Run up flow of a couple stress fluid between parallel plates

Consider the flow of an incompressible fluid between two parallel plates, initially induced by a constant pressure gradient. After steady state is attained, the pressure gradient is suddenly with drawn while the plates are impulsively started simultaneously. The arising flow is referred to as run up flow and the present paper aims at studying this flow in the context of a couple stress fluid. Using Laplace transform technique, the expression for velocity is obtained in Laplace transform domain which is later inverted to the space time domain using a numerical approach. The variation of velocity with respect to various flow parameters is presented through graphs

Stokes' Problems for an Incompressible Couple Stress Fluid

Stokes’ first and second problems for an incompressible couple stress fluid are considered under isothermal conditions. The problems are solved through the use of Laplace transform technique. Inversion of the Laplace transform of the velocity component in each case is carried out using a standard numerical approach. Velocity profiles are plotted and studied for different times and different values of couple stress Reynolds number. The results are presented through graphs in each case

Pulsatile Flow Through a Curved Pipe – An Analytical Study

In this paper, the unsteady flow of Newtonian fluid through a curved pipe due to a pulsatile pressure gradient has been considered. The flow is three dimensional and the partial differential equations governing the flow are highly coupled and non-linear. Approximate analytical solutions of the governing partial differential equations have been obtained without neglecting any term containing the curvature ratio. Perturbation series in terms of curvature ratio has been used for obtaining the solutions. It is interesting to note that the solutions are valid for large as well as small values of Womersley number. The effect of different parameters such as, Reynolds number, Womersley number and curvature ratio on the flow through curved pipe is discussed in this paper. It is found that the axial velocity is qualitatively periodic in nature, as expected. The Reynolds number and curvature ratio are found to shift the axial velocity towards the outer boundary of the curved pipe

A Magnetohydrodynamic Time Dependent Model of Immiscible Newtonian and Micropolar Fluids through a Porous Channel: a Numerical Approach

The objective of the present article is to study the magnetohydrodynamic(MHD) unsteady flow and heat transfer of two immiscible micropolar and Newtonian fluids through horizontal channel occupied with porous medium. Initially, fluids in both regions as well as both plates are at rest. At an instant of time, the flow in both regions is generated by a constant pressure gradient. The governing non-linear and coupled partial differential equations of Eringen’s micropolar fluid and Newtonian fluid are solved subject to suitable initial, boundary and interface conditions. The numerical results for velocity, microrotation and temperature are obtained using Crank-Nicolson finite difference approach. The results obtained for velocities, microrotation and temperatures are presented through figures. The analysis regarding volume flow rate, skin-friction co-efficient and Nusselt number is also done and is presented through tables. It is explored that, velocity, microrotation and temperature are increasing with time and accomplishing steady state at higher time level. Velocity is decreasing with micropolarity parameter and Hartmann number, and increasing with Darcy number. Temperature enhances with increasing Brinkmann number, and declines with Prandtl number and ratio of thermal conductivities

The Influence of Heat Transfer on Peristaltic Transport of MHD Second Grade Fluid through Porous Medium in a Vertical Asymmetric Channel

In this paper, we study the influence of heat transfer on the peristaltic transport of an incompressible magnetohydrodynamic second grade fluid in vertical symmetric and asymmetric channels. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in the wave frame of reference moving with velocity of the wave. Perturbation solutions are obtained for the stream function, temperature and pressure gradient under long wave length assumption. Pressure difference and frictional force are discussed through numerical integration. The influence of various parameters of interest on the flow are discussed and also the graphical results are obtained for different wave forms

Pulsatile Flow Through a Curved Pipe – An Analytical Study

610-616In this paper, the unsteady flow of Newtonian fluid through a curved pipe due to a pulsatile pressure gradient has been considered. The flow is three dimensional and the partial differential equations governing the flow are highly coupled and non-linear. Approximate analytical solutions of the governing partial differential equations have been obtained without neglecting any term containing the curvature ratio. Perturbation series in terms of curvature ratio has been used for obtaining the solutions. It is interesting to note that the solutions are valid for large as well as small values of Womersley number. The effect of different parameters such as, Reynolds number, Womersley number and curvature ratio on the flow through curved pipe is discussed in this paper. It is found that the axial velocity is qualitatively periodic in nature, as expected. The Reynolds number and curvature ratio are found to shift the axial velocity towards the outer boundary of the curved pipe

Effect of endoscope on the peristaltic transport of a couple stress fluid with heat transfer: Application to biomedicine

In this investigation, we have studied the problem of peristaltic flow with heat transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave travelling down its wall. The problem has been formulated in cylindrical coordinate system. The equations governing the flow have been simplified under the long wavelength and low Reynolds number assumptions. The exact solution is obtained for the temperature profile. The perturbation solutions for the velocity and pressure gradient are obtained for small couple stress parameter. Pressure difference per wavelength and frictional forces on the tube walls have been computed numerically. Results are demonstrated for various flow parameters. The better pumping results occur in vertical tube, while less pumping is seen in horizontal tube. The size of trapped bolus is small in triangular wave as compared to other waves. The present study has a wide range of applications in bio-medical engineering like the transport phenomenon in peristaltic micro pumps

Some analytical solutions for flows of Casson fluid with slip boundary conditions

In the present paper, we have studied three fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible Casson fluid between parallel plates using slip boundary conditions. The equations governing the flow of Casson fluid are non-linear in nature. Analytical solutions of the non-linear governing equations with non-linear boundary conditions are obtained for each case. The effect of the various parameters on the velocity and volume flow rate for each problem is studied and the results are presented through graphs. It is observed that, the presence of Casson number decreases the velocity and volume flow rate of the fluid. Increasing of slip parameter increases the velocity and volume flow rate in both Poiseuille and generalized Couette flows