Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking sheet

This paper presents a numerical analysis of a stagnation-point flow towards a nonlinearly stretching/shrinking sheet immersed in a viscous fluid. The stretching/shrinking velocity and the external flow velocity impinges normal to the stretching/shrinking sheet are assumed to be in the form U ~ xm, where m is a constant and x is the distance from the stagnation point. The governing partial differential equations are converted into ordinary ones by a similarity transformation, before being solved numerically. The variations of the skin friction coefficient and the heat transfer rate at the surface with the governing parameters are graphed and tabulated. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique for m > 1/3

Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature

In this paper we study the flow and heat transfer characteristics of a viscous fluid over a nonlinearly stretching sheet in the presence of non-uniform heat source and variable wall temperature. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme is used to obtain the solution of the boundary value problem. The effects of various parameters (such as the power law index n, the Prandtl number Pr, the wall temperature parameter λ, the space dependent heat source parameter A* and the temperature dependent heat source parameter B*) on the heat transfer characteristics are analyzed. The numerical results for the heat transfer coefficient (the Nusselt number) are presented for several sets of values of the parameters and are discussed. The results reveal many interesting behaviors that warrant further study on the effects of non-uniform heat source and the variable wall temperature on the heat transfer phenomena at the nonlinear stretching sheet. © 2011 Elsevier Ltd. All rights reserved.postprin

Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet

In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles

Ferromagnetic Liquid Flow due to Gravity-Aligned Stretching of an Elastic Sheet

The flow of a ferromagnetic liquid due to gravity-aligned stretching of an elastic sheet in the presence of a magnetic dipole is considered. The fluid momentum and thermal energy equations are formulated as a six parameter problem and a numerical study is made using the shooting method based on Runge – Kutta Fehlberg and Newton Raphson methods. Extensive computation on the velocity and temperature profiles is presented for a wide range of values of the parameters. It was found that the primary effect of the magnetothermomechanical interaction is to decelerate the fluid motion as compared to the hydrodynamic case. The results have possible industrial applications in ferromagnetic liquid based systems involving stretchable materials

Steady and unsteady mhd mixed convection flow of casson and casson nanofluid over a nonlinear stretching sheet and moving wedge

Casson fluid is a shear thinning fluid which is one of the non-Newtonian fluids that exhibit yield stress. In this fluid, if a shear stress less than the yield stress is applied, it behaves like a solid, whereas if vice-versa the fluid starts to move. The advantage of Casson fluid is that it can be reduced to Newtonian fluid at very high wall shear stress. Due to these reasons, the steady and unsteady two-dimensional, electrically conducting mixed convection flow of Casson fluid was studied in this thesis. Flow that was generated due to nonlinear stretching sheet and moving wedge filled with and without nanoparticles were given attention. Specific problems were studied with various effects include, porous medium, thermal radiation, chemical reaction, slip and convective boundary conditions. Similarity transformations were used to convert nonlinear governing equations into nonlinear ordinary differential equations. The obtained equations were then solved numerically via the implicit finite difference scheme, known as Keller-box method. Moreover, an algorithm was developed in MATLAB software in order to obtain the numerical solutions. The accuracy of the numerical results was validated through comparison with the results available in the published journal. The effects of pertinent parameters on velocity, temperature and concentration profiles as well as wall shear stress, heat and mass transfer rates were displayed graphically and also presented in tabular form. Findings reveals that, when Casson fluid parameter increases the momentum boundary layer thickness reduces in both cases, nonlinear stretching sheet and moving wedge. It is noticed that in the case of moving wedge, the strength of magnetic parameter reduces the wall shear stress. Whereas, opposite trend is observed in the case of nonlinear stretching sheet. In both geometries, the influence of Brownian motion and thermophoresis parameters on the nanoparticles concentration is notably more pronounced

Magnetohydrodynamic boundary layer flow of a viscoelastic fluid past a nonlinear stretching sheet in the presence of viscous dissipation effect

This paper numerically investigates the viscous dissipation effect on the boundary layer flow of an electrically-conducting viscoelastic fluid (Walter's B liquid) past a nonlinear stretching sheet. The partial differential equations governing the flow problem are transformed into ordinary differential equations through similarity variables. The transformed equations are then solved using the Keller box method. A careful evaluation of the influence of the pertinent parameters on the velocity field and temperature distributions through various plots is done for the prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions. The computed coefficient of skin friction, the rate of heat transfer (Nusselt number), and the temperature at the wall are also presented in tabular form. It is revealed from this table that the magnitude of the heat transfer is reduced with the increase in the Eckert number Ec, viscoelastic parameter K, and magnetic parameter M for the PST case by about 12%, 20%, and 29%, respectively. Similarly, the temperature at the wall for the PHF case also decreases with the increase in Ec and M by about 8% and 24%, respectively. It is obvious that the application of the PST condition excels at keeping the viscoelastic fluid warmer than the PHF condition. This implies that applying the PHF condition is better for cooling the sheet faster. The temperature at the wall is unchanged with the changes in the pertinent parameters in the PST case, and it is ascertained that the present results are in close agreement with the previous published results

Fluid flow over a nonlinearly stretching sheet

Numerical solutions are obtained for a class of nonlinear third order differential equations arising in fluid flows over a nonlinearly stretching sheet, using a similarity transformation which is different from that of the linearly stretching sheet problem. Furthermore, using the Schauder theory, existence of a solution of the third order differential equation over a large but finite interval is established. Moreover, the analytical solutions are obtained and are compared with the corresponding numerical solutions. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of nonlinear stretching on the flow characteristics. (c) 2006 Elsevier Inc. All rights reserved

Fluid Flow Over A Nonlinearly Stretching Sheet

Numerical solutions are obtained for a class of nonlinear third order differential equations arising in fluid flows over a nonlinearly stretching sheet, using a similarity transformation which is different from that of the linearly stretching sheet problem. Furthermore, using the Schauder theory, existence of a solution of the third order differential equation over a large but finite interval is established. Moreover, the analytical solutions are obtained and are compared with the corresponding numerical solutions. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of nonlinear stretching on the flow characteristics. © 2006 Elsevier Inc. All rights reserved

Stability analysis of fluid flow over a nonlinearly stretching sheet

We discuss the stability of solutions to a class of nonlinear third-order ordinary differential equations arising in the viscous flow over a nonlinearly stretching sheet. In particular, we consider solutions over the semi-infinite interval [0, a). These results complement the available existence and uniqueness results in the literature. We find that, in general, there is one stable solution branch and one unstable solution branch. Furthermore, it is observed that the stable solution becomes more stable with an increase in the nonlinearity due to the stretching sheet, while the unstable solution branch becomes more unstable given such an increase in the nonlinearity. The stable solution is the physically meaningful solution

Stability Analysis Of Fluid Flow Over A Nonlinearly Stretching Sheet

We discuss the stability of solutions to a class of nonlinear third-order ordinary differential equations arising in the viscous flow over a nonlinearly stretching sheet. In particular, we consider solutions over the semi-infinite interval [0, ∞). These results complement the available existence and uniqueness results in the literature. We find that, in general, there is one stable solution branch and one unstable solution branch. Furthermore, it is observed that the stable solution becomes more stable with an increase in the nonlinearity due to the stretching sheet, while the unstable solution branch becomes more unstable given such an increase in the nonlinearity. The stable solution is the physically meaningful solution. © 2010 Springer-Verlag