and Technology 2010年第5期15卷 561-565页

作者：王英奎江春波 State Key Laboratory of Hydroscience and Engineering Tsinghua University

The surface vortex in a spillway tunnel intake was investigated in a physical model of the Xiluodu hydropower *** velocity fields were measured using the particle tracking velocimetry *** tangential velocity formula of the surface flow field was derived based on the Navier-Stokes equations,and this formula greatly improved the consistency between the numerical and experimental ***,the formula has the advantage of describing the tangential velocity more accurately than previous *** current research is based on established engineering practices,and the results provide a valuable reference for actual projects designed to prevent and eliminate surface vortexes.

关键词： surface vortex axisymmetric flow particle tracking velocimetry(PTV) tangential velocity

Necessary and Sufficient Conditions for the Separability and the R-Separability of the Irrotational Stokes Equation and Applications

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Journal of Applied Mathematics and Physics 2020年第11期8卷 2379-2401页

作者： Eleftherios Protopapas Maria Hadjinicolaou School of Applied Mathematical and Physical Sciences National Technical University of Athens Athens Greece Applied Mathematics Laboratory School of Science and Technology Hellenic Open University Patras Greece

In the present manuscript, we formulate and prove rigorously, necessary and sufficient conditions for all kinds of separation of variables that a solution of the irrotational Stokes equation may exhibit, in any orthogonal axisymmetric system, namely: simple separation and R-separation. These conditions may serve as a road map for obtaining the corresponding solution space of the irrotational Stokes equation, in any orthogonal axisymmetric coordinate system. Additionally, we investigate how the inversion of the coordinate system, with respect to a sphere, affects the type of separation. Specifically, we prove that if the irrotational Stokes equation separates variables in an axisymmetric coordinate system, then it R-separates variables in the corresponding inverted coordinate system. This is a quite useful outcome since it allows the derivation of solutions for a problem, from the knowledge of the solution of the same problem in the inverted geometry and vice-versa. Furthermore, as an illustration, we derive the eigenfunctions of the irrotational Stokes equation governing the flow past oblate spheroid particles and inverted oblate spheroidal particles.

关键词： axisymmetric flow Stokes Operator Analytical Solution Separation and R-Separation of Variables axisymmetric Orthogonal Coordinate Systems