MHD Flow of A Third Grade Fluid with Heat Transfer And Slip Boundary Condition Down An Inclined Plane

In this work, we consider the combine effects of slip boundary ohmic heating on MHD flow of a third grade fluid down an inclined plane. The couple non-linear ordinary differential equations arising from the model were solved using both the regular and homotopy perturbation. Effects of the various thermo physical parameters are studied and depicted graphically. Keywords: Slip boundary, MHD, Third grade fluid, Ohmic heating, inclined plane

On Modified Algorithm for Fourth-Grade Fluid

This paper shows the analysis of the thin film flow of fourth-grade fluid on the outer side of a vertical cylinder. Solution of the governing nonlinear equation is obtained by Rational Homotopy Perturbation Method (RHPM); comparison with exact solution reflects the reliability of the method. Analysis shows that this method is reliable for even high nonlinearity. Graphs and tables strengthen the idea

Temperature Dependent Viscosity of a Third Order Thin Film Fluid Layer on a Lubricating Vertical Belt

This paper aims to study the influence of heat transfer on thin film flow of a reactive third order fluid with variable viscosity and slip boundary condition. The problem is formulated in the form of coupled nonlinear equations governing the flow together with appropriate boundary conditions. Approximate analytical solutions for velocity and temperature are obtained using Adomian Decomposition Method (ADM). Such solutions are also obtained by using Optimal Homotopy Asymptotic Method (OHAM) and are compared with ADM solutions. Both of these solutions are found identical as shown in graphs and tables. The graphical results for embedded flow parameters are also shown

The Influence of Slip Condition on the Thin Film Flow of a Third Order Fluid

Abstract: This paper deals with the influence of slip condition on a thin film flow of a third order fluid. We investigate the thin film flow of non-Newtonian fluid (i) when moves down an inclined plane and (ii) when moves on a moving belt with slip condition using the traditional perturbation technique and HPM. The results obtained using both techniques are compared. The expressions for volume flux and average film velocity are also expressed

Unsteady magnetohydrodynamics thin film flow of a third grade fluid over an oscillating inclined belt embedded in a porous medium

In the present work we examine the motion of an incompressible unidirectional magnetohydrodynamics thin film flow of a third grade fluid over an oscillating inclined belt embedded in a porous medium. Moreover, heat transfer analysis has been also discussed in the present work. This physical problem is modeled in terms of non-linear partial differential equations. These equations together with physical boundary conditions are solved using two analytical techniques namely optimal homotopy asymptotic method and homotopy perturbation method. The comparisons of these two methods for different time level are analyzed numerically and graphically. The results exposed that both methods are in closed agreement and they have identical solutions. The effects of various non-dimensional parameters have also been studied graphically

Recent Trends in Coatings and Thin Film–Modeling and Application

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value

Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa-Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu & Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & Fractals 2005;26:177-85] who used the homotopy analysis method to find a different family of solitary wave solutions

Application of lie group analysis and computational methods to the analysis of the flow of a thin non-Newtonian fluid

This thesis is primarily concerned with the application of Lie group analysis and numerical methods to the analysis of the flow of a thin non-Newtonian fluid. In fact due to the increasing importance of non-Newtonian fluids in industry and technological applications during the last decades, researchers have written many papers and developed methods to solve the equations resulting from the modelling of the flow of such fluids. It is worth noting here that these equations are highly nonlinear due to the nonlinear dependence of the fluid’s viscosity on the velocity gradient, adding more complexity/nonlinearity to the nonlinear Navier-Stokes equations. We show the importance of combining Lie group analysis and computational methods to describe the flow of a thin non-Newtonian fluid. Lie group analysis provides a systematic way, when well handled, to find exact solutions to certain classes of nonlinear differential equations. When it is impossible to obtain exact solutions, we can therefore make use of approximate methods and numerical schemes. For the case of the axisymmetric spreading of a power-fluid over a horizontal plane, we use the method of separation of variables combined with the linearization criterion given by Lie to find new exact solutions. We also extend the study of Newtonian fluids to power-law fluids by applying the Lie group method. We determine group-invariant solutions that generalize those of Newtonian fluids and take into account the effects of shear-thinning and shear-thickening. Finally the homotopy analysis method is applied to solve the flow of a generalized second-grade fluid on a moving belt

Mixed convection dissipative viscous fluid flow over a rotating cone by way of variable viscosity and thermal conductivity

AbstractThe effects of temperature-dependent viscosity and thermal conductivity on the flow and heat transfer characteristics of a viscous fluid over a rotating vertical cone are premeditated. The properties of the fluid are assumed to be constant except for the density difference with the temperature. Also, the effect of viscous dissipation is considered in the energy equation. The highly nonlinear unsteady equations are converted into a system of nonlinear ordinary differential equations which is solved by using Homotopy analysis method. The interesting findings for different pertinent parameters on momentum, energy, skin friction coefficient and local Nusselt number are demonstrated in the form of graphs and tables. A comparison has been made with literature as a limiting case of the well-chosen unsteady problem

Lie symmetry analysis and numerical solutions for thermo-solutal chemicallyreacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermo-solutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of non-reactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (micro-rotation component), temperature and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number and reaction parameter. Numerical results for steady state skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined