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Transient flow of magnetized maxwell nanofluid: Buongiorno model perspective of Cattaneo-Christov theory

Applied mathematics and mechanics(English Edition) 2020年第4期41卷 655-666页

作者： m.khan A.AHmED J.AHmED Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan

The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties.The maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy.The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws,respectively.Additionally,the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the maxwell fluid.The governing partial differential equations(PDEs)for the flow and energy transport phenomena are obtained by using the maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation.Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations(ODEs).The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution.The results for the time relaxation parameter in the flow,thermal energy,and mass transport equations are discussed graphically.It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid.Further,larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid.moreover,the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field.The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.

关键词： transient flow Cattaneo-Christov theory maxwell nanofluid Buongiorno model homotopy analysis method (HAm) solution

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Thermal analysis in swirl motion of maxwell nanofluid over a rotating circular cylinder

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Applied mathematics and mechanics(English Edition) 2020年第9期41卷 1417-1430页

作者： A.AHmED m.khan J.AHmED Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan

In this paper,the mechanism of thermal energy transport in swirling flow of the maxwell nanofluid induced by a stretchable rotating cylinder is studied.The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow.Further,the novel features of heat generation/absorption,thermal radiation,and Joule heating are studied to control the rate of heat transfer.The effects of Brownian and thermophoretic forces exerted by the maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno.The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations(PDEs)and transformed into nonlinear ordinary differential equations(ODEs)with the help of the suitable flow ansatz.Numerically acquired results through the technique bvp4c are reported graphically with physical explanation.Graphical analysis reveals that there is higher transport of heat energy in the maxwell nanoliquid for a constant wall temperature(CWT)as compared with the prescribed surface temperature(PST).Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing maxwell nanofluid.moreover,the temperature distribution increases with increasing values of the radiation parameter and the Eckert number.It is also noted that an increase in Reynolds number reduces the penetration depth,and as a result the flow and transport of energy occur only near the surface of the cylinder.

关键词： maxwell nanofluid rotating cylinder heat source/sink Joule heating convective condition numerical solution

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Boundary layer flow of maxwell fluid due to torsional motion of cylinder: modeling and simulation

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Applied mathematics and mechanics(English Edition) 2020年第4期41卷 667-680页

作者： m.khan A.AHmED J.AHmED Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan

This paper investigates the boundary layer flow of the maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature.The torsional motion of the cylinder is considered with the constant azimuthal velocity E.The partial differential equations(PDEs)governing the torsional motion of the maxwell fluid together with energy transport are simplified with the boundary layer concept.The current analysis is valid only for a certain range of the positive Reynolds numbers.However,for very large Reynolds numbers,the flow becomes turbulent.Thus,the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers.The numerical simulations for the flow,heat,and mass transport phenomena are carried out in view of the bvp4c scheme in mATLAB.The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid.It is also noted that the phenomenon of stress relaxation,described by the Deborah number,causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion.The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers.An excellent validation of the numerical results is assured through tabular data with the existing literature.

关键词： torsional motion maxwell fluid magnetic field stretchable rotating cylinder bvp4c scheme

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Exact solutions of mHD second Stokes flow of generalized Burgers fluid

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Applied mathematics and mechanics(English Edition) 2015年第2期36卷 211-224页

作者： m.khan R.mALIK A.ANJUm Department of mathematics Quaid-i-Azam University

This work concerns with the exact solutions of magnetohydrodynamic（mHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The mHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.

关键词： generalized Burgers fluid magnetohydrodynamic（mHD） flow porous medium exact solution

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Chemically reactive and radiative von Kármán swirling flow due to a rotating disk

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Applied mathematics and mechanics(English Edition) 2018年第9期39卷 1295-1310页

作者： m.khan J.AHmED L.AHmAD Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan Department of mathematics Shaheed Benazir Bhutto UniversitySheringal Upper Dir 18000Pakistan

A new mathematical model is presented to study the heat and mass transfer characteristics of magnetohydrodynamic(mHD) maxwell fluid flow over a convectively heated stretchable rotating disk. To regulate the fluid temperature at the surface, a simple isothermal model of homogeneous-heterogeneous reactions is employed. The impact of nonlinear thermal radiative heat flux on thermal transport features is studied. The transformed nonlinear system of ordinary differential equations is solved numerically with an efficient method, namely, the Runge-Kutta-Felberg fourth-order and fifth-order(RKF45)integration scheme using the mAPLE software. Achieved results are validated with previous studies in an excellent way. major outcomes reveal that the magnetic flux reduces the velocity components in the radial, angular, and axial directions, and enhances the fluid temperature. Also, the presence of radiative heat flux is to raise the temperature of fluid. Further, the strength of homogeneous-heterogeneous reactions is useful to diminish the concentration of reaction.

关键词： rotating stretchable disk magnetic field nonlinear radiative heat flux homogeneous-heterogeneous chemical reaction

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Slip effects on shearing flows in a porous medium

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Acta mechanica Sinica 2008年第1期24卷 51-59页

作者： m.khan T.Hayat Y.Wang Department of mathematics Quaid-i-Azam University Islamabad 44000 Pakistan Chair of Fluid Dynamics Department of Mechanical Engineering Darmstadt University of TechnologyHochschulstrasse 164289 Darmstadt Germany

This paper deals with the magnetohydrodynamic （mHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. modified Darcy＇s law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.

关键词： Porous medium. magnetohydrodynamic flow Slip effect

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Von Kármán rotating flow of maxwell nanofluids featuring the Cattaneo-Christov theory with a Buongiorno model

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Applied mathematics and mechanics(English Edition) 2020年第8期41卷 1195-1208页

作者： A.AHmED m.khan J.AHmED A.HAFEEZ Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan

This research paper analyzes the transport of thermal and solutal energy in the maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity.The significant features of thermal and solutal relaxation times of fluids are studied with a Cattaneo-Christov double diffusion theory rather than the classical Fourier’s and Fick’s laws.A novel idea of a Buongiorno nanofluid model together with the Cattaneo-Christov theory is introduced for the first time for the maxwell fluid flow over a rotating disk.Additionally,the thermal and solutal distributions are controlled with the impacts of heat source and chemical reaction.The classical von Karman similarities are used to acquire the non-linear system of ordinary differential equations(ODEs).The analytical series solution to the governing ODEs is obtained with the well-known homotopy analysis method(HAm).The validation of results is provided with the published results by the comparison tables.The graphically presented outcomes for the physical problem reveal that the higher values of the stretching strength parameter enhance the radial velocity and decline the circumferential velocity.The increasing trend is noted for the axial velocity profile in the downward direction with the higher values of the stretching strength parameter.The higher values of the relaxation time parameters in the Cattaneo-Christov theory decrease the thermal and solutal energy transport in the flow of maxwell nanoliquids.The higher rate of the heat transport is observed in the case of a larger thermophoretic force.

关键词： maxwell fluid nanoparticle Cattaneo-Christov theory rotating disk homotopy analysis method(HAm)

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Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

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Applied mathematics and mechanics(English Edition) 2020年第7期41卷 1083-1094页

作者： A.HAFEEZ m.khan A.AHmED J.AHmED Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan

A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.

关键词： Oldroyd-B nanofluid rotating disk magnetohydrodynamic(mHD) Cattaneo-Christov theory analytical solution

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On the mHD flow of fractional generalized Burgers' fluid with modified Darcy's law

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Acta mechanica Sinica 2007年第3期23卷 257-261页

作者： T.Hayat m.khan S.Asghar Department of mathematics Quaid-i-Azam University 45320Islamabad 44000Pakistan COmSATS Institute of Information Technology H-8 Islamabad 44000Pakistan

This work is concerned with applying the fractional calculus approach to the magnetohydrodynamic （mHD） pipe flow of a fractional generalized Burgers＇ fluid in a porous space by using modified Darcy＇s relationship. The fluid is electrically conducting in the presence of a constant applied magnetic field in the transverse direction. Exact solution for the velocity distribution is developed with the help of Fourier transform for fractional calculus. The solutions for a Navier-Stokes, second grade, maxwell, Oldroyd-B and Burgers＇ fluids appear as the limiting cases of the present analysis.

关键词： modeling Generalized Burgers＇ fluid,Fractional calculus Exact solution

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magnetohydrodynamic Stagnation Point Flow of a maxwell Nanofluid with Variable Conductivity

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Communications in Theoretical Physics 2019年第12期71卷 1493-1500页

作者： m.Irfan m.khan W.A.khan m.Alghamdi Department of mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Department of mathematics Faculty of ScienceKing Khalid UniversityAbha 61413Kingdom of Saudi Arabia

This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto maxwell nanofluid.The Buongiorno’s theory has been established to picture the inducement of Brownian and thermophrotic diffusions effects.Additionally,the aspect of heat sink/source is reported.The homotopic analysis method(HAm)has been worked out for the solution of nonlinear ODEs.The behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for maxwell nanofluid are sketched and discussed.The attained outcomes specify that both the temperature and concentration of maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration fields.It is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion parameter.moreover,for the confirmation of our study comparison tables are reported.

关键词： maxwell nanofluid stagnation point flow magnetohydrodynamic(mHD) variable conductivity chemical reaction

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