The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The ...The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.展开更多
The magnetohydrodynamic (MHD) graphene-polydimethylsiloxane (PDMS) nanofluid flow between two squeezing parallel plates in the presence of thermal radiation effects is investigated. The energy efficiency of the system...The magnetohydrodynamic (MHD) graphene-polydimethylsiloxane (PDMS) nanofluid flow between two squeezing parallel plates in the presence of thermal radiation effects is investigated. The energy efficiency of the system via the Bejan number is studied extensively. The governing partial differential equations are converted by using the similarity transformations into a set of coupled ordinary differential equations. The set of these converted equations is solved by using the differential transform method (DTM). The entropy generation in terms of the Bejan number, the coefficient of skin-friction, and the heat transfer rate is furthermore investigated under the effects of various physical parameters of interest. The present study shows that the Bejan number, the velocity and thermal profiles, and the rate of heat transfer decrease with a rise in the Deborah number De while the skin-friction coefficient increases. It is also observed that the entropy generation due to frictional forces is higher than that due to thermal effects. Thus, the study bears the potential application in powder technology as well as in biomedical engineering.展开更多
A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite dif...A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite difference scheme method.The stability of this finite difference scheme method is discussed.The distributions of the velocity and phase difference are given numerically and graphically.The effects of the Reynolds number,relaxation time,and aspect ratio of the cross section on the oscillatory flow are investigated.The results show that when the relaxation time of the Maxwell model and the Reynolds number increase,the resonance phenomena for the distributions of the velocity and phase difference enhance.展开更多
In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is...In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied. For the flow into mould cavity the constitutive equation of power-law fluid is used as a Theological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid flow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting difference method. The numerical results show that the splitting difference method is suitable for the 2D problem of non-Newtonian fluid. The present application of the splitting diffference method is at first developed by us for non-Newtonian case. For the unsteady flow in the tube the finite difference scheme is given which leads to a tridiagonal system of equations.展开更多
An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarit...An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.展开更多
The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtoni...The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot＇s theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.展开更多
This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fr...This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail.展开更多
文摘The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.
基金financial support through the Junior Research Fellowship (JRF) (No. 21/06/2015(i)EU-V)
文摘The magnetohydrodynamic (MHD) graphene-polydimethylsiloxane (PDMS) nanofluid flow between two squeezing parallel plates in the presence of thermal radiation effects is investigated. The energy efficiency of the system via the Bejan number is studied extensively. The governing partial differential equations are converted by using the similarity transformations into a set of coupled ordinary differential equations. The set of these converted equations is solved by using the differential transform method (DTM). The entropy generation in terms of the Bejan number, the coefficient of skin-friction, and the heat transfer rate is furthermore investigated under the effects of various physical parameters of interest. The present study shows that the Bejan number, the velocity and thermal profiles, and the rate of heat transfer decrease with a rise in the Deborah number De while the skin-friction coefficient increases. It is also observed that the entropy generation due to frictional forces is higher than that due to thermal effects. Thus, the study bears the potential application in powder technology as well as in biomedical engineering.
基金Project supported by the National Natural Science Foundation of China(Nos.11672164 and41831278)the Taishan Scholars Project Foundation of Shandong Province of China
文摘A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite difference scheme method.The stability of this finite difference scheme method is discussed.The distributions of the velocity and phase difference are given numerically and graphically.The effects of the Reynolds number,relaxation time,and aspect ratio of the cross section on the oscillatory flow are investigated.The results show that when the relaxation time of the Maxwell model and the Reynolds number increase,the resonance phenomena for the distributions of the velocity and phase difference enhance.
基金The project supported by the National Natural Science foundation of China
文摘In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied. For the flow into mould cavity the constitutive equation of power-law fluid is used as a Theological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid flow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting difference method. The numerical results show that the splitting difference method is suitable for the 2D problem of non-Newtonian fluid. The present application of the splitting diffference method is at first developed by us for non-Newtonian case. For the unsteady flow in the tube the finite difference scheme is given which leads to a tridiagonal system of equations.
基金the financial support of National Board for Higher Mathematics(NBHM),DAE,Mumbai,Indiapartially supported by Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.40974067,40674059 and 10534040)the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant No.200807)Scientific Forefront and Interdisciplinary Innovation Project of Jilin University(Grant No.200903319)
文摘The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot＇s theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.
基金Project supported by the China Postdoctoral Science Foundation(No.2015M580069)
文摘This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail.
