Falkner-Skan Boundary Layer Flow Research Articles

Falkner–Skan boundary layer flow of a fluid with pressure-dependent viscosity past a stretching wedge with suction or injection

In this paper we study the boundary layer flow of a particular class of non-Newtonian fluids, namely piezo-viscous fluids, past a stretching wedge (Falkner–Skan flow). These fluids are essentially Navier–Stokes fluids with pressure-dependent viscosity. We consider the two-dimensional steady flow and introduce some similarity variables, so that the problem is reduced to a third-order nonlinear BVP. We solve the problem numerically by means of a shooting procedure combined with Newton’s method, and we find local similarity solutions. We investigate the behaviour of the velocity field, of the drag and of the thickness of the boundary layer for different values of the involved parameters, making a comparison between the piezo-viscous and the Newtonian case. We find that, depending on some material parameters, the effect of pressure is that of reducing or increasing the boundary layer with respect to the Newtonian case.

Falkner-Skan Boundary Layer Flow Over a Static Wedge

The objective of the present study is to analyse the problem of Falkner-Skan boundary layer flow past a wedge considering velocity slip condition. The governing partial differential equations for physical system are converted into an ordinary differential equation using similarity transformations. The resulting equation is then solved by differential transform method(DTM) empowered by Pade approximations. The velocity profiles are shown and the influence of slip parameter on the flow is discussed. The validity of our solutions is verified by published results.

Analysis of MHD Falkner–Skan Boundary Layer Flow and Heat Transfer Due to Symmetric Dynamic Wedge: A Numerical Study via the SCA-SQP-ANN Technique

This article considers Falkner–Skan flow over a dynamic and symmetric wedge under the influence of a magnetic field. The Hall effect on a magnetic field is negligible for small magnetic Reynolds numbers. The magnetic field B(x) is considered over x-axis, which is in line with the wedge i.e., parallel, while the flow is transverse over the y-axis. This study has numerous device-centric applications in engineering, such as power generators, cooling reactor and heat exchanger design, and MHD accelerators. The Third and second-ordered ordinary differential equations characterize the system. A novel hybrid computational technique is designed for the surrogate solutions of the Falkner–Skan flow system. The designed technique is based on the sine–cosine optimization algorithm and sequential quadratic programming. Reference solutions are calculated by using the Runge–Kutta numerical technique. Performance matrices evaluate the accuracy and stability of our surrogate solutions, mean-absolute deviation (MAD), root-mean-square error (RMSE), and error in Nash-–Sutcliffe efficiency (ENSE). Furthermore, graphical representations in terms of convergence graphs, mesh graphs, stem graphs, stairs plots, and boxplots are presented to establish the symmetry, reliability, and validity of our solutions.

Heat Transfer Analyses for Falkner-Skan Boundary Layer Flow (BLF) past a Static Wedge with respect to Velocity Slip Condition and Temperature-Dependent Thermal Conductivity

This article is mainly studying the heat transfer for Falkner-Skan BLF passing a wedge, by considering N and A, they are: slip condition and variable thermal conductivity respectively. So, by using scaling group of transformation technique, the BLEs that are governing the problem has been transformed to a set of ODEs. Then, by using Runge–Kutta–Fehlberg method, the system is solved numerically to obtain that the heat transfer rate and the fluid temperature are decreasing whenever the A increase. Also, there is an increase of the N to increase the rate of the heat transfer and velocity as well. N is also decreasing both of the shear stress coefficient and temperature. Nevertheless, the shear stress coefficient and the velocity rate of the heat transfer respectively are increasing with m while the fluid temperature decreases with m, such that, m is the Falkner-Skan power law parameter. A compression is done between the results obtained at the end of this paper with previous published results.

Computational study of Falkner–Skan flow of chemically reactive Cross nanofluid with heat generation/absorption

The numerical investigation of magnetohydrodynamic Falkner–Skan boundary layer flow of Cross nanofluid past a wedge in moving fluid is fundamental subject of current paper. The present work is the principal endowment in presenting the flow and heat transfer characteristics of Cross nanofluid past wedge geometry. Moreover, the consequence of heat generation/absorption and diffusion of chemically reactive species is also examined. Instead of conventional no-slip condition at the surface of wedge, Newtonian heat and mass conditions are utilized. The governing problem consisting of highly nonlinear coupled equations is numerically elucidated by the legendry shooting technique. The outcomes of analysis reveal that the wedge angle parameter resulted in boosting the fluids velocity while the temperature and concentration profiles exhibited decaying trend. Enrichment in fluid temperature and nanoparticle concentration fields is found by invoking the Newtonian heat and mass conditions. The increasing values of the heat generation or absorption parameter caused diminution of local Nusselt number. Additionally, an outstanding comparison with the results already reported in the literature is demonstrated for special case.

Correlating convection heat transfer for Falkner-Skan flow

Forced convection heat transfer in a laminar Falkner-Skan boundary layer flow with constant wall temperature is considered over a wide range of pressure gradient parameter β and entire range of Prandtl number Pr. A new asymptotic behavior for the Nusselt number Nux for large β and arbitrary Pr is discovered by examining the dependence of the ratio of the heat transfer for arbitrary Pr to its small Pr limit on Pr/β. Correlations for Nux are developed for −0.19883774 ≤ β < ∞ and all Pr for boundary layer flows without flow reversal. The thermal boundary layer for point-sink flow, which is the limiting case of Falkner-Skan problem as β → ∞, is analyzed. The peculiar behavior of Nux = 0 as β → ∞ in the Falkner-Skan thermal problem is caused by the loss of self-similarity for the solution of boundary layer temperature in the point-sink flow.

Haar wavelet quasilinearization approach for MHD Falkner–Skan flow over permeable wall via Lie group method

PurposeThis paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.Design/methodology/approachUsing the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem.FindingsA new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis.Originality/valueTo find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.

Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method

Purpose – The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field. Design/methodology/approach – The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials. Findings – The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems. Originality/value – In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

A Comparative Study Between two Explicit and Minimal Strategies for the Case of Magnetohydrodynamical Falkner–Skan Flow over a Permeable Wall

In this paper, two efficient and powerful explicit and minimal approaches based on the Hankel- Padé method and Laplace Adomian decomposition method coupled with Padé approximation, respectively, are discussed and employed to obtain approximate results of similarity solutions for the magnetohydrodynamical (MHD) Falkner-Skan boundary layer flow over a permeable wall. The values of skin friction coefficients of the problem are computed with high accuracy. The presented results through tables and figures show the efficiency, reliability, and accuracy of the two presented approaches. Finally, the effects of various model parameters on the boundary layer flow are investigated graphically

Finite Difference Solution of the Falkner—Skan Wedge Flow Equation

A simple numerical method for the solution of the Falkner–Skan boundary layer flow is presented. A third-order ordinary differential equation is recast into two ordinary differential equations, one first order and the other second order. Finite difference approximations of both equations are sequentially solved iteratively with any arbitrary initial conditions. Numerical solutions were found to be in good agreement with published data over a wide range of wedge flows.

Heat transfer analysis for Falkner–Skan boundary layer nanofluid flow past a wedge with convective boundary condition considering temperature-dependent viscosity

This article presents the similarity solutions for the steady two-dimensional Falkner–Skan boundary layer flow of a nanofluid over wedge with convective boundary condition. The model used for the nanofluid is the one that incorporates the variable viscosity and nanoparticle volume fraction parameter. Numerical results for the dimensionless velocity and temperature as well as skin friction and Nusselt number are presented graphically for different values of the controlling parameters. Four different types of nanoparticles, namely, copper (Cu), alumina (Al2O3), titania (TiO2) and silver (Ag) as well as two different types of the base fluid, namely, water and ethylene glycol are considered. It is shown that the skin friction and dimensionless heat transfer rate increase with an increase in nanoparticle volume fraction, wedge, viscosity and convective parameters. Comparisons with the published results for the skin friction and Nusselt number are presented and found to be in good agreement.

Approximate solutions to MHD Falkner-Skan flow over permeable wall

The magnetohydrodynamic (MHD) Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method (DTM) with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.