Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.     

Fluctuating flow of an elastico-viscous fluid along an infinite porous plate with an applied magnetic field

The problem of oscillating free stream flow of an elastico-viscous, incompressible, and electrically conducting fluid along an infinite plate with suction varying periodically with time, is considered in the presence of a transverse magnetic field. The effect of the elasticity of the fluid, the magnetic fluid, and the fluctuation of suction velocity on the velocity and the skin friction is examined.     

Radiation effect on temperature distribution in three-dimensional Couette flow with suction or injection

A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidal one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the temperature distribution than the injection or radiation parameter.     

Rotationally symmetric flow over a rotating disk

The rotationally symmetric flow over a rotating disk in an incompressible viscous fluid is analyzed by a new method when the fluid at infinity is in a state of rigid rotation (in the same or in the opposite sense) about the same axis as that of the disk. Asymptotic expansions for the velocity field over the entire flow field are obtained for the general class of one-parameter rotationally symmetric flows. This method is further extended to the case when a uniform suction or injection is assumed at the rotating disk. Fluid motion induced by oscillatory suction of small amplitude at the rotating disk is also discussed.An initial-value analysis reveals that resonance is possible only when the angular velocity of the rotating fluid is greater than that of the rotating disk.     

Effect of suction upon unsteady laminar free convection flow on a vertical infinite flat plate

Summary Unsteady laminar free convection flow past a vertical infinite flat plate subjected to suction is considered. Exact solutions of momentum and energy equations are obtained in two cases: (1) When the plate temperature is proportional to some power of time and (2) when the heat flux at the plate is proportional to some power of time. It is assumed that the suction velocity varies as (time)^–1/2. Expressions for the temperature and velocity profiles are obtained in closed forms in both the cases. Effect of suction on velocity, temperature, skin friction and rate of head transfer is studied for Prandtl numbers 0.02, 0.1, 0.72, 1 and 10.     

Finite Element Solution of Mixed Convection on a Moving Vertical Cylinder with Suction in a Moving Micropolar Fluid Medium

In this paper the problem of mixed convection on a moving vertical cylinder with suction in a moving micropolar fluid medium has been investigated, using finite element method. The effect of important parameters, namely micropolar parameter, suction parameter and velocity coefficient parameter have been discussed on the velocity, microrotation and temperature functions when the velocity of the cylinder is greater than the free stream velocity. Skin friction and the Nusselt number have also been computed, which are given in the table. The temperature distribution is effected moderately by the motion of the cylinder as well with the buoyancy parameter.     

TiO_2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO_2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem(BVP). The BVP is analytically solved with the homotopy analysis method(HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO_2 nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO_2 nanoparticles increases. This confirms the fact that the occurrence of the TiO_2 nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased.An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water,while the Nusselt number of the nanofluid is larger than that of pure water. However,both the parameters increase if the magnetic field intensity increases.     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

Oscillatory Motion of a Viscous Fluid in Contact with a Flat Layer of a Porous Medium

Analytical solutions are obtained for two problems of transverse internal waves in a viscous fluid contacting with a flat layer of a fixed porous medium. In the first problem, the waves are considered which are caused by the motion of an infinite flat plate located on the fluid surface and performing harmonic oscillations in its plane. In the second problem, the waves are caused by periodic shear stresses applied to the free surface of the fluid. To describe the fluid motion in the porous medium, the unsteady Brinkman equation is used, and the motion of the fluid outside the porous medium is described by the Navier–Stokes equation. Examples of numerical calculations of the fluid velocity and filtration velocity profiles are presented. The existence of fluid layers with counter-directed velocities is revealed.     

Three dimensional free convection flow and heat transfer along a porous vertical plate

The free convection flow along a vertical porous plate with transverse sinusoidal suction velocity distribution is investigated. Due to this type of suction velocity at the plate the flow becomes three dimensional one. For the asymptotic flow condition, the wall shear stress in the direction of main flow for different values of buoyancy parameter G is obtained. For G=0, the skin friction in the direction of free stream and the rate of heat transfer from the plate to the fluid are given. It is found that these results differ from those obtained by Gersten and Gross.     

TiO<Subscript>2</Subscript>-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO₂-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO₂ nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO₂ nanoparticles increases. This confirms the fact that the occurrence of the TiO₂ nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.     

Unsteady Motion of a Viscous Liquid between Rotating Parallel Walls in the Presence of a Crossflow

The paper considers the unsteady flow of a viscous incompressible fluid inside an infinitely long slot with uniform injection or suction of the fluid through the porous walls of the slot. The plates with the fluid are rotated rigidly with constant angular velocity. The unsteady flow is induced by nontorsional vibrations of the upper plate. The flowvelocity field and the tangential stress vectors exerted by the fluid on the upper and lower walls of the slot are determined. In this case, one can find an exact solution of the threedimensional nonstationary Navier–Stokes equations. No restrictions are imposed on the motion pattern of the plate.     

Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field

This paper studies the two dimensional flow of an electrically conducting fluid which is an optically thin gray gas past a stationary vertical infinite plate in the presence of radiation. It is assumed that the temperature of the plate and the suction at the plate are constant. The presence of the induced magnetic field is also taken into account. Numerical solutions for the velocity and the induced magnetic field are derived and the effects of the radiation parameter are discussed.     

Radiation effect on forced convective flow and heat transfer over a porous plate in a porous medium

Heat transfer analysis has been presented for the boundary layer forced convective flow of an incompressible fluid past a plate embedded in a porous medium. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. In case of porous plate, fluid velocity increases for increasing values of suction parameter whereas due to injection, fluid velocity is noticed to decrease. The non-dimensional temperature increases with the increasing values of injection parameter. A novel result of this investigation is that the flow separation occurred due to suction/injection may be controlled by increasing the permeability parameter of the medium. The effect of thermal radiation on temperature field is also analyzed.     

Hydromagnetic Stokes flow in a rotating fluid with suspended small particles

An initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about an axis normal to the plate. The flow is generated in the fluid-particle system due to non-torsional oscillations of a given frequency superimposed on the plate in the presence of a transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities, and the wall shear stress. The small and the large time behaviour of the solutions is discussed in some detail. The ultimate steady-state solutions and the structure of the associated boundary layers are determined with physical implications. It is shown that rotation and magnetic field affect the motion of the fluid relatively earlier than that of the particles when the time is small. The motion for large times is set up through inertial oscillations of frequency equal to twice the angular velocity of rotation. The ultimate boundary layers are established through inertial oscillations. The shear stress at the plate is calculated for all values of the frequency parameter. The small and large-time behaviour of the shear stress is discussed. The exact solutions for the velocity of fluid and the wall shear stress are evaluated numerically for the case of an impulsively moved plate. It is found that the drag and the lateral stress on the plate fluctuate during the non-equilibrium process of relaxation if the rotation is large. The present analysis is very general in the sense that many known results in various configurations are found to follow as special cases.     

Unsteady circulatory flow about a circular cylinder with suction

Summary The complete Navier-Stokes equations which describe the unsteady flow of a viscous incompressible fluid when an infinite circular cylinder is given an impulsive twist, and simultaneously a constant suction velocity is imposed on the cylinder, are integrated using Laplace transforms. It is found that points which are at a greater distance from the cylinder are nearer to steadiness than points which are closer to the cylinder. Unsteady flow through a concentric annulus has also been considered.     

Transport Phenomenon in a Third-Grade Fluid Over an Oscillating Surface

The heat and mass transfer effects on the flow of a conducting third-grade fluid over an oscillating vertical porous plate with chemical reactions are considered. Highly nonlinear governing equations of the third-grade fluid are solved analytically by using a multi-parameter perturbation technique and compared with the numerical results obtained by the parallel shooting method. The fluid flow velocity, temperature, and concentration are analyzed as functions of the Hartmann number, suction parameter, Prandtl and Schmidt numbers, and chemical reaction parameter.     

The Rayleigh and Stokes problems with an incompressible non-Newtonian fluid

Summary The Rayleigh problem or impulsive motion of a flat plate has been solved using a perturbation scheme when the surrounding fluid is representable by the constitutive equations of Oldroyd or Coleman and Noll. The shear stress and normal stress at the wall were expressed analytically for this unsteady motion. Further, an exact solution of the equations was found for a special case of the constitutive equations.The motion of the fluid above a harmonically oscillating plate or the Stokes problem has been determined for a special non-Newtonian fluid. The penetration of the shear wave into the fluid, the energy dissipation, the velocity profiles and the shear and normal stresses at the wall were expressed and compared to an equivalent Newtonian fluid.Some of the features of these non-Newtonian fluids were examined in simple shearing flows, and techniques to calculate some of the material constants discussed.     

Effects of thermal radiation and variable fluid viscosity on stagnation point flow past a porous stretching sheet

Similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet subject to suction. Fluid viscosity is assumed to vary as a linear function of temperature. Thermal radiation term is considered in the energy equation. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. With the help of them the partial differential equations corresponding to momentum and energy equations are transformed into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing values of the ratio of the free stream velocity to the stretching velocity. Velocity increases with the increasing temperature dependent fluid viscosity parameter when the free-stream velocity is less than the stretching velocity but opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. Temperature at a point of the surface is found to decrease with increasing thermal radiation.     

The effects of the side walls on the flow of a second grade fluid in ducts with suction and injection

The effects of the side walls on the flow in ducts with suction and injection are examined. Three illustrative examples are given. The first example considers the effect of the side walls on the flow over a porous plate. The second example considers the flow between two parallel porous plates and the third example is devoted to the investigation of the flow in a rectangular duct with two porous walls. Exact solution of the governing equation using the no-slip boundary condition and an additional condition are obtained. The expression of the velocity, the volume flux and the vorticity are given. It is found that for large values of the cross-Reynolds number near the suction region the flow for a Newtonian fluid does not satisfy the boundary condition, but it does not behave in the same way for a second grade fluid. Three examples considered show that there are pronounced effects of the side walls on the flows of a second grade fluid in ducts with suction and injection.