Peristaltic pumping induced by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid mixed with rigid spherical particles is investigated theoretically taking the slip effect on the wall into account. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms and the slip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth-order terms yield the Poiseuille flow and the first-order terms give the Orr-Sommerfeld equation. The results show that the slip conditions have significant effect within certain range of concentration. The phenomenon of reflux (the mean flow reversal) is discussed under slip conditions. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid and is affected by slip condition. A motivation of the present analysis has been the hope that such theory of two-phase flow process under slip condition is very useful in understanding the role of peristaltic muscular contraction in transporting biofluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixture by peristalsis.

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In this paper forced convection from steady rotating circular cylinder in a cross stream of nanofluid is theoretically investigated. The nanofluid is formed by adding Nanometric particles of copper to water. The flow and energy governing equations are solved using Fourier spectral method. The main influencing parameters on flow and thermal fields are Reynolds number, particles volume fraction and the cylinder speed ratio (peripheral velocity of rotating cylinder/ uniform free stream velocity). The Reynolds number is considered up to 200, the volume fraction of nanoparticles is considered up to 0.05 while the cylinder speed ratio is considered up to 1. The effects of Reynolds number, solid particle volume fraction and cylinder speed ratio on both flow and thermal fields are considered. The study has shown very good agreement with the previous results in the literature for cases of fixed and rotating cylinder in cross stream of a Newtonian fluid. The study has also shown that increasing of volume fraction of nanoparticles increases the heat transfer rate for both fixed and rotating cylinder while increasing the cylinder speed ratio for the given range of parameters is found to decrease heat transfer rate. Also, the study has shown that increasing nanoparticles volume fraction increases drag coefficient for stationary cylinder, while increasing nanoparticles volume fraction decreases drag coefficient for low speed ratios, has no significant effect on lift coefficient, and has a slight increasing effect on Strouhal number. Also, increasing speed ratio α decreases both lift and drag coefficient (for low speed ratios).

The dynamic formulations of manipulators lead to a set of highly nonlinear and strongly coupled differential equations which represents the dynamic model of a manipulator. Beside many other forces, this model describes the actuator forces (or torques) which cause the manipulator joints to move. In this paper, manipulator joints are modeled as elastic springs with joint stiffness in order to impose elastic forces to the dynamic system model and to monitor their influences when speeding up the manipulator end-effector. The kinematic relationships are described by using the zero-reference-position method. Both the inverse and direct dynamics problems are developed by appl~ng Kane's dynamical equations as an analytical tool. A Stanford-type manipulator is considered as a numerical example. The implications of the results are monitored, compared and justified.

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