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Boundary Layer Flow and Heat Transfer with Variable Fluid Properties on a Moving Flat Plate in a Parallel Free Stream
Norfifah Bachok,Anuar Ishak,Ioan Pop
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/372623
Abstract: The steady boundary layer flow and heat transfer of a viscous fluid on a moving flat plate in a parallel free stream with variable fluid properties are studied. Two special cases, namely, constant fluid properties and variable fluid viscosity, are considered. The transformed boundary layer equations are solved numerically by a finite-difference scheme known as Keller-box method. Numerical results for the flow and the thermal fields for both cases are obtained for various values of the free stream parameter and the Prandtl number. It is found that dual solutions exist for both cases when the fluid and the plate move in the opposite directions. Moreover, fluid with constant properties shows drag reduction characteristics compared to fluid with variable viscosity.
Viscous Dissipation and Variable Viscosity Effects on MHD Boundary Layer Flow in Porous Medium Past a Moving Vertical Plate with Suction  [PDF]
P. K. Singh
International Journal of Engineering Science and Technology , 2012,
Abstract: This paper deals with the problem of a steady two dimensional boundary layer flow of an incompressible, viscous and electrically conducting fluid, with heat and mass transfer, past a moving vertical porous plate in the presence of uniform magnetic field applied normal to the plate, taking into account the effects of variable viscosity and viscous dissipation. The equations of motion, heat and mass transfer are transformed into a system of coupled ordinary differential equations in the non-dimensional form which are solved numerically. The effects of various parameters such as Prandtl number, Eckert number and Schmidt number on the velocity, temperature and concentration fields are discussed with the help of graphs.
Effects of Variable Viscosity on Hydromagnetic Boundary Layer along a Continuously Moving Vertical Plate in the Presence of Radiation and Chemical Reaction  [PDF]
Utpal Jyoti Das
Journal of Electromagnetic Analysis and Applications (JEMAA) , 2013, DOI: 10.4236/jemaa.2013.51002

The flow and heat transfer of an incompressible viscous electrically conducting fluid over a continuously moving vertical infinite plate with uniform suction and heat flux in porous medium, taking account of the effects of the variable viscosity, has been considered. The solutions are obtained for velocity, temperature, concentration and skin friction. It is found that the velocity increases as the viscosity of air or porous parameter increases whereas velocity decreases when Schmidt number increases. The skin friction coefficient is computed and discussed for various values of the parameters.

A Mixed Convection Boundary Layer Flow over a Vertical Wall in a Porous Medium, with Exponentially Varying Fluid Viscosity  [PDF]
Eunice Mureithi
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.28087

This study investigates a mixed convection boundary layer flow over a vertical wall embedded in a highly porous medium. The fluid viscosity is assumed to decrease exponentially with temperature. The boundary layer equations are transformed into a non-similar form using an appropriate non-similar variable ξ and a pseudo-similar variable η. The non-similar equations are solved using an efficient local non-similarity method. The effect of viscosity variation parameter on the heat transfer, skin friction and the velocity and temperature distribution within the boundary layer is investigated. The viscosity variation parameter, the viscous dissipation parameter and non-simi-larity variable are shown to have a significant effect on velocity and thermal boundary layer and also on the skin friction coefficient and heat transfer at the wall.

Mixed Convection Boundary Layer Flow over a Moving Vertical Flat Plate in an External Fluid Flow with Viscous Dissipation Effect  [PDF]
Norfifah Bachok, Anuar Ishak, Ioan Pop
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0060766
Abstract: The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.
Numerical Solution of MHD Boundary Layer Flow of Non-Newtonian Casson Fluid on a Moving Wedge with Heat and Mass Transfer and Induced Magnetic Field  [PDF]
Nabil T. El-Dabe, Ahmed Y. Ghaly, Raafat R. Rizkallah, Karem M. Ewis, Ameen S. Al-Bareda
Journal of Applied Mathematics and Physics (JAMP) , 2015, DOI: 10.4236/jamp.2015.36078
Abstract: The paper investigates the numerical solution of the magnetohydrodynamics (MHD) boundary layer flow of non-Newtonian Casson fluid on a moving wedge with heat and mass transfer. The effects of thermal diffusion and diffusion thermo with induced magnetic field are taken in consideration. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying the similarity transformation and solved numerically by using finite difference method (FDM). The effects of various governing parameters, on the velocity, temperature and concentration are displayed through graphs and discussed numerically. In order to verify the accuracy of the present results, we have compared these results with the analytical solutions by using the differential transform method (DTM). It is observed that this approximate numerical solution is in good agreement with the analytical solution. Furthermore, comparisons of the present results with previously published work show that the present results have high accuracy.
Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters
M. M. Rashidi,E. Momoniat,B. Rostami
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/780415
Abstract: In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). It is clear that by the use of second auxiliary parameter, the straight line region in -curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a) prescribed surface temperature (PST) and (b) prescribed heat flux (PHF). The effect of involved parameters on velocity and temperature is investigated.
MHD Boundary Layer Flow of a Non-Newtonian Fluid on a Moving Surface with a Power-Law Velocity
CHEN Xue-Hui,ZHENG Lian-Cun,ZHANG Xin-Xin,

中国物理快报 , 2007,
Abstract: A theoretical analysis for MHD boundary layer flow on a moving surface with the power-law velocity is presented. An accurate expression of the skin friction coefficient is derived. The analytical approximate solution is obtained by means of Adomian decomposition methods. The reliability and efficiency of the approximate solutions are verified by numerical ones in the literature.
Comment on "The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface" by M. Ali  [PDF]
Asterios Pantokratoras
Physics , 2007,
Abstract: The problem of forced convection along an isothermal moving plate is a classical problem of fluid mechanics that has been solved for the first time in 1961 by Sakiadis (1961). It appears that the first work concerning mixed convection along a moving plate is that of Moutsoglou and Chen (1980). Thereafter, many solutions have been obtained for different aspects of this class of boundary layer problems. In the previous works the fluid properties have been assumed constant. Ali (2006) in a recent paper treated, for the first time, the mixed convection problem with variable viscosity. He used the local similarity method to solve this problem but there are doubts about the validity of his results. For that reason we resolved the above problem with the direct numerical solution of the boundary layer equations without any transformation.
Comment on "The effect of variable viscosity on the flow and heat transfer on a continuous stretching surface"  [PDF]
Asterios Pantokratoras
Physics , 2007,
Abstract: The problem of forced convection along an isothermal, constantly moving plate is a classical problem of fluid mechanics that has been solved for the first time in 1961 by Sakiadis (1961). Thereafter, many solutions have been obtained for different aspects of this class of boundary layer problems. Solutions have been appeared including mass transfer, varying plate velocity, varying plate temperature, fluid injection and fluid suction at the plate. The work by Hassanien (1997) belongs to the above class of problems, including a linearly varying velocity and the variation of fluid viscosity with temperature. The author obtained similarity solutions considering that viscosity varies as an inverse function of temperature. However, the Prandtl number, which is a function of viscosity, has been considered constant across the boundary layer. It has been already confirmed in the literature that the assumption of constant Prandtl number leads to unrealistic results (Pantokratoras, 2004, 2005). The objective of the present paper is to obtain results considering both viscosity and Prandtl number variable across the boundary layer. The differences of the two methods are very large in some cases.
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