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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

Radiation efects on MhD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition

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Chinese Journal of Aeronautics 2013年第6期26卷 1389-1397页

作者： Noreen Sher Akbar S.Nadeem Rizwan Ul haq z.h.khan DBS&h CEMENational University of Sciences and TechnologyIslamabad 44000Pakistan Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan School of Mathematical Sciences Peking University

The aim of the present paper is to study the numerical solutions of the steady MhD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching *** effects of radiation and convective boundary condition are also taken into *** model used for the nanofluid incorporates the effects of Brownian motion and *** resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity *** solutions have been obtained for the velocity,temperature and nanoparticle fraction *** influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.

关键词： Convective boundary condition Nanoparticles Numerical solutions Radiation effects Stagnation point Stretching surface

Numerical Study of Unsteady MhD Flow and Entropy Generation in a Rotating Permeable Channel with Slip and hall Effects

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Communications in Theoretical Physics 2018年第11期69卷 641-650页

作者： z.h.khan O.D.Makinde R.Ahmad W.A.khan State Key Laboratory of hydraulics and Mountain River Engineering College of Water Resource & HydropowerSichuan University Key Laboratory of Advanced Reactor Engineering and Safety Ministry of Education Tsinghua University Faculty of Military Science Stellenbosch University School of Mathematics and Physics University of Queensland Faculty of Engineering Sciences GIK Institute of Engineering Sciences and Technology Department of Mechanical Engineering College of Engineering Prince Mohammad Bin Fahd University

This article investigates an unbiased analysis for the unsteady two-dimensional laminar flow of an incompressible, electrically and thermally conducting fluid across the space separated by two infinite rotating permeable *** influence of entropy generation, hall and slip effects are considered within the flow analysis. The problem is modeled based on valid physical arguments and the unsteady system of dimensionless PDEs (partial differential equations) are solved with the help of Finite Difference Scheme. In the presence of pertinent parameters, the precise movement of the flow in terms of velocity, temperature, entropy generation rate, and Bejan numbers are presented graphically, which are parabolic in nature. Streamline profiles are also presented, which exemplify the accurate movement of the flow. The current study is one of the infrequent contributions to the existing literature as previous studies have not attempted to solve the system of high order non-linear PDEs for the unsteady flow with entropy generation and hall effects in a permeable rotating channel. It is expected that the current analysis would provide a platform for solving the system of nonlinear PDEs of the other unexplored models that are associated to the two-dimensional unsteady flow in a rotating channel.

关键词： unsteady flow rotating permeable channel MhD slip hall effects entropy analysis finite difference method

Finite Difference Analysis of Time-Dependent Viscous Nanofluid Flow Between Parallel Plates

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Communications in Theoretical Physics 2019年第11期71卷 1293-1300页

作者： Salman Ahmad T.hayat A.Alsaedi z.h.khan M.Waleed Ahmed khan Department of Mathematics Quaid-I-Azam University 45320Islamabad 44000Pakistan Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityP.O.Box 80257Jeddah 21589Saudi Arabia State Key Laboratory of hydraulics and Mountain River Engineering College of Water Resource and HydropowerSichuan UniversityChengdu 610065China Key Laboratory of Advanced Reactor Engineering and Safety Ministry of EducationTsinghua UniversityBeijing 100084China

This article computes effect of uniform magnetic field on nanofluid flow filling porous medium inside parallel sheets. Darcy's law is used to characterize porous medium. Flow is caused by stretching of the lower sheet. The governing systems are computed using Finite difference technique. This scheme is used due to its more general and powerful nature to solve nonlinear problems. Results are obtained and discussed graphically. Nusselt number, skin friction, streamlines,velocity and temperature are emphasized.

关键词： finite difference scheme porous medium magnetic field nanofluid parallel stretchable sheets

Wavelet analysis of stagnation point flow of non-Newtonian nanofluid

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Applied Mathematics and Mechanics(English Edition) 2019年第8期40卷 1211-1226页

作者： M.hAMID M.USMAN R.U.hAQ4 z.h.khan Wei WANG School of Mathematical Sciences Peking UniversityBeijing 100871China BIC-ESAT College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering SciencePeking UniversityBeijing 100871China Department of Electrical Engineering Bahria UniversityIslamabad 44000Pakistan State Key Laboratory of hydraulics and Mountain River Engineering College of Water Resource & HydropowerSichuan UniversityChengdu 610065China Key Laboratory of Advanced Reactor Engineering and Safety Ministry of Education Tsinghua UniversityBeijing 100084China

The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.

关键词： Williamson nanofluid heat and mass transfer stagnation point flow assisting and opposing flow Chebyshev wavelet method

Dual solutions in MhD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

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Applied Mathematics and Mechanics(English Edition) 2014年第7期35卷 813-820页

作者： N.S.AKBAR z.h.khan R.U.hAQ S.NADEEM Department of Basic Science & humanities College of Electrical & Mechanical Engineering(CEME) National University of Sciences and Technology Islamabad 46000 Pakistan School of Mathematical Sciences Peking University Department of Mathematics University of Malakand Khyber Pakhtunktwo 18800 Pakistan Department of Mathematics Quaid-i-Azam University Islamabad 44000 Pakistan

The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MhD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.

关键词： stagnation-point flow shrinking sheet Prandtl fluid magnetohydrody-namic (MhD) dual solution shooting method

heat transfer analysis of bi-viscous ciliary motion fluid

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International Journal of Biomathematics 2015年第2期8卷 219-231页

作者： Noreen Sher Akbar z. h. khan DBS h CEMENational University of Sciences and Technology Islamabad Pakistan Department of Mathematics University of MalakandChakdara Dir. (Lower) Khyber Pakhtunkhwa Pakistan

The impulsion system of cilia motion is deliberated by biviscosity fluid model. The problem of two-dimensional motion of biviscosity fluid privileged in a symmetric channel with ciliated walls is considered. The features of ciliary structures are resolute by the supremacy of viscous effects above inertial possessions by the long-wavelength and low Reynolds approximation. Closed-form solutions for the longitudinal pressure gradient, temperature and velocities are obtained. The pressure gradient and volume flow rate for different values of the biviscosity are also premeditated. The flow possessions for the biviscosity fluid resolute as a function of the cilia and metachronal wave velocity.

关键词： Ciliary motion symmetric channel biviscosity fluid heat transfer exact solutions.

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

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Communications in Theoretical Physics 2020年第12期72卷 71-82页

作者： z.h.khan M Usman T zubair M hamid R U haq State Key Laboratory of hydraulics and Mountain River Engineering College of Water Resource and HydropowerSichuan UniversityChengdu610065China BIC-ESAT College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering SciencePeking UniversityBeijing 100871China Institute of Ocean Research Peking UniversityBeijing 100871China School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mechanics and Engineering Science Fudan UniversityShanghai 200433China Department of Electrical Engineering Bahria UniversityIslamabad CampusIslamabad 44000Pakistan

This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching *** influence of thermophoresis and Brownian motion is also considered in transport *** nonlinear ODE set is obtained from the governing nonlinear equations via suitable *** numerical experiments are performed using the Galerkin scheme.A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme(RK-4)is available to show the credibility of the Galerkin *** numerical exploration is carried out for various governing parameters,namely,Brownian motion,steadiness,thermophoresis,stretching ratio,velocity slip,concentration slip,thermal slip,and fluid parameters,and hartmann,Prandtl and Schmidt *** velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing,but the behavior is reversed for assisting *** Brownian motion and thermophoresis parameters cause an increase in temperature for both cases(assisting and opposing).The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis *** the outcomes and the behavior of emerging parameters are illustrated *** comparison analysis and graphical plots endorse the appropriateness of the Galerkin *** is concluded that said method could be extended to other problems of a complex nature.

关键词： Eyring-Powell fluid stagnation point flow Brownian motion and thermophoresis Galerkin method

Model Predictions of Charged-Particle Azimuthal Distributions and Forward-Backward Correlations in pp Interactions at s1/2= 900 GeV

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Communications in Theoretical Physics 2019年第10期71卷 1172-1178页

作者： R.khan M.Ajaz Y.Ali h.Younis G.khan z.Wazir A.zaman A.khan Department of Physics Abdul Wali Khan UniversityMardan23200Pakistan Department of Physics COMSATS UniversityIslamabad44000Pakistan Department of Physics International Islamic UniversityIslamabad44000Pakistan

We report inelastic interactions of protons at the center of mass energy s1/2 = 900 Ge V, by using different event generators to study the forward-backward(FB) correlation in summed transverse momentum and multiplicity of produced charged particles. The transverse momentum, p T ≥ 100 Me V, and pseudorapidity, | η |have been employed for both the correlations. The simulation results are compared with the ATLAS experimental data, obtained with the same values of | η | and p T at s1/2 = 900 Ge V. We also measure the jet and jet-like structure as a function of azimuthal distributions in the events relative to the highest transverse momentum particle. Three overlapping regions of pseudorapidity, | η |h transverse momentum, p T > 500 Me V. For FB correlations, EPOS, and Sybill2.3 c results are in a good agreement with the data as compared to the other ***, for the azimuthal distribution, EPOS-LhC, DPMJETIII, and Sibyll2.3 c show good agreement with the data for full η region. In general, EPOS provides a better description of the data for both the quantities studied in this paper.

关键词： forward-backward correlation CRMC models LhC ATLAS

Infrared Spectroscopic Analysis of Chrysene and 1.2-Benzanthracence in Wax films

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Chinese Physics Letters 2006年第9期23卷 2407-2410页

作者： Md. Naziruddin khan A. S. AI-Dwayyan z. h. zaidi Department of Applied Sciences A1-Falah School of Engineering and Technology Dhauj Faridabad-Haryana-121004 India Department of Physics College of Science King Saud University Riyadh KSA Department of Physics Jamia Millia Islamia New Delhi-25 India

Chrysene and 1.2-benzanthracene are successfully doped in a solid wax film and their vibrational spectra in gooo--400cm^-1 are discussed. The harmonic frequencies and relative intensities of both the molecules observed in the film are compared with theoretical values calculated by the density functional theory （DFT） model as well as with the previous experimental data. The effects on spectra due to change of matrix and some additional bands observed in the wax film are also reported. Excellent agreement in the spectral positions and strengths between the experiments and DFT values are found.

关键词： POLYCYCLIC AROMATIC-hYDROCARBONS EMISSION SPECTRA MOLECULES NAPhThALENE hYPOThESIS EXCITATION CATIONS BANDS