Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is...Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is tempted by time dependent shear stress applied on one plate. The governing partial differential equations of a model under consideration are transformed into ordinary differential equations by Laplace transform method and then solved for temperature and velocity fields. The obtained results for temperature fields are expressed in terms of complementary error function. The influences of involved parameters likes Hartmann number, Grashf number, Prandlt number and porosity parameter, on temperature and velocity profiles are shown graphically. There is no such result regarding Maxwell fluid in the existing literature.展开更多
Stokes＇ first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by...Stokes＇ first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.展开更多
Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the ...Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.展开更多
文摘Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is tempted by time dependent shear stress applied on one plate. The governing partial differential equations of a model under consideration are transformed into ordinary differential equations by Laplace transform method and then solved for temperature and velocity fields. The obtained results for temperature fields are expressed in terms of complementary error function. The influences of involved parameters likes Hartmann number, Grashf number, Prandlt number and porosity parameter, on temperature and velocity profiles are shown graphically. There is no such result regarding Maxwell fluid in the existing literature.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10372007 and 10572006） and the New , Century Training Programme Foundation for the Talents by Chinese Ministry of Education.
文摘Stokes＇ first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.
基金supported by the National Natural Science Foundation of China(No.11072224)research grantsfrom Institute of Crustal Dynamics(No.ZDJ2012-20) and overseas-returned scholar,Personnel Ministry of China
文摘Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.
