Abstract:
An analysis is carried out to investigate the effects of MHD free convection heat transfer of power-law non-Newtonian fluids along a stretching sheet. This has been done under the simultaneous action of suction, heat generation/absorption, thermal radiation and uniform transverse magnetic field. The stretching sheet is assumed to continuously moving with a power-law velocity and maintaining a uniform surface heat flux. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The resulting non-linear equations are solved numerically using Nachtsheim-Swigert shooting iterative technique along with sixth order Runge-Kutta integration scheme. Numerical results for the non-dimensional velocity and temperature profiles are shown graphically and discussed. The effects of skin-friction coefficient and the local Nusselt number which are of physical and engineering interest are studied and presented graphically as well as in the form of tables for the variation of different physically important parameters. A comparison of the present study is also performed with the previously published study and found excellent agreement.

Abstract:
In the present approach, the problem of MHD mixed convective flow and heat and mass transfer of an electrically conducting non-Newtonian power-law fluid past a vertical stretching surface in the presence of thermal radiation, heat generation and chemical reaction is considered. The stretching velocity, temperature and concentration are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary coupled differential equations by means of similarity transformations. These equations are then solved numerically by the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration schemes. The numerical solution is found to be dependent on several governing parameters, including the magnetic parameter, powerlaw index, thermal conductive parameter/mixed convection parameter, mass convective parameter, radiation parameter, modified Prandtl number, heat source parameter, chemical reaction parameter and Schmidt number. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature and distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. Comparison with previously published work is performed and excellent agreement is observed. The resultsobtained several many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.

Abstract:
The steady magneto hydrodynamic (MHD) boundary layer flow and combined heat and mass transfer of a non-Newtonian fluid over an inclined stretching sheet have been investigated in the present analysis. The effects of the flow parameters on the velocity, temperature, species concentration, local skin friction, local Nusselt number, and Sherwood number are computed, discussed and have been graphically represented in figures and tables for various values of different parameters. The numerical results are carried out for several values of the combined effects of magnetic parameter M, stretching parameter λ, Prandtl number Pr, Eckert number Ec, Schmidt number Sc, Soret number S_{0}, slip parameter A and Casson parameter n on velocity, temperature and concentration profiles and also the skin-friction coefficient ？f？\"(0)？local Nusselt number -θ'(0)？and local Sherwood number -ψ'(0)？are discussed and presented in tabular form. The results pertaining to the present study indicate that the velocity profiles decrease as the increase of magnetic field parameter, but reverse trend arises for the effect of Casson parameter and stretching ratio parameter for both Newtonian and non-Newtonian fluids. The temperature profiles increase forthe effect of magnetic parameter, Prandtl number and Eckert number in case of Newtonian and non-Newtonian fluids. The concentration profile increases for the effect of Soret number while concentration profile decreases for the increasing values of Schmidt number, magnetic parameter, Prandtl number and Eckert number for both Newtonian and non-Newtonian fluids. By considering the cooling plate the numerical results for the skin-friction coefficient f？\"(0) , local Nusselt number？-θ'(0) and local Sherwood number ？-ψ'(0) are presented in Tables 1-3.

Abstract:
The mixed convection flow with mass transfer over a stretching surface with suction or injection is examined. By using Lie group analysis, the symmetries of the equations are calculated. A four-finite parameter and one infinite parameter Lie group transformations are obtained. Two different cases are discussed, one for the scaling symmetry and the other for spiral symmetry. The governing partial differential equations are transformed into ordinary differential equations using these symmetries. It has been noted that the similarity variables and functions available in the literature become special cases of the similarity variables and functions discussed in this paper. 1. Introduction The study of continuously stretching sheets has many applications in manufacturing industries. Application of stretching sheets can be found in the areas like paper production, hot rolling, glass blowing, continuous casting of metals, and wire drawing. First of all Sakiadis [1, 2] investigated the boundary layer behavior on stretching surfaces and presented numerical solution for the sheet having constant speed. Extension to this problem where velocity is proportional to the distance from the slit was given by Crane [3]. Flow and heat transfer in the boundary layer on stretching surface was studied by Tsou et al. [4]. Fox et al. [5] presented different methods (analytical or numerical) for solving problems of stretching sheet with suction and injection. Heat and mass transfer on stretched surface with suction and injection was introduced by Erickson et al. [6]. P. S. Gupta and A. S. Gupta [7] studied the same problem for linearly stretching sheet. Heat transfer past a moving continuous plate with variable temperature was studied by Soundalgekar and Murty [8] and Grubka et al. [9]. Ali [10] presented similarity solutions for stretched surface with suction and injection. Hayat et al. [11] investigated the effect of heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid. Lie group analysis is a classical method discovered by Norwegian mathematician Sophus Lie for finding invariant and similarity solutions [12–15]. Yürüsoy and Pakdemirli [16] presented exact solution of boundary layer equations of a special non-Newtonian fluid over a stretching sheet by the method of Lie group analysis. They extended their work to creeping flow of second-grade fluid [17]. Sivasankaran et al. [18, 19] studied the problem of natural convection heat and mass transfer flow

Abstract:
The main aim of this article is to introduce the approximate solution for MHD flow of an electrically conducting Newtonian fluid over an impermeable stretching sheet with a power law surface velocity and variable thickness in the presence of thermal-radiation and internal heat generation/absorption. The flow is caused by the non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The obtaining PDEs are transformed into non-linear system of ODEs using suitable boundary conditions for various physical parameters. We use the Chebyshev spectral method to solve numerically the resulting system of ODEs. We present the effects of more parameters in the proposed model, such as the magnetic parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented, moreover, the local skin-friction and Nusselt numbers. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The obtained numerical results confirm that the introduced technique is powerful mathematical tool and it can be implemented to a wide class of non-linear systems appearing in more branches in science and engineering.

Abstract:
The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from t=0 (initial state) to (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity (f’), micro-rotation (g), temperature (θ), nanoparticle volume fraction (Φ) at final steady state flow, skin friction function (), Nusselt number function () and Sherwood number function () have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.

Abstract:
We present a theoretical analysis for heat transfer in power law non-Newtonian fluid by assuming that the thermal diffusivity is a function of temperature gradient. The laminar boundary layer energy equation is considered as an example to illustrate the application. It is shown that the boundary layer energy equation subject to the corresponding boundary conditions can be transformed to a boundary value problem of a nonlinear ordinary differential equation when similarity variables are introduced. Numerical solutions of the similarity energy equation are presented.

Abstract:
In this paper, the Magnetohydrodynamic (MHD) Flow of
Viscous Fluid over a Nonlinear Stretching Sheet is investigated numerically.
The partial differential equations governing the flow are reduced to a non
linear ordinary differential equations by using similarity transformations. The
resulting
transformed equations are numerically solved by an explicit finite difference
scheme known as the Keller Box Method. The velocity profiles are determined
and the effects of the magnetic parameter and non linear stretching parameter
on the flow characteristics are investigated. In addition to this the numerical
results for the local skin friction coefficients are computed. Comparison with
the exact solution and previously reported analytic solutions is made and
excellent agreement is noted. Moreover, the velocity profile obtained by Keller
box method is in a better agreement to the exact solution than by the Homotopy
Analysis Method. It is also found that, an increase in the magnetic parameter
or non-linearity parameter causes a decrease in the velocity profile and
velocity distribution.

Abstract:
The heat tranfer and flow of a non-Newtonian fluid past a stretching sheet is analyzed in this paper. Results in a non-dimensional form are presented here for the velocity and temperature profiles assuming different kind of boundary conditions.

Abstract:
This paper presents the study of momentum and heat transfer characteristics in a hydromagnetic flow of dusty fluid over an inclined stretching sheet with non-uniform heat source/sink, where the flow is generated due to a linear stretching of the sheet. Using a similarity transformation, the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations and are solved numerically by Runge-Kutta-Fehlberg fourth-fifth-order method using symbolic software Maple. Our numerical solutions are shown to agree with the available results in the literature and then employ the numerical results to bring out the effects of the fluid-particle interaction parameter, local Grashof number, angle of inclination, heat source/sink parameter, Chandrasekhar number, and the Prandtl number on the flow and heat transfer characteristics. The results have possible technological applications in liquid-based systems involving stretchable materials. 1. Introduction Investigations of boundary layer flow and heat transfer are important due to its applications in industries, and many manufacturing processes such as aerodynamic extrusion of plastic sheets, cooling of metallic sheets in a cooling bath, which would be in the form of an electrolyte, and polymer sheet extruded continuously from a die are few practical applications of moving surfaces. Glass blowing, continuous casting, and spinning of fibers also involve the flow due to stretching surface. During its manufacturing process, a stretched sheet interacts with the ambient fluid thermally and mechanically. The thermal interaction is governed by the surface heat flux. This surface heat flux can either be prescribed, or it is the output of a process in which the surface temperature distribution has been prescribed. Newton’s law of viscosity states that shear stress is proportional to velocity gradient. Thus, the fluids that obey this law are known as Newtonian fluids. Crane [3] investigated the flow due to a stretching sheet with linear surface velocity and obtained the similarity solution to the problem. Later, this problem has been extended to various aspects by considering non-Newtonian fluids, more general stretching velocity, magnetohydrodynamic (MHD) effects, porous sheets, porous media, and heat or mass transfer. Andresson et al. [4] extended the work of Crane [3] to non-Newtonian power law fluid over a linear stretching sheet. Grubka and Bobba [5] analyzed heat transfer studies by considering the power-law variation of surface temperature. Saffman [6] has discussed the