Three‐dimensional flow of upper‐convected Maxwell (UCM) fluid

An analysis has been carried out for three‐dimensional fluid over a stretching surface. Similarity transformations are invoked for the conversion of nonlinear partial differential equations to the ordinary differential equations. Computations for the series solution are made by using homotopy analysis method. Graphical results are obtained. Attention has been particularly given to the influence of Deborah number. Copyright © 2010 John Wiley & Sons, Ltd.     

Radiative mixed convection flow of an Oldroyd-B fluid over an inclined stretching surface

A mixed convection flow of an Oldroyd-B fluid in the presence of thermal radiation is investigated. The flow is induced by an inclined stretching surface. The boundary layer equations of the Oldroyd-B fluid in the presence of heat transfer are used. Appropriate transformations reduce partial differential equations to ordinary differential equations. A computational analysis is performed for convergent series solutions. The values of the local Nusselt number are numerically analyzed. The effects of various parameters on velocity and temperature are discussed.     

Three-dimensional flow of a viscoelastic fluid on an exponentially stretching surface

An analysis of a three-dimensional viscoelastic fluid flow over an exponentially stretching surface is carried out in the presence of heat transfer. Constitutive equations of a second-grade fluid are employed. The governing boundary layer equations are reduced by appropriate transformations to ordinary differential equations. Series solutions of these equations are found, and their convergence is discussed. The influence of the prominent parameters involved in the heat transfer process is analyzed. It is found that the effects of the Prandtl number, viscoelastic parameter, velocity ratio parameter, and temperature exponent on the Nusselt number are qualitatively similar.     

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.     

Analytic solution for axisymmetric flow over a nonlinearly stretching sheet

An analysis is performed for the boundary-layer flow of a viscous fluid over a nonlinear axisymmetric stretching sheet. By introducing new nonlinear similarity transformations, the partial differential equations governing the flow are reduced to an ordinary differential equation. The resulting ordinary differential equation is solved using the homotopy analysis method (HAM). Analytic solution is given in the form of an infinite series. Convergence of the obtained series solution is explicitly established. The solution for an axisymmetric linear stretching sheet is obtained as a special case.     

Hall and heat transfer effects on the steady flow of a generalized Burgers’ fluid induced by a sudden pull of eccentric rotating disks

This study looks at the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid between two heated disks rotating about noncoaxial axes normal to the disks. The steady flow and heat transfer analysis is investigated by providing exact analytic solutions. The effect of Hall current is taken into consideration. Calculations are carried out for velocity, temperature, force, and torque exerted by the fluid on one of the disks. The physical interpretation for the emerging parameters is discussed with the help of graphs. The results are compared with those available in the existing literature.     

Exact solution to peristaltic transport of power-law fluid in asymmetric channel with compliant walls

Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a power-law fluid.Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments.Exact solutions are established for the stream function and velocity.The streamlines pattern and trapping are given due attention.Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.     

Transient oscillatory and constantly accelerated non-Newtonian flow in a porous medium

This paper looks at the magnetohydrodynamic (MHD) analysis for transient flow of an Oldroyd-B fluid in a porous medium. The presented analysis takes into account the modified Darcy's law. The flow is induced due to constantly accelerated and oscillating plate. Expressions for the corresponding velocity field and the adequate tangential stress are determined by means of the Fourier sine transform. The influence of various parameters of interest on the velocity and tangential stress has been shown and discussed. A comparison for different kinds of fluids is also provided.     

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.     

Real‐time FTIR monitoring of the mechanism of initiation of isobutylene polymerizations by epoxide/Lewis acid systems

Real‐time Fourier Transformation Infrared (FTIR) spectroscopy with a fiber optic transmission probe (TR) was used to monitor the polymerization of isobutylene (IB) initiated by α‐methylstyrene epoxide (MSE) and 1,2‐epoxi‐2,4,4‐trimethylpentane (TMPO‐1) in conjunction with TiCl₄ and BCl_3. In the presence of an equimolar amount of BCl₃, MSE and TMPO‐1 underwent ring opening via S_N1 mechanism. In contrast to TiCl₄‐coinitiated reactions, no oligoether formation via S_N2 mechanism was observed. TMPO‐1 with excess BCl₃ initiated IB polymerization, yielding a telechelic PIB carrying α‐primary OH and ω‐tertiary Cl functionalities with 70% initiator efficiency. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3611–3618, 2008