Dynamics and ‘normal stress’ evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers

The problem of determining the force acting on a particle in a fluid where the motion of the fluid and the particle is given has been considered in some detail in the literature. In this work, we propose an example of a new class of problems where, the fluid is quiescent and the effect of an external periodic force on the motion of the particle is determined at low non-zero Reynolds numbers. We present an analysis of the dynamics of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers including the effects of both convective and unsteady inertia. The inclusion of both forms of inertia leads to a nonlinear integro — differential equation which is solved numerically for the velocity and displacement of the individual particle. We show that a ‘normal stress’ like parameter can be evaluated using standard techniques of Batchelor. Hence this system allows for an experimentally accessible measurable macroscopic parameter, analogous to the ‘normal stress’, which can be related to the dynamics of individual particles. We note that this ‘normal stress’ arises from the internal fluctuations induced by the periodic force. In addition, a preliminary analysis leading to a possible application of separating particles by shape is presented. We feel that our results show possibilities of being technologically important since the ‘normal stress’ depends strongly on the controllable parameters and our results may lead to insights in the development of active dampeners and smart fluids. Since we see complex behaviour even in this simple system, it is expected that the macroscopic behaviour of such suspensions may be much more complex in more complex flows

The effects of a constant bias force on the dynamics of a periodically forced spherical particle in a Newtonian fluid at low Reynolds numbers

We make use of the formulation developed by Lovalenti and Brady 1 for the hydrodynamic force acting upon a spherical particle undergoing arbitrary time dependent motion in an arbitrary time dependent uniform flow field at low Reynolds numbers, to derive an expression for the effects of a constant bias force acting on a periodically forced rigid spherical particle in a Newtonian fluid. We use Newton's second law to relate the total force acting on the particle to the motion of the particle. The total force is given by: Totalforce=F ext+ FH, where, F ext is the external force inclusive of both the periodic force and the constant bias force. F H is the hydrodynamic force derived by Lovalenti and Brady 1 including both unsteady and convective inertia. The equation derived contains a nonlinear history term and is nonlinear. This equation is solved numerically using an adaptive step size Runge - Kutta scheme. We obtain several phase plots (plots between particle displacement and particle velocity), which show the effects of low Reynolds numbers, the periodic force and the effects of the constant bias force on the particle motion. It is observed that at low magnitudes of the periodic forcing the external constant force dominates and the particle moves along the direction of the external constant force. As we increase the magnitude of the periodic forcing, the periodic force is seen to dominate and the particle is seen to oscillate along a mean position with a slight drift along the direction of the periodic force and the external constant force, when they are imposed in the same direction. However the motion of the particle becomes more complicated when the directions of the periodic forcing and external constant force are opposite to each other. We also observe a reflection in phase space when the directions of both the forces are reversed. The phase plots typically are of a half sinusoidal, sinusoidal and a coiled (solenoidal) pattern. These plots include the effects of both periodic force and the constant bias force. As the Reynolds numbers increases the drift of the particle reduces, which indicates the effects of inertia. We present a preliminary analysis of the dynamics in this paper. © 2010 American Institute of Physics

Impacts of Brownian Motion, Thermophoresis and Ohmic Heating on Chemically Reactive Pulsatile MHD Flow of Couple Stress Nanofluid in a Channel

In this study, the magnetohydrodynamic pulsatile flow of a couple stress nanofluid in a channel has been discussed in detail by adopting Buongiorno’s nanofluid model. The impacts of Brownian motion, thermophoresis, Ohmic heating, viscous dissipation and chemical reaction on heat, and mass transfer of blood based nanofluid are considered. The current concept is significant in the field of nano-drug supply, dynamics of physiological fluids, and biomedicines. The governing partial differential equations are converted into a set of ODEs (ordinary differential equations) by employing a perturbation scheme. The resulting non-dimensional system is numerically interpreted to determine the impact of various emerging parameters on flow variables by utilizing the shooting technique with the support of the Runge-Kutta procedure. The outcomes reveal that the temperature rises with the magnifying viscous dissipation, Brownian motion, and thermophoresis parameters, whereas the opposite trend can be seen with an escalation in the couple stress parameter. Heat transfer rate is an accelerating function of Brownian motion and thermophoresis parameters while it is a decelerating function of couple stress parameter and Hartmann number. Mass transfer rate declines with increasing values of thermophoresis parameter and Lewis number

MHD flow of a nanofluid in an expanding or contracting porous pipe with chemical reaction and heat source/sink

AbstractIn the present investigation, an analytical analysis has been carried out to study the influence of chemical reaction on MHD flow of a nanofluid in an expanding or contracting porous pipe in the presence of heat source/sink. The pipe wall expands or contracts uniformly at a time dependent rate. Similarity transformations have been invoked to reduce the governing flow equations into coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method (HAM) is employed to obtain the analytical solutions of the ordinary differential equations. The convergence of the obtained series solutions is analyzed. The effects of various physical parameters such as wall expansion ratio, Brownian motion parameter, thermophoresis parameter, Lewis number, chemical reaction parameter and heat source/sink parameter on flow variables have been discussed. Further, for the case of hydrodynamic viscous fluid, we find a good agreement between the HAM solutions and solutions already reported in the literature

Thermal-diffusion and diffusion-thermo effects on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation

The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed

Influence of heat transfer on MHD flow in a pipe with expanding or contracting permeable wall

The present study investigates the effects of heat transfer on MHD laminar viscous flow in a pipe with expanding or contracting permeable wall. The pipe wall expands or contracts uniformly at a time dependent rate. The governing equations are reduced to ordinary differential equations by using a similarity transformation. An analytical approach, namely the homotopy analysis method (HAM) is applied in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Further, we find a good agreement between the HAM solutions and solutions already reported in the literature

A wireless rural education and learning system based on disk oriented MPEG streaming multimedia

The Internet is enabling us to address some educational challenges, bringing learning to students instead of bringing students to learning. It is allowing for the creation of learning communities that defy the constraints of time and distance as it provides access to knowledge that was once difficult to obtain. This is true in the classroom, on the college campus, and in the corporate training rooms. We describe the design of a rural education and learning system in a wireless multimedia environment which runs on a cost-effective computer system. The education system may be classified as a multiple clients and a single server system where each client runs in a class-room where students are free to select the subject of their choice. The client is also facilitated with VCR operations and guaranteed data delivery by using the MNSP (multimedia network service platform) at the server and at the clients end. The system has been implemented in 5,10, 20 classroom environments with 50 different subjects teaching materials. It has been observed that the response to each of the user's requirements, like subject material requirement retrieval and VCR operation, etc., are quite good. We have also made a field trial in a five-classroom school in a rural area, which has been quite encouragin