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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

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

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Chinese Physics B 2013年第2期22卷 314-319页

作者： Krishnendu Bhattacharyya Tasawar Hayat Ahmed Alsaedi Department of Mathematics The University of BurdwanBurdwan-713104West BengalIndia Department of Mathematics Quaid-I-Azam University 45320Islamabad 44000Pakistan Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is *** similarity transformations,the governing equations are converted to an ordinary differential equation and then solved *** introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet *** similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the *** stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.

关键词： magnetohydrodynamic boundary layer Casson fluid stretching/shrinking sheet wall mass transfer analytic solution

Dual Solutions of MHD Boundary Layer Flow of a Micropolar Fluid with Weak Concentration over a stretching/shrinking sheet

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Communications in Theoretical Physics 2017年第4期67卷 449-457页

作者： Z.H.Khan M.Qasim Naeema Ishfaq W.A.Khan Department of Mathematics University of MalakandChakdaraDir(Lower)Khyber PakhtunkhwaPakistan Department of Mathematics COMSATS Institute of Information TechnologyPark RoadChak ShahzadIslamabadPakistan School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mechanical and Industrial Engineering College of Engineering Majmaah UniversityMajmaah 11952Kingdom of Saudi Arabia

We investigate the dual solutions for the MHD flow of micropolar fluid over a stretching/shrinking sheet with heat transfer. Suitable relations transform the partial differential equations into the ordinary differential *** forms solutions are also obtained in terms of confluent hypergeometric function. This is the first attempt to determine the exact solutions for the non-linear equations of MHD micropolar fluid model. It is demonstrated that the microrotation parameter helps in increasing Nusselt number and the dual solutions exist for all fluid flow parameters under consideration. The dual behavior of dimensionless velocity, temperature, microrotation, skin-friction coefficient,local Nusselt number is displayed on graphs and examined.

关键词： MHD micropolar fluid stretching/shrinking sheet exact and dual solutions

Chemically Radiative MHD Flow of a Micropolar Nanofluid over a stretching/ shrinking sheet with a Heat Source or Sink

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Fluid Dynamics & Materials Processing 2024年第2期20卷 257-274页

作者： Parakapali Roja Shaik Mohammed Ibrahim Thummala Sankar Reddy Giulio Lorenzini Department of Mathematics Annamacharya Institute of Technology and SciencesKadapa516126India Department of Engineering Mathematics College of EngineeringKoneru Lakshmaiah Education FoundationVaddeswaram522302India Department of Mathematics Annamacharya Institute of Technology and SciencesKadapa516003India Department of Engineering and Architecture University of ParmaParma43124Italy

This study examines the behavior of a micropolar nanoﬂuidﬂowing over a sheet in the presence of a transverse magneticﬁeld and thermal *** addition,chemical(ﬁrst-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve *** impact of several parameters is *** is shown that the micro-rota-tional velocity of theﬂuid rises with the micropolar ***,the radiation parameter can have a remarkable inﬂuence on theﬂow and temperature proﬁles and on the angular momentum distribution.

关键词： Chemical(ﬁrst order homogeneous)reaction magnetohydrodynamics micropolar nanoﬂuid stretching/shrinking sheet heat source

MHD stagnation point flow of nanofluid with SWCNT and MWCNT over a stretching surface driven by Arrhenius kinetics

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Applied Mathematics(A Journal of Chinese Universities) 2022年第3期37卷 366-382页

作者： Sohail Nadeem Shafiq Ahmad Alibek Issakhov Ibrahim M.Alarifi Department of Mathematics Quaid-I-Azam UniversityIslamabad 44000Pakistan Al-Farabi Kazakh National University av.al-Farabi 71050040AlmatyKazakhstan Department of Mechanical and Industrial Engineering College of engineering Majmaah UniversityAl-Majmaah 11952RiyadhSaudi Arabia

The intention of the current research is to address the conclusion of non-isothermal heterogeneous reaction on the stagnation-point flow of SWCNT-engine oil and MWCNT-engine oil nanofluid over a shrinking/stretching ***,exemplify the aspect of heat and mass transfer the upshot of magnetohydrodynamics(MHD),thermal radiation,and heat generation/absorption coefficient are *** bvp4 c from Matlab is pledged to acquire the numerical explanation of the problem that contains nonlinear system of ordinary differential equations(ODE).The impacts of miscellaneous important parameters on axial velocity,temperature field,concentration profile,skin friction coefficient,and local Nusselt number,are deliberated through graphical and numerically erected tabulated *** solid volume fraction diminishes the velocity distribution while enhancing the temperature ***,the rate of shear stress declines with increasing the magnetic and stretching parameter for both SWCNT and MWCNT.

关键词： heat generation surface reaction CNTs based nanofluid stretching/shrinking sheet thermal radiation

Insight into the dynamics of non-Newtonian Carreau fluid when viscous dissipation,entropy generation,convective heating and diffusion are significant

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 34-46页

作者： ZHOU Shuang-shuang Muhammad Ijaz Khan Sami Ullah Khan Sumaira Qayyum School of Science Hunan City UniversityYiyang 413000China Department of Mechanical Engineering Prince Mohammad Bin Fahd UniversityP.O.Box1664Al-Khobar 31952Kingdom of Saudi Arabia Department of Mathematics Namal UniversityMianwali 42250Pakistan Department of Mathematics Quaid-I-Azam University 45320Islamabad 44000Pakistan

The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation *** novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized *** convective boundary assumptions are directed in order to examine the heat and mass transportation of *** thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno *** problem formulated in dimensionless form is solved by NDSolve *** graphical analysis for parameters governed by the problem is performed with physical *** affiliation of entropy generation and Bejan number for different parameters is inspected in *** numerical data for illustrating skin friction,heat and mass transfer rate is also *** motion of the fluid is highest for the viscosity ratio *** temperature of the fluid rises via thermal Biot *** generation rises for greater Brinkman number and diffusion parameter.

关键词： heat generation surface reaction CNTs based nano uid stretching/shrinking sheet thermal radiation