Flow Of Second Grade Fluid Research Articles

MHD flows of a second grade fluid between two side walls perpendicular to a plate through a porous medium

Exact analytical solutions for magnetohydrodynamic (MHD) flows of an incompressible second grade fluid in a porous medium are developed. The modified Darcy's law for second grade fluid has been used in the flow modelling. The Hall effect is taken into account. The exact solutions for the unsteady flow induced by the time-dependent motion of a plane wall between two side walls perpendicular to the plane has been constructed by means of Fourier sine transforms. The similar solutions for a Newtonian fluid, performing the same motion, appear as limiting cases of the solutions obtained here. The influence of various parameters of interest on the velocity and shear stress at the bottom wall has been shown and discussed through several graphs. A comparison between a Newtonian and a second grade fluids is also made.

On the comparison of the methods used for the solutions of the governing equation for unsteady unidirectional flows of second grade fluids

In order to solve the governing equation for unsteady unidirectional flows of second grade fluids, the use of the Laplace and the Fourier transform methods are discussed. Three characteristic examples which are unsteady flow between two parallel plates, unsteady pipe flow and unsteady flow over a plane wall are considered. It is found that the solution for unsteady flow in bounded regions obtained by the Laplace and the Fourier transform methods are exactly the same as the case of the unsteady flow of a Newtonian fluid. It is shown that the Laplace transform method for small values of time is useful for flows of Newtonian fluids but it is not convenient for flows in unbounded regions of second grade fluids. Furthermore, it is explained that for some unsteady flows of second grade fluids, the solution obtained by using the Laplace transform does not satisfy the initial condition and therefore the Fourier transform method is used.

Analytic solution for MHD Transient rotating flow of a second grade fluid in a porous space

This article looks into the unsteady rotating magnetohydrodynamic (MHD) flow of an incompressible second grade fluid in a porous half space. The flow is induced by a suddenly moved plate in its own plane. Both the fluid and plate rotate in unison with the same angular velocity. Analytic solution of the governing flow problem is obtained by using Fourier sine transform. Based on the modified Darcy's law, expression for velocity is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. Several existing solutions of Newtonian fluid have been also deduced as limiting cases.

Analytic solution for MHD flow of a third order fluid in a porous channel

The present study investigates the channel flow of a third order fluid. The fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel. Expression for velocity is developed by an analytic method, namely the homotopy analysis method (HAM). Convergence of the obtained solution is properly checked. The feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs. It is observed that unlike the flow of second grade fluid, the obtained solution for a third order fluid is non-similar. Also, the behavior of Hartmann number on the velocity is different to that of the Reynold's number.

Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second-grade fluid over a non-isothermal stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation, work due to deformation, internal heat generation/absorption and thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) a sheet with prescribed surface temperature (PST case) and (ii) a sheet with prescribed heat flux (PHF case).

Mixed convection flow of second grade fluid along a vertical stretching flat surface with variable surface temperature

In the present study we have explored the effects of thermal buoyancy on flow of a viscoelastic second grade fluid past a vertical, continuous stretching sheet of which the velocity and temperature distributions are assumed to vary according to a power-law form. The governing differential equations are transformed into dimensionless form using appropriate transformations and then solved numerically. The methods here employed are (1) the perturbation method together with the Shanks transformation, (2) the local non-similarity method with second level of truncation and (3) the implicit finite difference method for values of ξ ( = Grx/Rex2, defined as local mixed convection parameter) ranging in [0, 10]. The comparison between the solutions obtained by the aforementioned methods found in excellent agreement. Effects of the elasticity parameter λ on the skin-friction and heat transfer coefficients have been shown graphically for the fluids having the values of the Prandtl number equal to 0.72, 7.03 and 15.0. Effects of the viscoelastic parameter and the mixed convection parameter, ξ, on the temperature and velocity fields have also been studied. We notice that with the increase in visco-elastic parameter λ, velocity decreases whereas temperature increases and that velocity gradient is higher than that of temperature.

On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.

Unsteady unidirectional flow of second grade fluid between the parallel plates with different given volume flow rate conditions

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of second grade fluids between the parallel plates are considered. The flow motion in the plates is induced by a given but arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved, which are a sudden started and a constant acceleration flow, respectively. Then we apply these two results to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, the oscillatory flow is also considered.

Moving boundary in a non-Newtonian fluid

Moving boundary value problem in non-Newtonian fluid is considered. Exact analytical solution for the flow of second-grade fluid for a rigid moving plate oscillating in its own plane, is obtained. The Doppler effect has been observed due to the motion of the plate. The shearing stress on the plate is also calculated. It is concluded that the solutions for stationary porous boundaries can be obtained from the solutions of moving rigid boundaries.

Unsteady Couette flows of second grade fluids in heated cylindrical domains

By means of finite Hankel transforms, the exact solutions corresponding to some unsteady flows of second grade fluids in heated cylindrical domains are obtained. For steady flows, both the velocity field and the temperature are identically to those resulting from the Navier-Stokes theory.

Exact solutions of non-Newtonian fluid flows with prescribed vorticity

The equations of motion of a non-Newtonian second-grade fluid flow are highly nonlinear partial differential equations. For this reason, there exists only a limited number of exact solutions. Due to the complexity of the equations, inverse methods described by Nemenyi [1] have become attractive in the study of non-Newtonian fluids. In these methods, certain physical or geometrical properties of the flow field are assumed a priori. Lin and Tobak [2] studied steady plane viscous incompressible flows for a chosen vorticity function by decomposing the nonlinear fourth-order partial differential equation in the streamfunction. This excellent approach yielded two second-order linear partial differential equations in the streamfunction. Hui [3] used this approach to study unsteady plane viscous incompressible flows. During the past decade, there has been substantial interest in flows of viscoelastic liquids due to the occurrence of these flows in industrial processes. In this paper, we study the steady and unsteady incompressible viscous non-Newtonian second-grade fluid flows in which the vorticity is proportional to the streamfunction perturbed by a uniform stream. The solutions obtained are exact solutions and represent various non-parallel flows of second-grade fluids. The plan of this paper is as follows: In Sect. 2, the equations of motion of an unsteady plane incompressible second-grade fluid are given, and the vorticity function is assumed to be∇ 2 ψ=A(ψ−Ux−BUy 2). In Sect. 3, solutions for the steady flow are obtained. In Sect. 4, solutions for unsteady flow are obtained.

Existence and Uniqueness of the Flow of Second-Grade Fluids with Slip Boundary Conditions

. This paper treats the solvability of the equations of motion for an incompressible fluid of grade two subject to nonlinear partial slip boundary conditions in a bounded simply‐connected domain. The existence of a unique classical solution, global in time, is proved under suitable regularity and growth restrictions on the initial data, the slip law and the body and surface forces. The method is based on a fixed-point formulation of the problem.

Conjugate heat transfer of a plate fin in a second-grade fluid flow

A conjugate heat transfer problem of a second-grade viscoelastic fluid past a plate fin was studied. Governing equations, including heat conduction equation of a fin, and continuity equation, momentum equation and energy equation of a second-grade fluid, were analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat-plate flow (β = 0) on the fin surface were obtained by a generalized Falkner-Skan flow derivation. These solutions were used to iterate with the heat conduction equation of the fin to obtain distributions of the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number ( Pr), the elastic number ( E) and the conduction-convection coefficient ( N ∞) are from 0.1 to 100, 0.001 to 0.3, and 0.5 to 2.0, respectively. Results indicated that elastic effect in the flow can increase the local heat transfer coefficient and enhance the heat transfer of a fin. Also, same as results from Newtonian fluid flow and conduction, analysis of a fin, a better heat transfer is obtained with a larger N ∞ and Pr.

Existence of threedimensional flows of second-grade fluids past an obstacle

Existence of threedimensional flows of second-grade fluids past an obstacle

Start-up flows of second grade fluids in domains with one finite dimension

A number of unidirectional transient flows of a second grade fluid in a domain with one finite dimension are studied. The method of integral transforms (Fourier, Hankel or Laplace) is applied to obtain exact solutions. A general theorem on start-up flows for second grade fluids is presented that allows us to determine unidirectional flows of second grade fluids once the corresponding solution is known within the context of the Navier-Stokes theory. In the process of obtaining solutions for the fluid of second grade, we find several new exact solutions within the context of the classical Navier-Stokes theory.

Unsteady unidirectional flows of second grade fluids in domains with heated boundaries

The thermal convection of a second grade fluid is studied within the context of unidirectional flows. Stokes' first problem in finite and infinite domains as well as pulsating Poiseuille flow in a pipe are analyzed. Due to the special nature of the flow, both the balance of linear momentum and the energy equation can be solved exactly.

Effect of injection or suction on the Falkner-Skan flows of second grade fluids

The boundary layer flow of an incompressible fluid of grade two past a wedge with surface injection or suction placed symmetrically with respect to the flow direction is investigated. The effects of the non-Newtonian nature of fluid on the shear stress at the wall and the velocity profiles for different injection/suction rates and different wedge angle factor β are studied.

Torsional Flows of Second Grade Fluids

Torsional Flows of Second Grade Fluids

Applying Quasi-Linearization to the Problem of Steady Laminar Flow of a Second Grade Fluid Between Two Rotating Porous Disks

The problem of steady laminar flow of an incompressible second grade fluid between two rotating porous disks has been investigated. The equations of motion are solved by regular perturbation method for small suction/injection parameter and by the quasilinearization method for higher values of suction/injection parameter. The results from both the methods have been compared for both the Newtonian and Non-Newtonian fluids. The effects of suction/injection parameter, rotation parameter and visco-elastic parameter on the velocity components and skin friction have been discussed numerically and shown graphically.