To gain some insight into the behaviour of low-gravity flows in the material processingin space, an approximate theory has been developed for the convective motion of fluidswith a small Grashof number Gr. The expansio...To gain some insight into the behaviour of low-gravity flows in the material processingin space, an approximate theory has been developed for the convective motion of fluidswith a small Grashof number Gr. The expansion of the variables into a series of Gr reducesthe Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.展开更多
In this article,an investigation is conducted to study the precise role of zirconium nanoparticles that exist in a slime-like fluid subject to specific adjustments.Since gliding is a technique of mobility used by bact...In this article,an investigation is conducted to study the precise role of zirconium nanoparticles that exist in a slime-like fluid subject to specific adjustments.Since gliding is a technique of mobility used by bacteria that lack motility components,bacteria travel on their own strength in gliding locomotion by secreting a layer of slime on the substrate.A model of an undulating sheet over a layer of slime of a Rabinowitsch fluid is investigated as a potential model of bacteria’s gliding motility.With the aid of long wavelength approximation,the equations governing the circulation of slime underneath the cells are established and analytically solved.The effects of pseudoplasticity,dilatation and non-Newtonian parameter on the behavior of zirconium concentration,speed of microorganism(bacteria),streamline patterns,and pressure rise for non-Newtonian and Newtonian fluids are compared.The power required for propulsion is also investigated.Physical interpretation for the pertinent variables has been graphically discussed against the parameters under consideration.It is found that with the increase in the concentration of zirconium nanoparticles,the bacterial flow is accelerated and attains its maximum near the rigid substrate wall while an opposite behavior is noticed in the rest region.展开更多
This work is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon(angioplasty) with time-variant overlapping stenosis. The nature of blood in small arteries is analyzed mat...This work is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon(angioplasty) with time-variant overlapping stenosis. The nature of blood in small arteries is analyzed mathematically by considering it as a Carreau nanofluid. The highly nonlinear momentum equations of nanofluid model are simplified by considering the mild stenosis case. The formulated problem is solved by a homotopy perturbation expansion in terms of a variant of the Weissenberg number to obtain explicit forms for the axial velocity, the stream function, the pressure gradient, the resistance impedance and the wall shear stress distribution. These solutions depend on the Brownian motion number, thermophoresis number, local temperature Grashof number G_r and local nanoparticle Grash of number B_r. The results were also studied for various values of the physical parameters, such as the Weissenberg number W_i, the power law index n, the taper angle φ, the maximum height of stenosis δ~*, the angle of inclination α, the maximum height of balloon σ~*, the axial displacement of the balloon z_d~*,the flow rate F and the Froud number Fr. The obtained results show that the transmission of axial velocity curves through a Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) is substantially lower than that through a Carreau nanofluid near the wall of balloon while the inverse occurs in the region between the balloon and stenosis. The streamlines have a clearly distinguished shifting toward the stenotic region and this shifting appears near the wall of the balloon, while it has almost disappeared near the stenotic wall and the trapping bolus in the case of horizontal arteries and Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) does not appear but for the case of Carreau nanofluid bolus appears.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘To gain some insight into the behaviour of low-gravity flows in the material processingin space, an approximate theory has been developed for the convective motion of fluidswith a small Grashof number Gr. The expansion of the variables into a series of Gr reducesthe Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.
基金Fundación Mujeres poráfrica for supporting this work through the fellowship awarded to her in 2020。
文摘In this article,an investigation is conducted to study the precise role of zirconium nanoparticles that exist in a slime-like fluid subject to specific adjustments.Since gliding is a technique of mobility used by bacteria that lack motility components,bacteria travel on their own strength in gliding locomotion by secreting a layer of slime on the substrate.A model of an undulating sheet over a layer of slime of a Rabinowitsch fluid is investigated as a potential model of bacteria’s gliding motility.With the aid of long wavelength approximation,the equations governing the circulation of slime underneath the cells are established and analytically solved.The effects of pseudoplasticity,dilatation and non-Newtonian parameter on the behavior of zirconium concentration,speed of microorganism(bacteria),streamline patterns,and pressure rise for non-Newtonian and Newtonian fluids are compared.The power required for propulsion is also investigated.Physical interpretation for the pertinent variables has been graphically discussed against the parameters under consideration.It is found that with the increase in the concentration of zirconium nanoparticles,the bacterial flow is accelerated and attains its maximum near the rigid substrate wall while an opposite behavior is noticed in the rest region.
文摘This work is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon(angioplasty) with time-variant overlapping stenosis. The nature of blood in small arteries is analyzed mathematically by considering it as a Carreau nanofluid. The highly nonlinear momentum equations of nanofluid model are simplified by considering the mild stenosis case. The formulated problem is solved by a homotopy perturbation expansion in terms of a variant of the Weissenberg number to obtain explicit forms for the axial velocity, the stream function, the pressure gradient, the resistance impedance and the wall shear stress distribution. These solutions depend on the Brownian motion number, thermophoresis number, local temperature Grashof number G_r and local nanoparticle Grash of number B_r. The results were also studied for various values of the physical parameters, such as the Weissenberg number W_i, the power law index n, the taper angle φ, the maximum height of stenosis δ~*, the angle of inclination α, the maximum height of balloon σ~*, the axial displacement of the balloon z_d~*,the flow rate F and the Froud number Fr. The obtained results show that the transmission of axial velocity curves through a Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) is substantially lower than that through a Carreau nanofluid near the wall of balloon while the inverse occurs in the region between the balloon and stenosis. The streamlines have a clearly distinguished shifting toward the stenotic region and this shifting appears near the wall of the balloon, while it has almost disappeared near the stenotic wall and the trapping bolus in the case of horizontal arteries and Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) does not appear but for the case of Carreau nanofluid bolus appears.
