Hall and ion‐slip effects on three‐dimensional flow of a second grade fluid

This investigation pursues the study of Hall and ion‐slip effects on steady three‐dimensional flow of an incompressible second grade fluid. The partial differential equations are reduced to ordinary differential equations by using similarity variables. The resulting problems are solved by employing homotopy analysis method (HAM). The convergence of derived solutions is ensured. The influence of different physical parameters on the dimensionless velocities is examined by sketching plots. Variation of skin friction coefficients for different involved parameters is seen through tabulated values. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of ion‐slip current on the thermal instability of mixed connection in a boundary layer flow

Effect of ion‐slip current on the thermal instability in a boundary layer is studied. The criterion on the position marking the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, the Reynolds number, the wave number, the Hall parameter, the ion‐slip parameter, and the Hartmann number. The flow becomes more stable as the magnetic field increases. However, the destabilizing effects are found on the flow when the Hall and ion‐slip currents are presented. The results of the present numerical prediction show reasonable agreement with the experimental data in the case of zero Hartmann number, ion‐slip parameter, and Hall parameter in the open literature. Copyright © 2011 John Wiley & Sons, Ltd.     

A computational solution of hydromagnetic‐free convective flow past a vertical plate in a rotating heat‐generating fluid with Hall and ion‐slip currents

Taking Hall and ion‐slip current into account, the unsteady magnetohydrodynamic heat‐generating free convective flow of a partially ionized gas past an infinite vertical plate in a rotating frame of reference is investigated theoretically. A computer program using finite elements is employed to solve the coupled non‐linear differential equations for velocity and temperature fields. The effects of Hall and ion‐slip currents as well as the other parameters entering into the problem are discussed extensively and shown graphically. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.     

Analysis on creeping channel flows of compressible fluids subject to wall slip

Creeping channel flows of compressible fluids subject to wall slip are widely encountered in industries. This paper analyzes such flows driven by pressure in planar as well as circular channels. The analysis elucidates unsteady flows of Newtonian fluids subject to the Navier slip condition, followed by steady flows of viscoplastic fluids, in particular, Herschel–Bulkley fluids and their simplifications including power law and Newtonian fluids, that slip at wall with a constant coefficient or a coefficient inversely proportional to pressure. Under the lubrication assumption, analytical solutions are derived, validated, and discussed over a wide range of parameters. Analysis based on the derived solutions indicates that unsteadiness alters cross-section velocity profiles. It is demonstrated that compressibility of the fluids gives rise to a concave pressure distribution in the longitudinal direction, whereas wall slip with a slip coefficient that is inversely proportional to pressure leads to a convex pressure distribution. Energy dissipation resulting from slippage can be a significant portion in the total dissipation of such a flow. A distinctive feature of the flow is that, in case of the pressure-dependent slip coefficient, the slip velocity increases rapidly in the flow direction and the flow can evolve into a pure plug flow at the exit.     

Influence of slip condition on the peristaltic transport in an asymmetric channel with heat transfer: An exact solution

The mechanism of peristaltic magnetohydrodynamic (MHD) flow based on slip and heat transfer effects is studied in an asymmetric channel. An incompressible viscous fluid fills the porous space inside the channel. Long wavelength and zero Reynolds number approximation are used in the flow modeling. Expressions of stream function, longitudinal pressure gradient, and temperature are developed. Various interesting phenomena associated with peristalsis, such as pumping and trapping, are discussed in detail. Further the effects of various pertinent parameters on temperature field and heat transfer coefficient are explained with the help of graphs and tables. It is found that pressure rise over one wavelength decreases in pumping region for large values of slip parameter. Similar behavior is observed for temperature field by increasing the slip parameter. However, the volume of trapped bolus decreases by increasing the slip parameter. Copyright © 2010 John Wiley & Sons, Ltd.     

Influence of hall effect and ion slip on velocity and temperature fields in an MHD channel

The combined influence of viscosity, Hall effect and ion slip on hydrodynamic fields and on heat transfer is investigated. The exact solutions for velocity, induced magnetic field and temperature are derived for the laminar MHD flow in a flat channel assuming a small magnetic Reynolds number, finely segmented electrodes, fully developed flow and uniform heat flux at channel walls. The internal generation of heat is not considered. The Kantorowitsch method of variational calculus is employed to approximate the complicated velocity distribution.     

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.     

Effects of slip and heat transfer analysis of flow over an unsteady stretching surface

In this paper, viscous flow and heat transfer over an unsteady stretching surface is investigated with slip conditions. A system of non-linear partial differential equations is derived and transformed to ordinary differential equations with help of similarity transformations. Numerical computations are carried out for different values of the parameters involved and the analysis of the results obtained shows that the flow field is influenced appreciably by the unsteadiness, and the velocity slip parameter. With increasing values of the unsteadiness parameter, fluid velocity and the temperature are found to decrease in both the presence and absence of slip at the boundary. Fluid velocity decreases due to increasing values of the velocity slip parameter resulting in an increase in the temperature field. Skin-friction decreases with the velocity slip parameter whereas it increases with unsteadiness parameter. The rate of heat transfer decreases with the velocity slip parameter while increases with unsteadiness parameter. Same feature is also noticed for thermal slip parameter.     

Hall effects on oscillating flow due to eccentrically rotating porous disk and a fluid at infinity

Hall effects on the viscous incompressible fluid due to non-coaxial rotations of an oscillating porous disk and a fluid at infinity are studied. The velocity field, shear stresses and temperature distribution are obtained in closed form. It is found that with increase in frequency parameter, the primary velocity increases near the disk and becomes almost stationary away from the disk. The secondary velocity also increases with increase in frequency parameter. It is seen that with increase in Hall parameter, the primary velocity increases near the disk and decreases away from the disk. The reversed effect is observed for the secondary velocity. The shear stresses at the disk are also obtained. It is found that the shear stresses due to the primary and the secondary velocities decrease with increase in Hall parameter. The heat transfer characteristic is also studied on taking viscous dissipation into account. It is found that the mean temperature at the disk decreases with increase in Hall parameter.     

Peristaltic flow of a nanofluid with slip effects

The problem of peristaltic flow of a nanofluid in an asymmetric channel is analyzed by taking into account the slip effects. The relevant equations for the nanofluid are presented and simplified by the long wavelength and small Reynolds number. Closed form solutions for stream function and pressure gradient are developed. However series expressions for temperature and Nanoparticle profiles are constructed. Finally, the influence of several parameters on the physical quantities of interest is discussed.     

Slip effects on unsteady stagnation-point flow and heat transfer over a shrinking sheet

This paper investigates the unsteady boundary layer stagnation-point flow and heat transfer over a linearly shrinking sheet in the presence of velocity and thermal slips. Similarity solutions for the transformed governing equations are obtained and the reduced equations are then solved numerically using fourth order Runge-Kutta method with shooting technique. The numerical results show that multiple solutions exist for certain range of the ratio of shrinking velocity to the free stream velocity (i.e., α) which again depend on the unsteadiness parameter β and the velocity slip parameter (i.e., δ). An enhancement of the velocity slip parameter δ causes more increment in the existence range of similarity solution. Fluid velocity at a point increases increases with the increase in the value of the velocity slip parameter δ, resulting in a decrease in the temperature field. The effects of the velocity and thermal slip parameters, unsteadiness parameter (β) and the velocity ratio parameter (α) on the velocity and temperature distributions are computed, analyzed and discussed. The reported results are in good agreement with the available published results in the literature.     

Numerical study of the combined effects of inertia,slip, and compressibility in extrusion of yield stress fluids

The axisymmetric extrudate swell flow of a compressible Herschel–Bulkley fluid with wall slip is solved numerically. The Papanastasiou-regularized version of the constitutive equation is employed, together with a linear equation of state relating the density of the fluid to the pressure. Wall slip is assumed to obey Navier’s slip law. The combined effects of yield stress, inertia, slip, and compressibility on the extrudate shape and the extrudate swell ratio are analyzed for representative values of the power-law exponent. When the Reynolds number is zero or low, swelling is reduced with the yield stress and eventually the extrudate contracts so that the extrudate swell ratio reaches a minimum beyond which it starts increasing asymptotically to unity. Slip suppresses both swelling and contraction in this regime. For moderate Reynolds numbers, the extrudate may exhibit necking and the extrudate swell ratio initially increases with yield stress reaching a maximum; then, it decreases till a minimum corresponding to contraction, and finally, it converges asymptotically to unity. In this regime, slip tends to eliminate necking and may initially cause further swelling of the extrudate, which is suppressed if slip becomes stronger. Compressibility was found to slightly increase swelling, this effect being more pronounced for moderate yield stress values and wall slip.     

Flow of fluids with pressure dependent viscosities in an orthogonal rheometer subject to slip boundary conditions

We consider slow steady flows of Navier–Stokes-like fluids with pressure dependent viscosities between rotating infinite parallel plates with Navier slip boundary conditions. We derive exact solutions which correspond to flows in orthogonal and torsional rheometers, and investigate the effect of the slip coefficient and the material parameters on the solutions. We find that even when inertial effects are ignored, vorticity boundary layers develop at the upper boundary due to the pressure dependence of the viscosity. These boundary layers diminish and eventually disappear with increased slippage.     

Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al_2O_3-Cu/H_2O hybrid nanofluid

The characteristics of heat transfer in the three-dimensional stagnationpoint flow past a stretching/shrinking surface of the Al₂O₃-Cu/H₂O hybrid nanofluid with anisotropic slip are investigated. The partial differential equations are converted into a system of ordinary differential equations by valid similarity transformations. The simplified mathematical model is solved computationally by the bvp4c approach in the MATLAB operating system. This solving method is...     

不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.     

Flow and heat transfer of an electrically conducting third grade fluid past an infinite plate with partial slip

The effects of partial slip on the steady flow and heat transfer of an electrically conducting, incompressible, third grade fluid past a horizontal plate subject to uniform suction and blowing is investigated. Two distinct heat transfer problems are studied. In the first case, the plate is assumed to be at a higher temperature than the fluid; and in the second case, the plate is assumed to be insulated. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. Numerical solutions for the governing nonlinear equations are obtained over the entire range of physical parameters. The effects of slip, magnetic parameter, non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. It is interesting to find that the velocity and the thermal boundary layers decrease with an increase in the slip, and as the slip increases to infinity, the flow behaves as though it were inviscid.     

Unsteady MHD flow over exponentially stretching sheet with slip conditions

The present paper examines the hydromagnetic three-dimensional flow induced by a stretched surface. An incompressible material saturates the porous medium. Velocity and thermal slip boundary conditions are considered. Suitable transformations are used to obtain the nonlinear ordinary differential equations. Series solutions of the resulting systems are constructed. The effects of various pertinent parameters on the axial velocity and temperature distributions are analyzed graphically. The skin friction and the Nusselt number are computed numerically and graphically.     

压力相关的壁面滑移在滑动间隙流体动压力产生中的作用

近年来,壁面滑移在纳米流变学、微流体力学、薄模润滑和微机电系统(MEMS)等领域越来越引起关注。以前大部分研究集中于表面初始极限剪应力对薄模润滑的壁面滑移和流体动力学的影响。本文通过一个极限剪切应力比例系数主要研究了与压力相关的壁面滑移滑动间隙流体动压力产生中的作用,发现极限剪切应力比例系数以相反的两种方式影响着流体膜的流体动力学:在高初始剪应力区使流体动力增加,但在低初始剪应力区使流体动力减小,这意味着就极限剪切应力比例系数影响流体动压力而言,存在一个初始极限剪切应力的转换点。但是在界面滑移存在时,较小的极限剪切应力比例系数总是产生较小的摩擦阻力。     

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur- face in the presence of magnetic field. To achieve this, one parameter linear group trans- formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method （HAM） to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non- Newtonian fluid （Powell-Eyring model） parameters ε and δon the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ε whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.