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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 sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.in addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,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

Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

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Applied Mathematics and Mechanics(English Edition) 2022年第1期43卷 127-140页

作者： i.WAiNi A.iSHAK i.pop Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan Universiti Teknikal Malaysia MelakaDurian Tunggal76100Malaysia Department of Mathematical Sciences Universiti Kebangsaan MalaysiaBangi43600Malaysia Department of Mathematics Babeş-Bolyai UniversityCluj-Napoca400084Romania

The magnetohydrodynamic(MHD)mixed convection flow past a shrinking vertical sheet with thermal radiation is considered.Besides,the effects of Cu-Al_(2)O_(3) nanoparticles and dust particles are considered.The similarity variables reduce the governing equations to the similarity equations,which are then solved numerically.The outcome shows that,for the shrinking case,the solutions are not unique.The rate of heat transfer and the friction factor enlarge with increasing the values of the copper nanoparticle volume fraction as well as the magnetic parameter.Meanwhile,the assisting flow and the rise of the thermal radiation reduce these quantities.Two solutions are found,and the boundary layer separation is dependent on the mixed convection parameter.

关键词： dusty fluid hybrid nanofluid magnetohydrodynamic(MHD) mixed convection shrinking sheet thermal radiation dual solution

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

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Applied Mathematics and Mechanics(English Edition) 2023年第4期44卷 641-652页

作者： A.V.ROSCA N.C.ROSCA i.pop Department of Statistics-Forecasts-Mathematics Faculty of Economics and Business AdministrationBabes-Bolyai UniversityCluj-Napoca 400084Romania Department of Mathematics Faculty of Mathematics and Computer ScienceBabes-Bolyai UniversityCluj-Napoca 400084Romania Academy of Romanian Scientists 3 Ilfov StreetBucharest 050044Romania

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

关键词： three-dimensional(3D)mixed convection flow stagnation point flow first-order slip velocity second-order slip velocity numerical solution stability analysis

Slip effects on unsteady mixed convection of hybrid nanofluid flow near the stagnation point

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Applied Mathematics and Mechanics(English Edition) 2022年第4期43卷 547-556页

作者： N.A.ZAiNAL R.NAZAR K.NAGANTHRAN i.pop Department of Mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaBangi 43600Malaysia Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan Universiti Teknikal Malaysia MelakaHang Tuah JayaDurian Tunggal 76100Malaysia institute of Mathematical Sciences Faculty of ScienceUniversiti MalayaKuala Lumpur 50603Malaysia Center for Data Analytics Consultancy and ServicesFaculty of ScienceUniversiti MalayaKuala Lumpur 50603Malaysia Department of Mathematics Babes-Bolyai UniversityR-400084 Cluj-NapocaRomania

The unsteady mixed convection of the Al_(2)O_(3)-Cu/H_(2)O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed.The bvp4c technique is used to solve the resulting ordinary differential equations.The combined effects of the velocity and thermal slip are addressed.The effects of different relevant physical parameters are studied numerically.The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases,while the unsteadiness parameter has an opposite effect in the opposing flow.The presence of the slip parameter is proven to increase the skin friction coefficient while reduce the local Nusselt number in the buoyancy opposing flow.A contradictory result is observed in the buoyancy assisting flow.Meanwhile,the heat transfer rate is reduced in the buoyancy of the assisting and opposing flows when the thermal slip effect is considered.

关键词： hybrid nanofluid mixed convection unsteady flow stagnation point

Comment on the paper “Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier's partial slip”

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Applied Mathematics and Mechanics(English Edition) 2018年第7期39卷 1057-1058页

作者： i.pop Department of Mathematics Babes-Bolyai University

The present comment concerns some doubtful results included in the abovepaper.

关键词： local inertia parameter magnetic parameter Eckert number

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

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Applied Mathematics and Mechanics(English Edition) 2020年第3期41卷 507-520页

作者： i.WAiNi A.iSHAK i.pop Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan Universiti Teknikal Malaysia MelakaHang Tuah JayaDurian Tunggal 76100MelakaMalaysia Department of Mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaUKM Bangi 43600SelangorMalaysia Department of Mathematics Babe¸s-Bolyai UniversityCluj-Napoca 400084Romania

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. it is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.

关键词： dual solution hybrid nanofluid stretching/shrinking wedge magnetic field radiation stability analysis

Fluid flow driven along microchannel by its upper stretching wall with electrokinetic effects

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Applied Mathematics and Mechanics(English Edition) 2018年第3期39卷 395-408页

作者： Hang XU i.pop Q.SUN Collaborative innovation Center for Advanced Ship and Deep-Sea Exploration State Key Lab of Ocean EngineeringSchool of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong University Department of Mathematics Babe§-Bolyai University Particulate Fluids Processing Centre Department of Chemical EngineeringThe University of Melbourne

We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. in this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method （HAM） to get the analytical solution of the model. in our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. it is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.

关键词： microchannel electrokinetic effect stretching wall electro-viscous flowmodel

Mixed convection boundary layer flow past vertical flat plate in nanofluid: case of prescribed wall heat flux

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Applied Mathematics and Mechanics(English Edition) 2015年第8期36卷 1091-1104页

作者： R.TRiMBiTAS T.GROSAN i.pop Department of Mathematics Babes-Bolyai University

An analysis is carried out to investigate the steady mixed convection bound- ary layer flow of a water based nanofluid past a vertical semi-infinite flat plate. Using an appropriate similarity transformation, the governing partial differential equations are transformed into the coupled, nonlinear ordinary （similar） differential equations, which are then solved numerically for the Prandtl number Pr = 6.2. The skin friction coeffi- cient, the local Nusselt number, and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction φ and the mixed convection parameter λ on the fluid flow and heat transfer characteristics are thoroughly examined. Different from an assisting flow, it is found that the solutions for an opposing flow are non-unique. in order to establish which solution branch is stable and physically realizable in practice, a stability analysis is performed.

关键词： Nanofluid boundary layer mixed convection heat flux dual solution

Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms

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Applied Mathematics and Mechanics(English Edition) 2015年第2期36卷 163-178页

作者： A.RAEES Hang XU Qiang SUN i.pop State Key Laboratory of Ocean Engineering School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong University Department of Mechanical Engineering National University of Singapore Department of Mathematics Babes-Bolyai University

Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented.The Buongiorno model is applied. Two kinds of boundary conditions, the passive and the active boundary conditions, are considered to investigate this film flow phenomenon.Through a set of similarity variables, the ordinary differential equations that describe the conservation of the momentum, the thermal energy, the nanoparticles, and the microorganisms are derived and then solved numerically by an efficient finite difference technique.The effects of various physical parameters on the profiles of momentum, thermal energy,nanoparticles, microorganisms, local skin friction, local Nusselt number, local wall mass flux, and local wall motile microorganisms flux are investigated. it is expected that the passively controlled nanofluid model can be much more easily achieved and applied in real circumstances than the actively controlled model.

关键词： gravity-driven nanofluid film flow bioconvection passively controlled model actively controlled model gyrotactic microorganisms convective boundary condition

Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet

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Applied Mathematics and Mechanics(English Edition) 2010年第11期31卷 1421-1428页

作者： N.BACHOK A.iSHAK i.pop Department of Mathematics Faculty of ScienceUniversiti Putra Malaysia School of Mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia institute of Mathematical Sciences Faculty of ScienceUniversity of Malaya Faculty of Mathematics University of Cluj

The unsteady viscous flow over a continuously permeable shrinking surface is studied. Similarity equations are obtained through the application of similar transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter, the shrinking parameter and the Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. it is found that, different from an unsteady stretching sheet, dual solutions exist in a certain range of mass suction and unsteadiness parameters.

关键词： unsteady three-dimensional flow boundary layer shrinking sheet dual solution