This work examines the flow of a micropolar fluid over a vertical porous plate at the MHD stagnation point under viscous dissipation, convective boundary conditions, and thermal radiation. The governing partial differ...This work examines the flow of a micropolar fluid over a vertical porous plate at the MHD stagnation point under viscous dissipation, convective boundary conditions, and thermal radiation. The governing partial differential equations and a set of similarity parameters were used to transform them into ordinary differential equations. The Runge-Kutta fourth-order algorithm is used in conjunction with the Newton Raphson shooting technique to numerically solve the generated self-similar equations. Results were tabulated both numerically and graphically, and examples for different controlling factors are quantitatively analyzed. According to the study, the vortex viscosity parameter (k) causes the velocity profiles to rise while the magnetic parameter, suction parameter, and radiation parameter cause them to fall. In contrast, as the flow’s suction and prandtl values rise, so do the magnetic parameter, radiation, and vortex viscosity, while the thickness of the thermal boundary layer decreases. .展开更多
Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical ...Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.展开更多
Natural and artificial chiral materials such as deoxyribonucleic acid (DNA), chromatin fibers, flagellar filaments, chiral nanotubes, and chiral lattice materials widely exist. Due to the chirality of intricately he...Natural and artificial chiral materials such as deoxyribonucleic acid (DNA), chromatin fibers, flagellar filaments, chiral nanotubes, and chiral lattice materials widely exist. Due to the chirality of intricately helical or twisted microstructures, such materials hold great promise for use in diverse applications in smart sensors and actuators, force probes in biomedical engineering, structural elements for absorption of microwaves and elastic waves, etc. In this paper, a Timoshenko beam model for chiral materials is developed based on noncentrosymmetric micropolar elasticity theory. The governing equations and boundary conditions for a chiral beam problem are derived using the variational method and Hamilton's principle. The static bending and free vibration problem of a chiral beam are investigated using the proposed model. It is found that chirality can significantly affect the mechanical behavior of beams, making materials more flexible compared with nonchiral counterparts, inducing coupled twisting deformation, relatively larger deflection, and lower natural frequency. This study is helpful not only for understanding the mechanical behavior of chiral materials such as DNA and chromatin fibers and characterizing their mechanical properties, but also for the design of hierarchically structured chiral materials.展开更多
A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection th...A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through yon Karman's similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.展开更多
The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using ...The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.展开更多
The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid, whose surface is subject...The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The problem is studied in the context of the generalized thermoelasticity Lord Shulman's (L-S) theory with one relaxation time, as well as with the classical dynamical coupled theory (CD). The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature, the couple stresses and the microstress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons of the results are made between the two theories with and without the rotation and the microstretch constants.展开更多
The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under...The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-Hiickel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and rnicrorotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.展开更多
The paper is devoted to a study of the electro-osmotic flow of a micropolar bio-fluid, when the flow takes place between two plates that are in a state of periodic vibrations. Considering blood as a micropolar fluid, ...The paper is devoted to a study of the electro-osmotic flow of a micropolar bio-fluid, when the flow takes place between two plates that are in a state of periodic vibrations. Considering blood as a micropolar fluid, it is found that the amplitude of oscillation of the microparticles of blood increases when the micropolar effect is pronounced more and more and that a rise in DebyeHtickel parameter enhances both the velocity and microrotation gradient. The results provide guidelines for the improvement of design of bio-sensing and micro-fluidic devices. The study leads to the conclusion that electrical double layers formed in the vicinity of the wall can significantly alter the flow dynamics of physiological fluids in micro-bio-fluidic devices.展开更多
文摘This work examines the flow of a micropolar fluid over a vertical porous plate at the MHD stagnation point under viscous dissipation, convective boundary conditions, and thermal radiation. The governing partial differential equations and a set of similarity parameters were used to transform them into ordinary differential equations. The Runge-Kutta fourth-order algorithm is used in conjunction with the Newton Raphson shooting technique to numerically solve the generated self-similar equations. Results were tabulated both numerically and graphically, and examples for different controlling factors are quantitatively analyzed. According to the study, the vortex viscosity parameter (k) causes the velocity profiles to rise while the magnetic parameter, suction parameter, and radiation parameter cause them to fall. In contrast, as the flow’s suction and prandtl values rise, so do the magnetic parameter, radiation, and vortex viscosity, while the thickness of the thermal boundary layer decreases. .
文摘Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.
基金supported by the National Natural Science Foundation of China (Grants 11472191, 11272230, and 11372100)
文摘Natural and artificial chiral materials such as deoxyribonucleic acid (DNA), chromatin fibers, flagellar filaments, chiral nanotubes, and chiral lattice materials widely exist. Due to the chirality of intricately helical or twisted microstructures, such materials hold great promise for use in diverse applications in smart sensors and actuators, force probes in biomedical engineering, structural elements for absorption of microwaves and elastic waves, etc. In this paper, a Timoshenko beam model for chiral materials is developed based on noncentrosymmetric micropolar elasticity theory. The governing equations and boundary conditions for a chiral beam problem are derived using the variational method and Hamilton's principle. The static bending and free vibration problem of a chiral beam are investigated using the proposed model. It is found that chirality can significantly affect the mechanical behavior of beams, making materials more flexible compared with nonchiral counterparts, inducing coupled twisting deformation, relatively larger deflection, and lower natural frequency. This study is helpful not only for understanding the mechanical behavior of chiral materials such as DNA and chromatin fibers and characterizing their mechanical properties, but also for the design of hierarchically structured chiral materials.
文摘A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through yon Karman's similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.
文摘The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.
文摘The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The problem is studied in the context of the generalized thermoelasticity Lord Shulman's (L-S) theory with one relaxation time, as well as with the classical dynamical coupled theory (CD). The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature, the couple stresses and the microstress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons of the results are made between the two theories with and without the rotation and the microstretch constants.
基金Supported by the National Natural Science Foundation of China(Nos.11472140 and 11362012)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(No.NJYT-13-A02)+1 种基金the Inner Mongolia Grassland Talent(No.12000-12102013)the Opening fund of State Key Laboratory of Nonlinear Mechanics
文摘The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-Hiickel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and rnicrorotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.
基金the Alexander von Humboldt Foundation,Germany for its partial supportthe Department of Science and Technology, Government of India (SERB Grant No. SB/S4/MS: 864/14)
文摘The paper is devoted to a study of the electro-osmotic flow of a micropolar bio-fluid, when the flow takes place between two plates that are in a state of periodic vibrations. Considering blood as a micropolar fluid, it is found that the amplitude of oscillation of the microparticles of blood increases when the micropolar effect is pronounced more and more and that a rise in DebyeHtickel parameter enhances both the velocity and microrotation gradient. The results provide guidelines for the improvement of design of bio-sensing and micro-fluidic devices. The study leads to the conclusion that electrical double layers formed in the vicinity of the wall can significantly alter the flow dynamics of physiological fluids in micro-bio-fluidic devices.