Some Exact Solutions to Equations of Motion of an Incompressible Third Grade Fluid

This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular cases, all the solutions of Moro et al[1].Comment: 6 pages, 7 figure

Stokes' first problem for some non-Newtonian fluids: Results and mistakes

The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing equations are derived from the conservation laws of mass and momentum and three correct known representations of their exact solutions given. Common mistakes made in the literature are identified. Simple numerical schemes that corroborate the analytical solutions are constructed.Comment: 10 pages, 2 figures; accepted for publication in Mechanics Research Communications; v2 corrects a few typo

Stokes' second problem for rotating MHD flow of a maxwell fluid in a porous medium

An analysis is presented to establish the exact solution of Stokes' second problem for magnetohydrodynamic (MHD) rotating flows of Maxwell fluid in a porous medium. Based on modified Darcy's law the expressions for dimensionless velocity are obtained by using Laplace transform method. The derived steady and transient solutions satisfying the involved differential equations and imposed boundary and initial conditions. The influence of various parameters on the velocity has been analyzed in graphs and discussed

Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method

The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves

Unsteady free convective heat transfer in third-grade fluid flow from an isothermal vertical plate : a thermodynamic analysis

The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The non-dimensional conservation equations for mass, momentum, and energy are solved using a Crank-Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems

Irreversibility analysis for reactive third-grade fluid flow and heat transfer with convective wall cooling

Inherent irreversibility in the flow of a reactive third grade fluid though a channel with convective heating is examined. It is well known that heat dissipated from the exothermic chemical reaction passes through fluid in an irreversible manner and as a result entropy is generated continuously within the channel. Analytical solutions of the resulting dimensionless non-linear boundary-value-problems arising from the governing equations were obtained by using a perturbation method. These solutions are utilized to obtain the entropy generation rate and Bejan number for the system. The influence of various important parameters on the entropy generation rate and Bejan number are shown graphically and discussed accordingly

Similarity Solutions for MHD Visco-Elastic Flow over a Permeable and Non-Linearly Quadratic Stretching Sheet

A notable study on similarity solutions for visco-elastic (Walters liquid B’ model) fluid flow over a permeable and nonlinearly stretching sheet is investigated in the presence uniform magnetic field. Recently Raptis and Perdikis [1] studied the similarity solutions for boundary layer flow over an impermeable quadratic non-linear stretching sheet using a stream function of the kind......

UNSTEADY MHD THREE DIMENSIONAL FLOW OF MAXWELL FLUID THROUGH POROUS MEDIUM IN A PARALLEL PLATE CHANNEL UNDER THE INFLUENCE OF INCLINED MAGNETIC FIELD

In this paper, we discuss the unsteady hydro magnetic flow of an electrically conducting Maxwell fluid in a parallel plate channel bounded by porous medium under the influence of a uniform magnetic field of strength Ho inclined at an angle of inclination with the normal to the boundaries. The perturbations are created by a constant pressure gradient along the plates. The time required for the transient state to decay and the ultimate steady state solution are discussed in detail. The exact solutions for the velocity of the Maxwell fluid consists of steady state are analytically derived, its behaviour computationally discussed with reference to the various governing parameters with the help of graphs. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed in detail

Radiative and magnetohydrodynamics flow of third grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

A mathematical analysis is presented to investigate the nonlinear, isothermal, steady-state, free convection boundary layer flow of an incompressible third grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation and heat generation/absorption. The transformed conservation equations for linear momentum, heat and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller Box Method. The numerical code is validated with previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer materials processing