Steady flow and heat transfer in a visco-elastic fluid between two coaxial rotating disks

Flow and heat transfer of an elastico-viscous liquid between two parallel uniformly porous disks rotating about a common axis, are studied by perturbation technique. It is seen that for such a fluid, drag increases with suction and decreases with injection, while the rate of heat transfer increases in the presence of either suction or injection.     

A quasilinearization approach to heat transfer in MHD visco-elastic fluid flow

The paper deals with the study of the flow of an incompressible electrically conducting visco-elastic fluid referred to as Walter’s liquid B over a porous non-isothermal stretching sheet using quasilinearization technique adopting a numerical approach. The sheet is assumed to stretch uni-directionally and the fluid above the sheet is at rest if there were no stretching. The temperature profiles are obtained numerically and these are displayed through graphs for diverse values of Prandtl number, visco-elastic parameter, magnetic parameter, source/sink parameter, wall temperature parameter and wall heat flux parameter. The results are compared with those available in literature obtained through analytical procedures and are seen to be in good agreement.     

Effect of Chemical reaction on MHD flow of a visco-elastic fluid through porous medium.

The effect of heat and mass transfer on free convective flow of a visco-elastic incompressible electrically conducting fluid past a vertical porous plate through a porous medium with time dependant oscillatory permeability and suction in the presence of a uniform transverse magnetic field, heat source and chemical reaction has been studied in this paper. The novelty of the present study is to analyze the effect of chemical reaction, time dependant fluctuative suction and permeability of the medium on a visco-elastic fluid flow. It is interesting to note that presence of sink contributes to oscillatory motion leading to flow instability. Further it is remarked that presence of heat source and low rate of thermal diffusion counteract each other in the presence of reacting species.     

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract

In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions.     

Steady supersonic flow past a curved cone

This paper studies the steady supersonic flow past a Lipschitz curved cone. Under the assumptions that the cone has an opening angle less than a critical value and has sufficiently small total variation of the tangent of the perturbation and that the Mach number of incoming flow is sufficiently large, the global weak solution is constructed via Glimm scheme for 1<γ<3.     

Steady flow of incompressible fluid between two co-rotating disks

This article provides an analytical solution of the Navier–Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of unknown components of velocity and pressure in a radial direction – in contrast to the Briter–Pohlhausen analytical solution, which is supported by simplified Navier–Stokes equations. The obtained infinite system of ordinary differential equations forms recurrent relations from which unknown functions can be calculated successively. The first and second approximations of solution are solved analytically and the third and fourth approximations of solutions are solved numerically. The numerical example demonstrates agreements with results obtained by other authors using different methods.     

Fast deterministic approximation for the multicommodity flow problem

In this paper we consider an optimization version of the multicommodity flow problem which is known as the maximum concurrent flow problem. We show that an approximate solution to this problem can be computed deterministically using O(k(ε ⁻² + logk) logn) 1-commodity minimum-cost flow computations, wherek is the number of commodities,n is the number of nodes, andε is the desired precision. We obtain this bound by proving that in the randomized algorithm developed by Leighton et al. (1995) the random selection of commodities can be replaced by the deterministic round-robin without increasing the total running time. Our bound significantly improves the previously known deterministic upper bounds and matches the best known randomized upper bound for the approximation concurrent flow problem. A preliminary version of this paper appeared inProceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, San Francisco CA, 1995, pp. 486–492.     

Haar wavelet approximation for magnetohydrodynamic flow equations

This study proposes Haar wavelet (HW) approximation method for solving magnetohydrodynamic flow equations in a rectangular duct in presence of transverse external oblique magnetic field. The method is based on approximating the truncated double Haar wavelets series. Numerical solution of velocity and induced magnetic field is obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. The calculations show that the accuracy of the Haar wavelet solutions is quite good even in the case of a small number of grid points. The HW approximation method may be used in a wide variety of high-order linear partial differential equations. Application of the HW approximation method showed that it is reliable, simple, fast, least computation at costs and flexible.     

A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow

In this paper the effects catheterization and non-Newtonian nature of blood in small arteries of diameter less than 100 μm, on velocity, flow resistance and wall shear stress are analyzed mathematically by modeling blood as a Herschel–Bulkley fluid with parameters n and θ and the artery and catheter by coaxial rigid circular cylinders. The influence of the catheter radius and the yield stress of the fluid on the yield plane locations, velocity distributions, flow rate, wall shear stress and frictional resistance are investigated assuming the flow to be steady. It is shown that the velocity decreases as the yield stress increases for given values of other parameters. The frictional resistance as well as the wall shear stress increases with increasing yield stress, whereas the frictional resistance increases and the wall shear stress decreases with increasing catheter radius ratio k (catheter radius to vessel radius). For the range of catheter radius ratio 0.3–0.6, in smaller arteries where blood is modeled by Herschel–Bulkley fluid with yield stress θ = 0.1, the resistance increases by a factor 3.98–21.12 for n = 0.95 and by a factor 4.35–25.09 for n = 1.05. When θ = 0.3, these factors are 7.47–124.6 when n = 0.95 and 8.97–247.76 when n = 1.05.     

Computational treatment of free convection effect on flow of elastico-viscous fluid past an accelerated plate with constant heat flux

Effect of free convection on the visco-elastic fluid (Walter - B’ type) flow past an infinite vertical plate accelerating in its own plane with constant heat flux is examined analytically. It is found that for given values of Grashof number, Prandtl number and Newtonian parameter; flow velocity at any point increases with the increase in time and non-Newtonian parameter, however, it decreases with both, the heating and cooling of the plate.     

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.     

Exact analytical solutions for the Poiseuille and Couette-Poiseuille flow of third grade fluid between parallel plates

Exact analytical solutions for the velocity profiles and flow rates have been obtained in explicit forms for the Poiseuille and Couette-Poiseuille flow of a third grade fluid between two parallel plates. These exact solutions match well with their numerical counter parts and are better than the recently developed approximate analytical solutions. Besides, effects of various parameters on the velocity profile and flow rate have been studied.     

On the analytic solution of nonlinear flow problem involving Oldroyd 8-constant fluid

The problem dealing with the steady flow of an Oldroyd 8-constant fluid over a suddenly moved plate is considered. The fluid is electrically conducting and a uniform magnetic field is applied in the transverse direction. An analytical solution of the nonlinear boundary value problem is obtained using homotopy analysis method (HAM). The behavior of the material constants and the magnetic field is seen on the velocity distribution. It is noted that the boundary layer thickness decreases by increasing the magnetic parameter.     

Approximate self-similar solutions for the boundary value problem arising in modeling of gas flow in porous media with pressure dependent permeability

The flow of a gas through porous medium is considered in the case of pressure dependent permeability and viscosity. Approximate self-similar solutions of the boundary-value problems are found.     

A note on series solution for generalized Couette flow

The problem of generalized Couette flow is considered in this paper. Using homotopy analysis method (HAM) the series solution is developed and its convergence is discussed. Finally, the results are presented graphically and the effects of emerging parameters are analyzed.     

Numerical and analytical simulation of peristaltic flow of a Jeffrey-six constant fluid

This paper describes the Peristaltic flow of a Jeffrey-six constant fluid in an endoscope. The two-dimensional equation of Jeffrey-six constant fluid is simplified by making the assumptions of long wave length and low Reynolds number. The reduced momentum equations are solved with three methods, namely (i) Perturbation method, (ii) Homotopy analysis method, and (iii) shooting method. The comparison of the three solutions shows a very good agreement between the three results. The expressions for pressure rise and frictional forces per wave length have been also computed numerically. Finally, the pressure rise, frictional forces are plotted for different parameters of interest.     

Steady state solutions in a model reacting flow problem

This paper examines the existence of steady state solutions in the Fickett-Majda model of detonation-combustion when heat sources are present and the chemical kinetics is governed by a single, reversible reaction. The problem reduces to studying the bifurcations of a nonlinear algebraic equation, and conditions for existence are obtained in terms of the heat release parameter and total energy of the source     

Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet

This paper deals with the unsteady axisymmetric flow and heat transfer of a viscous fluid over a radially stretching sheet. The heat is prescribed at the surface. The modelled non-linear partial differential equations are solved using an analytic approach namely the homotopy analysis method. Unlike perturbation technique, this approach gives accurate analytic approximation uniformly valid for all dimensionless time. The explicit expressions for velocity, temperature and skin friction coefficient are developed. The influence of time on the velocity, temperature and skin friction coefficient is discussed.     

Couette flow of viscoelastic fluid with constitutive relation involving general Caputo-type fractional derivative

In this paper, the general Caputo-type fractional differential operator introduced by Pr. Anatoly N. Kochubei is applied to the linear theory of viscoelasticity. Firstly, using the general Caputo-type derivative, a generalized linear viscoelastic constitutive equation is proposed for the first time. Secondly, the momentum equation for the plane Couette flow of viscoelastic fluid with the constitutive relation is given as an integrodifferential equation and the analytical solution of the equation is established by employing the separation of variables method. Lastly, for special cases of the general constitutive relation, the analytical solutions are obtained in terms of the Mittag-Leffler functions.