A study of heat and mass transfer of Non-Newtonian fluid with surface chemical reaction

Considering the significance of non-Newtonian fluid usage in manufacturing such as molten plastics, polymeric materials, pulps, and so on, significant efforts have been made to investigate the phenomenon of non-Newtonian fluids. In this article the influences of heat and mass transfer on non-Newtonian Walter's B fluid flow over uppermost catalytic surface of a paraboloid is encountered. An elasticity of the fluid layer is considered in the freestream together with heat source/sink and has the tendency to cause heat flow in the fluid saturated domain. The flow problem of two-dimensional Walter's B fluid is represented using Law of conservation of mass, momentum, heat, and concentration along with thermal and solutal chemical reactive boundary conditions. The governing equations are non-linear partial differential equation and are non-dimensionalized by employing stream function and similarity transformation. The final dimensionless equations yielded are coupled non-linear ordinary differential equations. Furthermore, shooting technique along with RK-4th order method is used to get the numerical results. Graphs and tables are modeled by using MATLAB software to check the effects of Walter's B parameter, Chemical reaction parameter and Thickness parameter on temperature, velocity, and concentration profiles. Tabular analysis shows the results of some physical parameters like skin friction coefficient, Nusselt number and Sherwood number due to the variation of Walter's B parameter, thickness parameter and chemical reactive parameter.     

MHD Williamson micropolar fluid flow pasting a non-linearly stretching sheet under the presence of non linear heat generation/ absorption

This work aims to study the MHD boundary layer flow of Williamson micropolar fluid pasting a non-linearly stretching sheet under the existence of nonlinear heat absorption/generation term, which arises in convection due to high temperature and is the novelty of the present work. The governing equations corresponding to the above physical configuration have been considered in view of the modified Darcy Law with appropriate boundary conditions. Thereafter making use of suitable similarity transformation by introducing stream function, the revised governing equations in the form of ODE with boundary conditions have been obtained. This boundary value problem have been solved numerically by using the shooting technique. The effect of various parameters on flow variables like velocity, temperature, and microrotation has been depicted through graphs. Also, the present analysis's results are compared with those obtained earlier to ensure the numerical validation of the present analysis. In particular, It is observed that the Hartmann number and Williamson parameter have the effect of increasing skin friction.     

On Laminar Boundary Layer Flow of Electrically Conducting Liquids Near an Accelerated Vertical Plate

The unsteady hydromagnetic flow of electrically conducting liquids whose Prandtl numbers are different from unity has been considered when the flow takes place near an infinite vertical flat plate subject to uniform heat flux and accelerated motion. A unified exact solution has been derived for the boundary layer velocity and skin friction for the cases of magnetic field being fixed relative to the fluid or to the vertical plate. The solution has been presented in real forms for fluids whose Prandtl numbers are greater than or less than unity. The response of the boundary layer fluid velocity to the variations in magnetic and buoyancy forces has been discussed for two sample fluids corresponding to the different Prandtl number categories. The influence of these forces on the skin friction has also been shown.     

A multi-domain spectral method for non-Darcian mixed convection flow in a power-law fluid with viscous dissipation

The purpose of this study is to investigate non-Darcian mixed convection flow, heat and mass transfer in a non-Newtonian power-law fluid over a flat plate embedded in porous medium with suction and viscous dissipation and also is to demonstrate the application and utility of a recently developed multi-domain bivariate spectral quasi-linearisation method (MD-BSQLM) in finding the solutions of highly nonlinear differential equations. The flow is subject to, among other source terms, internal heat generation, thermal radiation and partial velocity slip. The coupled system of nonlinear partial differential equations are solved using a MD-BSQLM to find the fluid properties, the skin friction, as well as the heat and mass coefficients. We have presented selected results that give the significance of some system parameters on the fluid properties. This MD-BSQLM has not been used before in the literature to find the nature of the solutions of power-law fluids. Indeed, validation of this numerical method for general fluid flows, heat and mass transfer problems has not yet been done. This study presents the first opportunity to evaluate the accuracy and robustness of the MD-BSQLM in finding solutions of non-Newtonian fluids.     

Effects of radiation on mixed convection stagnation-point flow of MHD third-grade nanofluid over a vertical stretching sheet

This paper considers the problem of the two-dimensional mixed convection stagnation-point flow of a magnetohydrodynamic non-Newtonian nanofluid bounded by a vertical stretching sheet. Convective surface boundary and zero surface nanoparticle mass flux conditions are employed. The effects of buoyancy, radiation, Brownian motion, thermophoresis, and viscous dissipation are taken into account. The stretching velocity is assumed to vary linearly with the distance from the stagnation point. The fluid is electrically conducted with uniform magnetic field, and the work done due to deformation is taken into consideration. The three-coupled partial differential boundary layer equations are reduced to ordinary differential equations by using proper similarity transformations. Analytical solution by homotopy analysis method is obtained. Effects of different physical parameters on the dynamics of the problem are analyzed and discussed.

     

Nuclear reactor application on Jeffrey fluid flow with Falkner-skan factor,Brownian and thermophoresis,non linear thermal radiation impacts past a wedge

In this paper, an impact of non-linear thermal radiation, Brownian and thermophoresis on an MHD through a wedge with dissipative impacts for Jeffrey fluid is investigated. In addition, heat transport analysis is carried out. This work's originality is attributable to the Jeffrey fluid formulation, nonlinear thermal radiation, Brownian and Thermophoresis. The boundary layer approximations are examined, to transform the governing equations into partial differential equations. Utilizing appropriate similarity transformations, the boundary value issue is expressed in ordinary differential form. BVP4C, a nonlinear numerical method, was utilized to determine the outcomes of velocity, concentration and temperature fields at multiple points of the measured quantities. The skin friction term, Sherwood and Nusselt numbers were analyzed in depth, and the findings are achieved graphically and tabularly. A comparison via the previously published data reveals a good degree of concordance. This research focuses mostly on the modelling of flow in a nuclear reactor. The boundary layer flow caused by a wedge surface play s a crucial role the aspects of geothermal and heat exchangers systems.     

Effect of viscous dissipation on MHD water-Cu and EG-Cu nanofluids flowing through a porous medium

This paper provides a comparative analysis of two different types of nanofluids for Stokes second problem. Additional effects of MHD, porosity and viscous dissipation are also considered. Two types of Newtonian liquids (water and ethylene glycol) are considered as base fluids with suspended nanosized Cu particles. A homogenous model of Newtonian nanofluids over a flat plate is used to describe this phenomenon with Stokes boundary conditions such that the ambient fluid is static and with uniform temperature. The problem is first written in terms of nonlinear partial differential equations with physical conditions; then after non-dimensional analysis, the Laplace transform method is used for its closed-form solution. Exact expressions are determined for the dimensionless temperature, velocity field, Nusselt number and skin friction coefficient and arranged in terms of exponential and complementary error functions satisfying the governing equations and boundary conditions. They are also reduced to the known solutions of Stokes second problem for Cu-water nanofluids. Results are computed using Maple software. The results showed that both skin friction and rate of heat transfer increase with increasing solid volume fraction of nanoparticles. MHD and porosity had an opposite effect on velocity for both types of nanofluids. The dimensionless temperature increases by increasing the Eckert and Hartmann numbers.

     

Steady-state hydrodynamics of a viscous incompressible fluid with spinning particles

The steady-state hydrodynamics of a viscous incompressible fluid with spinning particles is studied on the basis of extended Stokes equations. The profiles of flow velocity and spin velocity in simple flow situations may be used to determine the vortex viscosity and spin viscosity of the molecular liquid or fluid suspension. As an example, one situation studied is the flow generated by a uniform torque density in a planar layer of infinite fluid. The spinning particles drive a nearly uniform flow on either side of the layer, in opposite directions on the two sides. The Green function of the extended Stokes equations is derived. The translational and rotational friction coefficients of a sphere with no-slip boundary conditions, and the corresponding flow profiles, are calculated.     

Diffusiophoresis of colloidal spheres in nonelectrolyte gradients at small but finite Péclet numbers

The diffusiophoretic motion of a spherical particle in a uniform imposed gradient of a nonionic solute is analyzed for small but finite Péclet numbers. The range of the interaction between the solute molecules and the particle surface is assumed to be small relative to the radius of the particle, but the polarization effect of the mobile solute in the thin diffuse layer surrounding the particle caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layer are used as the boundary conditions for the fluid domain outside the diffuse layer. Through the use of a method of matched asymptotic expansions along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and an approximate expression for the diffusiophoretic velocity of the particle good to O(Pe ²) is obtained analytically. The analysis shows that the first correction to the particle velocity is O(Pe ²). The normalized particle velocity is found to decrease monotonically with the Péclet number and to increase monotonically with the dimensionless relaxation coefficient. The stronger the polarization effect in the diffuse layer, the weaker the convective effect on the diffusiophoresis. Received: 25 May 2000 Accepted: 6 September 2000     

Simulation of Flow Field for Pulsatile Blood Flow in a Femoral Artery Based on Cosserat Continua

This investigation describes unsteady, pulsatile, laminar, and locally fully developed blood flow velocity and rotation fields during cardiac cycle in the femoral artery using Cosserat continuum mechanics approach. After solving the continuity, linear momentum, and angular momentum equations for flow of blood through artery, the time and position dependent velocity and rotation fields have been calculated. It is shown that the maximum values of velocity occur at the inlet core, while the maximum values of rotation occur on the arterial boundary. It is also demonstrated that the flow of blood in artery is laminar and a good agreement with existing data is established. A time dependent Gaussian equation for non-Newtonian blood viscosity coefficient γ_v has also been found.     

Chemical reaction and Soret effects on MHD convective flow of second grade fluid through an absorbent medium with ramped wall temperature as well as ramped surface concentration

In the present paper, the heat generating and/or absorption as well as thermo-diffusion on the unsteady free convection MHD gyrating flow of radiation and chemical reactive second grade fluid past an unbounded perpendicular plate during absorbent medium have been discussed. Here, it is assumed that, the confining plate has the ramped wall temperature with ramped surface concentration and isothermal temperature with ramped surface concentration. The analytical solutions for the governing equations are found by utilization of Laplace transformation methodology. The velocity, temperature and concentration profiles are analyzed with quite few figures. It is determined that, velocity, temperature and concentration distribution sketches in case of ramped temperature as well as ramped surface concentration are not as much of as those of isothermal temperature as well as ramped surface concentration. In addition to the idioms of skin friction, Nusselt number as well as Sherwood number are achieved and characterized numerically with tabular format.     

Boundary Effects on Diffusiophoresis of Cylindrical Particles in Nonelectrolyte Gradients

The diffusiophoretic motion of a long circular cylinder in a transversely imposed gradient of a nonionic solute near a large plane wall parallel to its axis is analyzed. The range of the interaction between the solute and the solid surfaces is assumed to be small relative to the particle radius and to the gap width between the particle and the wall, but the polarization effect of the mobile solute in the thin diffuse layers adjacent to the solid surfaces caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layers are used as the boundary conditions for the fluid domain outside the diffuse layers. Through the use of cylindrical bipolar coordinates along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and the wall effects on the diffusiophoresis of the cylinder are computed for various cases. For the diffusiophoretic motion of a cylinder normal to a plane, the particle mobility decreases monotonically with the decrease of the distance of the particle axis from the wall. The stronger the polarization effect in the diffuse layer, the weaker the wall effect on the diffusiophoresis. The effect of the normal plane on the diffusiophoresis of a cylinder is much more significant than that for a sphere at the same separation. For the diffusiophoresis of a cylinder parallel to a plane, the boundary effect is a complicated function of the relevant parameters (not necessarily varies monotonically with the extent of separation) mainly due to the existence of a diffusio-osmotic flow caused by the tangential fluid velocity at the plane wall. Copyright 2000 Academic Press.     

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ?-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ?-potential at the interface of the two fluids. The higher values of ?-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ?-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Rheology of dilute polyelectrolyte solutions in narrow channels

The shear flow of dilute polyelectrolyte solutions bounded by either neutral or repulsive walls is modeled using a nonlinear dumbbell with conformation-dependent friction. Assuming that the configurational probability density function depends on the internal coordinates (r) and the distance of the center of mass of the molecule to the walls, coupled differential equations for the tensor moments <rr> are obtained. Coulombic repulsion between beads is considered to simulate the charge repulsion between ionized sites distributed along the backbone of a real polyelectrolyte. The repulsive interaction between the polyelectrolyte molecule and the charged walls is that of the DLVO model and the molecule is considered to be a charged sphere. Numerical solutions for the components of the tensor <rr> are worked out with the preaverage approach, and only when neutral walls considered are exact solutions obtained. Viscosity results show that in the limit of very wide channels, the corresponding viscosity in the bulk is obtained. The wall repulsion on the charged molecules produces migration of molecules towards the center of the channel resulting in a depleted layer with lower viscosity next to the walls. The calculated slip phenomenon using the method employed by Grisafi and Brunn is dependent on the beads repulsion and the shear rate. The slip velocity obtained with the Mooney method shows similarities with available experimental results for polyelectrolyte solutions. Birefringence calculations are performed in narrow and wide channels for different bead repulsions, with interesting results for both flexible and rigid molecules. Received: 26 September 1998 Accepted in revised form: 11 March 1999     

Backtracking of a sphere slowing down in a viscous compressible fluid

It is shown on the basis of the linearized Navier-Stokes equations that a sphere set in motion by a sudden impulse, and slowing down in a viscous compressible fluid, can temporarily reverse its velocity at a late stage of the motion before finally slowing down with a positive velocity. For the effect to occur, the fluid needs to be sufficiently compressible, and the bulk viscosity needs to be sufficiently small relative to the shear viscosity. More generally, the velocity decays nonmonotonically, without necessarily passing through zero. The results are derived from the frequency-dependent friction coefficient, and hold for general boundary condition on the surface of the sphere.     

Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

A combined analytical–numerical study is presented for the slow motion of a spherical particle coated with a layer of adsorbed polymers perpendicular to an infinite plane, which can be either a solid wall or a free surface. The Reynolds number is assumed to be vanishingly small, and the thickness of the surface polymer layer is assumed to be much smaller than the particle radius and the spacing between the particle and the plane boundary. A method of matched asymptotic expansions in a small parameter λ incorporated with a boundary collocation technique is used to solve the creeping flow equations inside and outside the adsorbed polymer layer, where λ is the ratio of the characteristic thickness of the polymer layer to the particle radius. The results for the hydrodynamic force exerted on the particle in a resistance problem and for the particle velocity in a mobility problem are expressed in terms of the effective hydrodynamic thickness (L) of the polymer layer, which is accurate to O(λ²). The O(λ) term forLnormalized by its value in the absence of the plane boundary is found to be independent of the polymer segment distribution and the volume fraction of the segments. The O(λ²) term forL, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant.     

Effect of the wall on the velocity autocorrelation function and long-time tail of Brownian motion in a viscous compressible fluid

Brownian motion of a particle situated near a wall bounding the fluid in which it is immersed is affected by the wall. Specifically, it is assumed that a viscous compressible fluid fills a half space bounded by a plane wall, and that the fluid flow satisfies stick boundary conditions at the wall. The fluctuation-dissipation theorem shows that the velocity autocorrelation function of the Brownian particle can be calculated from the frequency-dependent admittance valid locally. The admittance can be found from the linearized Navier-Stokes equations. The t(-3/2) long-time tail of the velocity relaxation function, valid in bulk fluid, is obliterated by the wall and replaced by a t(-5/2) long-time tail of positive amplitude for motions parallel to the wall and by a t(-5/2) long-time tail of negative amplitude for motions perpendicular to the wall. In both cases the amplitude of the t(-5/2) long-time tail turns out to be independent of fluid compressibility and bulk viscosity.     

Enhanced performance for pressure-driven membrane processes: the argument for fluid instabilities

The performance of pressure-driven membrane processes may be significantly improved when unsteady fluid instabilities are superimposed on crossflow. The role of fluid mechanics, in particular unsteady secondary flows resulting from surface roughness, flow pulsations and centrifugal instabilities, coupled to solute mass transfer is discussed with respect to depolarization and defouling of membranes. Various possible mechanisms including wall shear rate and repeated renewal of the mass boundary layer are analyzed. The secondary flow pattern in a spiral crossflow filter has been visualized and shows a uniform velocity field with a steep gradient adjacent to the membrane surface. Unsteady flows of this type have been used with ultrafiltration and microfiltration membranes to show the efficacy of secondary flows. Significant dissipation with repeated renewal of the mass transfer boundary layer due to secondary flows is used to explain the multiple increase in membrane permeation rates.