Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.     

Effect of elastic wall motion on oscillatory flow of micropolar fluid in an annular tube

Summary Oscillatory flow of a micropolar fluid in an annular tube is investigated. The outer wall of the tube is taken to be elastic and the variation in the diameter of the elastic wall due to pulsatile nature of pressure gradient is assumed to be small. The wall motion is governed by a tube law. The nonlinear equations governing the fluid flow and the tube law are solved using perturbation analysis. The steady-streaming phenomenon due to the interaction of convected inertia with viscous effects is studied. The analysis, is carried out for zero mean flow rate. It presents the effects of the elastic nature of the wall combined with micropolar fluid parameters on the mean pressure gradient and wall shear stress for different catheter sizes and frequency parameters. It is found that the effect of micropolarity is of considerable importance for small steady-streaming Reynolds number. Also, it is observed that the relationship between mean pressure gradient and the flow rate depends on the amplitude of the diameter variation, flow rate waveforms and the phase difference between them.     

Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001     

Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion

The unsteady laminar free convection flow between two long vertical parallel plates with ramped wall temperature at one boundary has been investigated in the presence of thermal radiation and chemical species concentration. The exact solutions of the momentum, energy and concentration equations have been obtained using the Laplace transform technique. The velocity and temperature profiles, skin-friction and Nusselt number variations are shown graphically and the numerical values of the volume flow rate, the total heat rate and species rate added to the fluid are presented in a table. The influence of different system parameters such as the radiation parameter (R), buoyancy ratio parameter (N), Schmidt number (Sc) and time (t) has been analyzed carefully. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convective flow due to ramped wall temperature has also been compared with the baseline case of flow due to constant wall temperature.     

Hydrodynamics of viscous fluid through porous slit with linear absorption

The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.     

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

The present theoretical assessment deals with the peristaltic-ciliary transport of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrication approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.     

Localised dynamics of laminar pulsatile flow in a rectangular channel

The exploitation of flow pulsation in low-Reynolds number micro/minichannel flows is a potentially useful technique for enhancing cooling of high power photonics and electronics devices. Although the mechanical and thermal problems are inextricably linked, decoupling of the local instantaneous parameters provides insight into underlying mechanisms. The current study performs complementary experimental and analytical analyses to verify novel representations of the pulsating channel flow solutions, which conveniently decompose hydrodynamic parameters into amplitude and phase values relative to a prescribed flow rate, for sinusoidally-pulsating flows of Womersley numbers 1.4 ≤ Wo ≤ 7.0 and a fixed ratio of oscillating flow rate amplitude to steady flow rate equal to 0.9. To the best of the authors’ knowledge, the velocity measurements – taken using particle image velocimetry – constitute the first experimental verification of theory over two dimensions of a rectangular channel. Furthermore, the wall shear stress measurements add to the very limited number of studies that exist for any vessel geometry. The amplification of the modulation component of wall shear stress relative to a steady flow (with flow rate equal to the amplitude of the oscillating flow rate) is an important thermal indicator that may be coupled with future heat transfer measurements. The positive half-cycle time- and space-averaged value is found to increase with frequency owing to growing phase delays and higher amplitudes in the near-wall region of the velocity profiles. Furthermore, the local time-dependent amplification varies depending on the regime of unsteadiness: (i) For quasi-steady flows, the local values are similar during acceleration and deceleration though amplification is greater near the corners over the interval 0 – 0.5π. (ii) At intermediate frequencies, local behaviour begins to differ during accelerating and decelerating periods and the interval of greater wall shear stress near the corners lengthens. (iii) Plug-like flows experience universally high amplifications, with wall shear stress greater near the corners for the majority of the positive half-cycle. The overall fluid mechanical performance of pulsating flow, measured by the ratio of bulk mean wall shear stress and pressure gradient amplifications, is found to reduce from an initial value of 0.97 at Wo = 1.4 to 0.28 at Wo = 7.0, demonstrating the increasing work input required to overcome inertia.     

Effect of variable porosity on laminar convection in a uniformly heated vertical porous channel

The present investigation is devoted to the study of fully developed mixed convective flow through a vertical porous channel. The lateral variations of porosity and thermal diffusivity in the bed near the wall, are approximated by exponential functions. The correlation between permeability and porosity is brought through Kozney-Carman approximation. The volume averaged one dimensional low speed momentum equation proposed by Vafai is employed for the analysis of the problem. Results are obtained for steady heating of ascending cold fluid and steady cooling of ascending hot fluid. For the above physical situations it is observed that the heat transfer rate, and ratio of friction factor increases with increase in porous parameter, whereas the ratio of mass flow rate decreases with increase in porous parameter. The velocity profiles exhibit hydrodynamic channelling and peak velocity shifts towards the wall for higher values of the porous parameter. For steady heating of ascending could fluid increase in Rayleigh number enhances the heat transfer rate, and mass flow rate, while it reduces the ratio of friction factor. An opposite trend is observed for the case of steady cooling of ascending hot fluid.     

Time varying NTU method for heat exchanger analysis with mass discharge

Transient operation of a co-current heat exchanger is analyzed in this paper, using a new predictive formulation for laminar and turbulent flows with mass discharge from the heat exchanger. The model includes time-varying mass discharge due to pressure regulated gas outflow. The temperature variations of the working fluid, heating fluid and the wall are predicted and validated against past data. It is found that the temperature of the working fluid rises sharply to a peak and then gradually decreases over time, due to mass discharge effects. The wall temperature decreases exponentially, and the temperature of the heating fluid falls sharply, and then gradually decreases. A benchmark case of a step change in the mass flow rate of the incoming fluid is analyzed and compared against past data for validation, after which results are presented and discussed for transient step changes of the incoming mass flow rate.     

Effect of wall conductances on convective magnetohydrodynamic channel flow

Summary The problem of convective magnetohydrodynamic channel flow in a vertical channel subjected simultaneously to an axial temperature gradient and a pressure gradient is examined when the thermal and the electrical conductance of the channel walls are arbitrary. The effects of wall conductances on the flow rate and heat transfer are found and discussed. When the vertical temperature gradient is negative, which is the case of heating from below, there exists a critical Rayleigh number at which the fluid becomes unstable. The critical Rayleigh number is also found as a function of the wall conductances.On leave from the State University of New York at Buffalo.     

Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate

The boundary layer flow of a viscoelastic fluid of the second-grade type over a rigid continuous plate moving through an otherwise quiescent fluid with constant velocity U is studied. Assuming the flow to be laminar and two-dimensional, local similarity solution is found with fluid's elasticity and plate's withdrawal speed as the main variables. Results are presented for velocity profiles, boundary layer thickness, wall skin friction coefficient and fluid entrainment in terms of the local Deborah number. A marked formation of boundary layer is predicted, even at low Reynolds numbers, provided the Deborah number is sufficiently large. The boundary layer thickness and the wall skin friction coefficient are found to scale with fluid's elasticity—both decreasing the higher the fluid's elasticity. The amount of fluid entrained is also predicted to decrease whenever a fluid exhibits elastic behavior.     

Magnetic field effect on heat transfer and fluid flow characteristics of blood flow in multi-stenosis arteries

Heat and fluid flow characteristics of blood flow in multi-stenosis arteries in the presence of magnetic field is considered. A mathematical model of the multi-stenosis inside the arteries is introduced. A finite difference scheme is used to solve the governing equations in terms of vorticity-stream function along with their boundary conditions. The effect of magnetic field and the degree of stenosis on wall shear stress and Nusselt number is investigated. It was found that magnetic field modifies the flow patterns and increases the heat transfer rate. The severity of the stenosis affects the wall shear stress characteristics significantly. The magnetic field torque will increase the thermal boundary layer thickness and the temperature gradient in the streaming blood, and hence increasing the local Nusselt number     

Numerical study of effects of pulsatile amplitude for transitional turbulent pulsatile flow in pipes with ring‐type constrictions

The effects of pulsatile amplitude on sinusoidal transitional turbulent flows through a rigid pipe in the vicinity of a sharp‐edged mechanical ring‐type constriction have been studied numerically. Pulsatile flows were studied for transitional turbulent flow with Reynolds number (Re) of the order of 10⁴, Womersley number (Nw) of the order of 50 with a corresponding Strouhal number (St) of the order of 0.04. The pulsatile flow considered is a sinusoidal flow with dimensionless amplitudes varying from 0.0 to 1.0. Transitional laminar and turbulent flow characteristics in an alternative manner within the pulsatile flow fields were observed and studied numerically. The flow characteristics were studied through the pulsatile contours of streamlines, vorticity, shear stress and isobars. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity, turbulent shear stress are smaller during the acceleration phase when compared with those during deceleration period. Various parametric equations within a pulsatile cycle have also been formulated through numerical experimentations with different pulsatile amplitudes. In the vicinity of constrictions, the empirical relationships were obtained for the instantaneous flow rate (Q), the pressure gradient (dp/dz), the pressure loss (P_loss), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max). Elliptic relation was observed between flow rate and pressure gradient. Quadratic relations were observed between flow rate and the pressure loss, the maximum values of shear stress, wall shear stress, turbulent kinematic energy and the turbulent viscosity. Linear relationships exist between the instantaneous flow rate and the maximum values of vorticity, wall vorticity and velocity. The time‐average axial pressure gradient and the time average pressure loss across the constriction were observed to increase linearly with the pulsatile amplitude. Copyright © 1999 John Wiley & Sons, Ltd.     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

Numerical analysis of a symmetrically heated vertical channel with obstruction

 In this paper, a numerical investigation of laminar natural convection flows in a vertical channel with obstructions is carried out. The main purpose was to analyze the effects of the locations of symmetric obstructions. The computations were performed in a two-dimensional domain and a symmetric uniform wall temperature has been taken as thermal boundary condition. The governing equations were solved using a control volume method and the SIMPLER algorithm for the velocity–pressure coupling was employed. The profiles of the local Nusselt number were given for three different locations of the obstructions. The variation of the average Nusselt number and inlet flow rate versus the modified Rayleigh number were investigated. The results demonstrated that the average Nusselt number decreases as the distance of the obstructions from the inlet increases. Received on 17 January 2000     

Fluid flow and heat transfer characteristics for a square prism (blockage ratio = 0.1) placed inside a wind tunnel

Experimental investigations in fluid flow and heat transfer have been carried out to study the effect of wall proximity due to flow separation around a square prism at Reynolds number 2.6 × 10⁴, blockage ratio 0.1, different height-ratios and various angles of attack. The static pressure distribution has been measured on all faces of the square prism. The results have been presented in the form of pressure coefficient, drag coefficient for various height-ratios. The pressure distribution shows positive values on the front face whereas on the rear face negative values of the pressure coefficient have been observed. The positive pressure coefficient for different height-ratios does not vary too much but the negative values of pressure coefficient are higher for all points on the surface as the bluff body approaches towards the upper wall of the wind tunnel. The drag coefficient decreases with the increase in angle of attack as the height-ratio decreases. The maximum value of drag coefficient has been observed at an angle of attack nearly 50° for the square prism at all height-ratios. The heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficient are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. Both local and average Nusselt numbers have been presented for various height-ratios. The variation of local Nusselt number has been shown with non-dimensional distance for different angles of attack. The variation of average Nusselt number has also been shown with different angles of attack. The local as well as average Nusselt number decreases as the height-ratio decreases for all non-dimensional distance and angle of attack, respectively, for the square prism. The average Nusselt number for the square prism varies with the angle of attack. But there is no definite angle of attack at which the value of average Nusselt number is either maximum or minimum.     

Modelling the flow of power law fluids in a packed bed using a volume-averaged equation of motion

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous microstructure model based on a cell model is used. Numerical solution of the resulting equation is effected using a penalty Galerkin finite element method. Experimental pressure drop values for dilute solutions of carboxymethylcellulose flowing in narrow tubes packed with uniformly sized spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model through the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the bed pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.     

On study of horizontal thin film flow of Sisko fluid due to surface tension gradient

The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method (ADM). The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile, and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.     

Pressure drop characteristics in a rotating smooth square channel with a sharp 180° bend

The results of an experimental study to investigate the local pressure drop characteristics in a square cross-sectioned smooth channel with a sharp 180° bend rotating about an axis normal to the free-stream direction are reported here. The sharp 180° turn was obtained by dividing a rectangular passage into two channels using a divider wall with a rounded tip at the location where the flow negotiates the turn. The study was carried out for three ratios of divider wall thickness to hydraulic diameter (W/D), namely, 0.24, 0.37 and 0.73 all with a rounded tip divider wall and only for a bend with a W/D ratio of 0.37, the influence of a sharp tip divider wall was studied. Experiments were conducted for a Reynolds number varying from 10 000 to 17 000 with the rotation number (ωD/V) varying from 0 to 0.38. The pressure drop distribution, normalized with the mainstream fluid dynamic pressure head, is presented for the leading, trailing and the outer surfaces. The results indicate that the local pressure drop characteristics in the bend region are significantly affected by a change in the rotation number but the influence of the Reynolds number is weak. The friction factor is less sensitive to rotation for the bend with a W/D ratio of 0.24 when compared to bends with W/D ratios of 0.37 and 0.73. Friction factor correlations are presented which fit the experimental data within 10% for the range of parameters studied.