Sakiadis Flow Research Articles

Boundary layer analysis of persistent moving horizontal needle in Blasius and Sakiadis magnetohydrodynamic radiative nanofluid flows

Abstract The boundary layer of a two-dimensional forced convective flow along a persistent moving horizontal needle in an electrically conducting magnetohydrodynamic dissipative nanofluid was numerically investigated. The energy equation was constructed with Joule heating, viscous dissipation, uneven heat source/sink, and thermal radiation effects. We analyzed the boundary layer behavior of a continuously moving needle in Blasius (moving fluid) and Sakiadis (quiescent fluid) flows. We considered Cu nanoparticles embedded in methanol. The reduced system of governing Partial differential equations (PDEs) was solved by employing the Runge–Kutta-based shooting process. Computational outcomes of the rate of heat transfer and friction factors were tabulated and discussed. Velocity and temperature descriptions were examined with the assistance of graphical illustrations. Increasing the needle size did not have a significant influence on the Blasius flow. The heat transfer rate in the Sakiadis flow was high compared with that in the Blasius flow.

Study of predictor corrector block method via multiple shooting to Blasius and Sakiadis flow

In this paper, a predictor corrector two-point block method is proposed to solve the well-know Blasius and Sakiadis flow numerically. The Blasius and Sakiadis flow will be modeled by a third order boundary value problem. The main motivation of this study is to provide a new method that can solve the higher order BVP directly without reducing it to a system of first order equation. Two approximate solutions will be obtained simultaneously in a single step by using predictor corrector two-point block method able to solve the third order boundary value problem directly. The proposed direct predictor corrector two-point block method will be adapted with multiple shooting techniques via a three-step iterative method. The advantage of the proposed code is that the multiple shooting will converge faster than the shooting method that has been implemented in other software. The developed code will automatically choose the guessing values in order to solve the given problems. Some numerical results are presented and a comparison to the existing methods has been included to show the performance of the proposed method for solving Blasius and Sakiadis flow.

Generalized magnetic effects in a Sakiadis flow of polymeric nano-liquids: Analytic and numerical solutions

This analysis explores the rheology of Sakiadis flow for the polymeric type liquid in the presence of applied magnetic field and internal heat generation/absorption phenomenon. Convective form of heat and mass transfer properties are investigated in the presence of thermal radiations. Mathematical modeling is performed for the conversion of physical problem into set of nonlinear equations. Suitable variables are utilized for the conversion of derived partial differential system into set of nonlinear ordinary differential equations. Various graphical and numerical results for the emerging physical quantities are displayed and discussed. Tabular values of local Nusselt and local Sherwood numbers are computed for the involved key parameters.

Effect of magnetic field on Blasius and Sakiadis flow of nanofluids past an inclined plate

A theoretical study on the effect of magnetic field on the classical Blasius and Sakiadis flow of nanofluids over an inclined plate is presented in this paper. The governing partial differential equations are converted into ordinary differential equations using suitable similarity transformations. The transformed boundary layer equations are solved numerically using MATLAB (bvp4c). Two types of nanoparticles are chosen namely copper and alumina in the base fluid of water with the Prandtl number (Pr=6.2). The effects of the governing physical parameters over the velocity, temperature, skin friction coefficient and reduced Nusselt number for both the Blasius and Sakiadis flows are displayed graphically. The characteristics of physical and engineering interest are discussed in detail.

Modified Laplace Adomian decomposition method for analysing the entropy generation of Sakiadis flow with radiation effect

In the recent paper, the modified Adomian decomposition method (ADM) with shooting method is applied to solve the Sakiadis flow problem. Traditionally, Sakiadis flow problem is solved numerically. However, a numerical solution could not easily differentiate and integrate because the data is discrete. In order to improve the problem, firstly, the analytic solution for the Sakiadis flow problem must be not discrete, so that the governing equations of Sakiadis flow could be differentiable and integrated. Hence, in this paper, the analytic solution can be obtained by using modified ADM with shooting method. Secondly, standard ADM only can get small interval, the analytic solution will diverge rapidly for a larger interval. The present method uses Modified Laplace ADM to converge the solution of the Sakiadis flow in the large interval. So this method is reliable and efficient in obtaining the analytic solution solutions that match well with those from the Runge-Kutta method, which is considered close to the exact solution. Finally, the entropy generation of the Sakiadis flow with radiation effect has been studied. The distribution of the entropy generation is discussed by discussing some parameters. For example, Pr, NR, Nsh, Nsf, Nsx, Be number.

Modified Laplace Adomian decomposition method for analysing the entropy generation of Sakiadis flow with radiation effect

In the recent paper, the modified Adomian decomposition method (ADM) with shooting method is applied to solve the Sakiadis flow problem. Traditionally, Sakiadis flow problem is solved numerically. However, a numerical solution could not easily differentiate and integrate because the data is discrete. In order to improve the problem, firstly, the analytic solution for the Sakiadis flow problem must be not discrete, so that the governing equations of Sakiadis flow could be differentiable and integrated. Hence, in this paper, the analytic solution can be obtained by using modified ADM with shooting method. Secondly, standard ADM only can get small interval, the analytic solution will diverge rapidly for a larger interval. The present method uses Modified Laplace ADM to converge the solution of the Sakiadis flow in the large interval. So this method is reliable and efficient in obtaining the analytic solution solutions that match well with those from the Runge-Kutta method, which is considered close to the exact solution. Finally, the entropy generation of the Sakiadis flow with radiation effect has been studied. The distribution of the entropy generation is discussed by discussing some parameters. For example, Pr, NR, Nsh, Nsf, Nsx, Be number.

Numerical analysis of Sakiadis flow problem considering Maxwell nanofluid

This article investigates the flow of Maxwell nanofluid over a moving plate in a calm fluid. Novel aspects of Brownian motion and thermophoresis are taken into consideration. Revised model for passive control of nanoparticle volume fraction at the plate is used in this study. The formulated differential system is solved numerically by employing shooting approach together with fourth-fifth-order-Runge-Kutta integration procedure and Newton?s method. The solutions are greatly influenced with the variation of embedded parameters which include the local Deborah number, the Brownian motion parameter, the thermophoresis parameter, the Prandtl number, and the Schmidt number. We found that the variation in velocity distribution with an increase in local Deborah number is non-monotonic. Moreover, the reduced Nusselt number has a linear and direct relationship with the local Deborah number.

A Legendre wavelet spectral collocation technique resolving anomalies associated with velocity in some boundary layer flows of Walter-B liquid

A Legendre wavelet spectral collocation method is proposed here to solve three boundary layer flow problems of Walter-B fluid namely the stagnation point flow, Blasius flow and Sakiadis flow. In the proposed method, we first transform the boundary value problems into initial value problems using shooting method. We then split the semi infinite domain into subintervals and the governing initial value problems are transformed to system of algebraic equations in each subinterval. The solutions of these algebraic equations yield an approximate solution of the differential equation in each subinterval. The overshoot in the velocity profile associated with the stagnation point and Blasius flows and undershoot in the Sakiadis flow is controlled. Physically realistic solutions are presented for both weakly and strongly viscoelastic parameters. The residual error validates the correctness, convergence and accuracy of the obtained solutions.

Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i) the shooting method and (ii) the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.

Blasius and Sakiadis Slip Flows of Nanofluid with Radiation Effects

AbstractThe steady two-dimensional boundary layer slip flow of a viscous incompressible Cu-water nanofluid past a moving radiating plate in a quiescent fluid (Sakiadis flow) and the flow induced over a stationary radiating flat plate by a uniform free stream (Blasius flow) are investigated simultaneously numerically. The experimental correlations for the effective density, thermal conductivity, and viscosity of nanofluid are used in the governing equations. Similarity equations of the governing transport equations are derived using similarity variables developed by a scaling group of transformation. The transformed equations are solved numerically using an implicit finite-difference numerical method. The emerging parameters are Prandtl number, radiation conduction, velocity ratio, thermal slip, and hydrodynamic slip. Sample results for the dimensionless axial velocity profiles, temperature profiles, friction factor, and rate of heat transfer have been presented graphically and discussed in detail. The fri...

Radiation, Heat Generation and Viscous Dissipation Effects on MHD Boundary Layer Flow for the Blasius and Sakiadis Flows with a Convective Surface Boundary Condition

This study is devoted to investigate the radiation, heat generation viscous dissipation and magnetohydrodynamic effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow) both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique alongside with the forth order of Runge-Kutta method and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Magnetic field parameter M, Grashof number Gr, Prandtl number Pr, radiation parameter NR, Heat generation parameter Q, Convective parameter

Non-similar Blasius and Sakiadis flow of a non-Newtonian Carreau fluid

The Blasius and Sakiadis flow of a non-Newtonian Carreau fluid is considered in the present paper. The boundary layer equations are transformed into non-dimensional form and a new dimensionless parameter (Deborah number) is introduced. The transformed boundary layer equations are solved with the finite difference method. The problem is non-similar and is governed by the Deborah number, the power-law index and the non-dimensional distance along the plate. Velocity profiles and wall shear stress have been calculated for both cases and a comparison is made between Blasius and Sakiadis flow.

Sakiadis flow of Maxwell fluid considering magnetic field and convective boundary conditions

In this paper we address the flow of Maxwell fluid due to constantly moving flat radiative surface with convective condition. The flow is under the influence of non-uniform transverse magnetic field. The velocity and temperature distributions have been evaluated numerically by shooting approach. The solution depends on various interesting parameters including local Deborah number De, magnetic field parameter M, Prandtl number Pr and Biot number Bi. We found that variation in velocity with an increase in local Deborah number De is non-monotonic. However temperature is a decreasing function of local Deborah number De.

Study on Sakiadis and Blasius flows of Williamson fluid with convective boundary condition

AbstractThe present analysis reports the behaviour of Sakiadis and Blasius flow of Williamson fluid with convective boundary condition. Using boundary layer approximations and suitable similarity transformations the governing partial differential equations along with the boundary conditions are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved numerically with the help of fourth and fifth order Runge-Kutta-Fehlberg method. It is found that the Blasius flow provides a thicker thermal boundary layerwhen compared with the Sakiadis flow.

Application of fixed point method to obtain semi-analytical solution to Blasius flow and its variation

The classical Blasius flow and its variation, Sakiadis flow, are investigated by the fixed point method (FPM), and the semi-analytical solutions are obtained. Different from early perturbation series solutions, the present semi-analytical solutions are valid in the whole region without using matching procedure. Moreover, these solutions can correctly provide the asymptotic property of the governing equations. The comparison of the present results with numerical results is carried out, which reveals that FPM is a convenient and effective tool for nonlinear problems.

On inherent irreversibility in Sakiadis flow of nanofluids

The problem of entropy generation and inherent irreversibility in the steady boundary layer shear flow of nanofluids over a moving flat plate is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation and then solved numerically by a Runge–Kutta–Fehlberg method with the shooting technique. Two types of nanofluids, namely, Cu–water and TiO2–water, are used. The effects of nanoparticle volume fraction, the type of nanoparticles, group parameter, and the local Reynolds number on the entropy generation rate, irreversibility ratio and the Bejan number are discussed. It is found that the entropy generation rate at the plate surface decreases with increasing nanoparticle volume fraction and the group parameter. Moreover, the heat transfer irreversibility at the plate surface with TiO2–water nanofluid is slightly higher than that at the plate surface with Cu–water nanofluid.

Sakiadis flow with nonlinear Rosseland thermal radiation

In a recent paper by Cortell (2008 Chin. Phys. Lett.25 1340–2) the effect of radiation on the classical Sakiadis flow along a moving plate in a calm fluid was considered. The results in that paper have been produced using a linearized Rosseland approximation, which is valid only for small temperature differences between the plate and the ambient fluid. In the present work, we extend the above work to a nonlinear Rosseland approximation, which is valid for both small and large temperature differences.

Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating

The combined effects of viscous dissipation and Newtonian heating on boundary layer flow over a moving flat plate are investigated for two types of water-based Newtonian nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu) and titania (TiO2). The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numerically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofluid is higher than that with TiO2-water.

On the Study of Viscoelastic Walters′ B Fluid in Boundary Layer Flows

Viscoelastic Walters′ B fluid flows for three problems, stagnation‐point flow, Blasius flow, and Sakiadis flow, have been investigated. In each problem, Cauchy equations are changed to a nondimensional differential equations using stream functions and with assumption of boundary layer flow. The fourth‐order predictor‐corrector finite‐difference method for solving these nonlinear differential equations has been employed. The results that have been obtained using this method are compared with the results of the last studies, and it is clarified that this method is more accurate. It is also shown that the results of last study about Sakiadis flow of Walter′s B fluid are not true. In addition, the effects of order of discretization in the boundaries are investigated. Moreover, it has been discussed about the valid region of Weissenberg numbers for the second‐order approximation of viscoelastic fluids in each case of study.

The Blasius and Sakiadis flow along a Riga-plate

In a previous paper (Pantokratoras and Magyari, 2009), the Electro-Magnetohydro dynamic (EMHD) free convection flow of a weakly conducting fluid from an electromagnetic actuator was considered. In the present note, we study the cases where the Riga-plate either moves with constant velocity (Sakiadis flow) or the Riga-plate is situated in a constant free stream (Blasius flow). The results are obtained with the numerical simulation of the governing equations. Velocity profiles are presented, as well as values of the skin friction. Results are presented for both impermeable and permeable Riga-plate with uniform suction or uniform injection.