Boundary Layer Stagnation Point Flow Research Articles

Dual solutions for stagnation-point flow and convective heat transfer of a Williamson nanofluid past a stretching/shrinking sheet

In this paper, the problem of boundary layer stagnation-point flow and heat transfer of a Williamson nanofluid on a linear stretching/shrinking sheet with convective boundary condition is studied. The effects of Brownian motion and thermophoresis are considered in the energy equation. The governing partial differential equations are first transformed into set of ordinary differential equations, which are then solved numerically using Runge–Kutta–Felhberg fourth–fifth order method with Shooting technique. The characteristics of the flow and heat transfer as well as skin friction and Nusselt number for various prevailing parameters are presented graphically and discussed in detail. A comparison with the earlier reported results has been done and an excellent agreement is shown. It is found that dual solutions exist for the shrinking sheet case. Further, it is observed that the thermal boundary layer thickness increases with increase in Williamson parameter for both solutions.

Unsteady MHD boundary layer stagnation point flow with heat and mass transfer in nanofluid in the presence of mass fluid suction and thermal radiation

The unsteady boundary layer stagnation point flow of heat and mass transfer in a nanofluid with magnetic field and thermal radiation is theoretically investigated. The resulting governing equations are nondimensionalized and are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with the previously published work is presented and the results are found to be in good agreement. The effects of unsteadiness parameter A , solid volume fraction \( \varphi\), magnetic field M, radiation parameter R, Schmidit number Sc and suction parameter w on the fluid flow, heat and mass transfer characteristic are discussed. Dual similarity solutions for the velocity, temperature and concentration profiles are obtained for some negative values of the unsteadiness parameter. It is found that the critical values of A for which the dual solution exists depend on the values of solid volume fraction parameter in the presence of the Schmidit number. Also, the magnetic field parameter as well as the mass fluid suction widen the range of A for which the solution exists. The results also indicate that momentum, thermal and concentration boundary layer thickness for the first solution are thinner than that of the second solution.

Significance of Viscous Dissipation and Chemical Reaction on Convective Transport in a Boundary Layer Stagnation Point Flow Past a Stretching/Shrinking Sheet in a Nanofluid

Significance of Viscous Dissipation and Chemical Reaction on Convective Transport in a Boundary Layer Stagnation Point Flow Past a Stretching/Shrinking Sheet in a Nanofluid

Reactive solute transfer in a stagnation-point flow over a shrinking sheet with a diffusive mass flux

Reactive solute transfer in a boundary-layer stagnation-point flow over a shrinking sheet with a uniform diffusive mass flux is investigated. The first-order chemical reaction is considered. By similarity transformations, the governing partial differential equations are converted into self-similar nonlinear ordinary differential equations. Then the transformed equations are solved numerically by using the shooting method. Dual solutions for the solute distribution are found. The study shows that the concentration at the point increases with increasing velocity ratio parameter for the first solution and decreases for the second solution. Due to an increase in the Schmidt number and reaction rate parameter, the concentration and concentration boundary layer thickness decrease in the presence of the mass flux.

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

Mixed Convection and Nonlinear Radiation in the Stagnation Point Nanofluid flow towards a Stretching Sheet with Homogenous-Heterogeneous Reactions effects

The effect of homogeneous-heterogeneous reactions on the steady two dimensional mixed convection stagnation point boundary layer flow of an incompressible, viscous, electrically conducting, nonlinear radiative heat transfer and chemically reacting copper- water nanofluid toward a linear stretching sheet are numerically investigated in this paper. The spectral local linearization method (SLLM) is used to find the solution for the fluid velocity, fluid temperature and species concentration. Such type of nanofluid flow model are usefull in many engineering process such as insulation system, heat exchanger devices and chemical catalytic.

Finite element solution of oblique stagnation-point flow of viscoelastic fluid and heat transfer with variable thermal conductivity

The oblique stagnation-point boundary layer flow of an incompressible viscoelastic fluid impinging on an infinite vertical plate and heat transfer characteristics with variable thermal conductivity is studied. The governing partial differential equations are transformed into non-dimensional, nonlinear coupled ordinary differential equations which are solved numerically by robust Galerkin finite element method. The streamline patterns and numerical results for the dimensionless shear rate and temperature profiles are displayed graphically for various physical parameters such as Prandtl number, Weissenberg number, thermal conductivity parameter and two parameters α and β, the later being a free parameter. The local Nusselt number is found to be the decreasing function of Weissenberg number whereas it increases with increasing values of Prandtl number. The present problem finds significant applications in cooling of nuclear reactors and electronic devices by fans, where the angle plays an important role in cooling.

Mixed Convection Boundary Layer Stagnation-Point Flow of a Jeffery Fluid Past a Permeable Vertical Flat Plate

Abstract This paper analyzes the combined effects of buoyancy force, mass flux, and variable surface temperature on the stagnation point flow and heat transfer due to a Jeffery fluid over a vertical surface. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then solved numerically using the function bvp4c from computer algebra software Matlab. Numerical results are obtained for skin friction coefficient, Nusselt number as well as dimensionless velocity and temperature profiles for various values of the controlling parameters namely mixed convection parameter λ, mass flux parameter s, elastic parameter (Deborah number) γ, and the ratio of relaxation and retardation time parameter λ1. The results indicate that dual solutions exist in a certain range of the mixed convection and mass flux parameters. In order to establish the physically realizable of these solutions, a stability analysis has also been performed. The results indicate that mixed convection and mass flux significantly affects the nature of the solutions, skin friction, and Nusselt number of a Jeffery fluid.

Melting heat transfer in boundary layer stagnation-point flow of a nanofluid towards a stretching–shrinking sheet

The present analysis deals with the study of two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow of a nanofluid towards a melting stretching sheet. Using similarity transformations, the governing differential equations were transformed into coupled, nonlinear ordinary differential equations, which were then solved numerically by using the Runge–Kutta fourth-order method along with the shooting technique for two types of nanoparticles namely copper (Cu) and silver (Ag) in the water-based fluid with Prandtl number Pr = 6.2, the skin friction coefficient, the local Nusselt number, the velocity and the temperature profiles are presented graphically and discussed.

Effect of time-dependent chemical reaction on stagnation point flow and heat transfer over a stretching sheet in a nanofluid

The unsteady two-dimensional boundary layer stagnation-point flow of a nanofluid over a heated stretching sheet is investigated numerically. The unsteadiness in the flow, temperature and nanoparticle concentration fields is caused by the time-dependence of the stretching velocity, the free stream velocity and the surface temperature and concentration. The transport model employed includes the effects of Brownian motion, thermophoresis and time-dependent chemical reaction. The resulting non-linear governing equations with the associated boundary conditions are solved numerically using the shooting technique with the aid of similarity transformation. The velocity, temperature and nanoparticle volume fraction profiles, as well as the local Nusselt and Sherwood numbers, are analyzed due to the effect of the involved parameters of interest, namely the Brownian motion paramter Nb, thermophoresis parameter Nt, unsteadiness parameter S, velocity ratio parameter , chemical reaction parameter , Prandtl number and Lewis number Le. It is found that the mass transfer process at the solid-fluid interface is stopped for some values of Le, Nb, and Nt despite of the continuity of the heat transfer process for the same parameter values.

The effect of unsteadiness on mixed convection boundary-layer stagnation-point flow over a vertical flat surface embedded in a porous medium

The unsteady mixed convection boundary-layer flow towards a stagnation point on a heated vertical surface embedded in a porous medium is considered. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using a similarity transformation. These are then solved numerically using the Keller-box method. These numerical results are complemented by asymptotic solutions for large values of A. The influence of dimensionless parameters λ (mixed convection), A (time variation), n (wall temperature variation) on the flow field and heat transfer is analyzed and discussed, dual solutions being found for both assisting and opposing buoyant flows.

Mixed convection stagnation flow towards a vertical shrinking sheet

The steady mixed convection stagnation-point boundary layer flow past a vertical stretching/shrinking sheet in a viscous fluid is numerically investigated. The numerical solutions are obtained by solving the similarity equations which are derived via the similarity transformation technique in order to reduce the nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Numerical techniques, namely the Keller-box method, along with the shooting method are used to solve the transformed ordinary differential equations. Results have been presented and discussed for the effects of the governing parameters on the skin friction coefficient and the local Nusselt number as well as for the velocity and temperature profiles. The present results show quite interesting flow behavior for the shrinking sheet problem compared to the stretching sheet problem. On the other hand, it is also found that dual solutions exist for the present problem. The streamlines for the two dimensional flow have also been presented.

Boundary layer stagnation-point flow of a third grade fluid over an exponentially stretching sheet

In this paper, the mixed convection steady boundary layer stagnation point flow and heat transfer of a third grade fluid over an exponentially stretching sheet is investigated. Both the analytical and numerical solutions are carried out. The analytical solutions are obtained through the homotopy analysis method (HAM) while the numerical solutions are computed by using the Keller box method (K-b). Comparison of the HAM and Keller-box methods is also given. The effects of important physical parameters are presented through graphs and the salient features are discussed.

Research on Fluid Mechanics with Slip Flow of Viscoelastic Fluid in the Micro Channel

Stagnation flow, an import research branch of fluid mechanics, describing the fluid motion near the stagnation region, exists on all solid bodies moving in a fluid. And stagnation point boundary layer flow problems described by partial differential equations have attracted many scholars attention nowadays. These problems have become difficult and hot in the study of applied mathematics, mechanics and materials engineering. This paper has transformed the governing boundary layer equations into a system of nonlinear differential equations through the similarity transformation, and the analytical approximations of solutions are derived by homotopy analysis method (HAM). In addition, the effects of physical factors (such as the slip parameter, Magnetic field parameter and Reynolds number) on the flow are examed and discussed graphically. They have a great impact on the speed.

Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.

ON BOUNDARY LAYER STAGNATION POINT FLOW OF A NANOFLUID OVER A PERMEABLE FLAT SURFACE WITH NEWTONIAN HEATING

This study investigates the boundary layer stagnation point flow of a nanofluid past a permeable flat surface with Newtonian heating. The model used for the nanofluid is the one that incorporates the combined effects of Brownian motion and thermophoresis. Using a local 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 applying the shooting iteration technique together with a fourth-order Runge-Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, and nanoparticle concentration distributions are shown for various values of the six thermophysical parameters controlling the flow regime: Prandtl number Pr, Lewis number Le, convection Biot number Bi, the Brownian motion parameter Nb, the thermophoresis parameter Nt, and the suction/injection parameter β. The expressions for the local skin friction, reduced Nusselt number, and reduced Sherwood number were obtained numerically and are discussed quantitatively.

Stagnation Point Flow of Burgers' Fluid and Mass Transfer with Chemical Reaction and Porosity

AbstractThis paper studies the influence of mass transfer in the magnetohydrodynamic (MHD) boundary layer stagnation point flow of Burgers' fluid over a shrinking sheet. Analysis has been carried out in the presence of first order chemical reaction. The two-dimensional flow equations are modeled and then simplified using boundary layer approach. Similarity variables are used to transform the partial differential equations into nonlinear ordinary differential equation. The resulting system is computed using homotopy analysis method (HAM). It is noted that retardation time in Burgers' fluid enhances the magnitude of the flow. The gradient of mass transfer and surface mass transfer for various interesting parameters are also tabulated and analyzed.

Boundary Layer Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid

An analysis is carried out to study the steady two-dimensional stagnation-point flow of a nanofluid over a stretching/shrinking sheet in its own plane. The stretching/shrinking velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb and thermophoresis parameter Nt. It is found that the local Nusselt number is a decreasing function, while the local Sherwood number is an increasing function of each parameters Pr, Le, Nb, and Nt. Different from a stretching sheet, the solutions for a shrinking sheet are nonunique.

Numerical Study of Stagnation Point Flow and Heat Transfer of Micropolar Fluid towards a Surface with Viscous Dissipation Effects

In this paper, we present numerical investigation of the problem of steady laminar two dimensional boundary layer stagnation point flow and heat transfer of a Micropolar fluid towards a heated surface in the presence of viscous dissipation. The governing boundary layer partial differential equations are reduced to a set of ordinary ones using similarity transformations. The solutions for different values of Eckert number, Micropolar parameters and Prandtl number are computed, analyzed and discussed. The study reveals that the reverse flow of heat near the surface may occur due to viscous dissipation which may further be enhanced by the increasing values of the Prandtl number. It may be recommended that the viscous dissipation should not be simply ignored while studying the boundary layer stagnation point flows.

Effects of thermal radiation and variable fluid viscosity on stagnation point flow past a porous stretching sheet

Similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet subject to suction. Fluid viscosity is assumed to vary as a linear function of temperature. Thermal radiation term is considered in the energy equation. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. With the help of them the partial differential equations corresponding to momentum and energy equations are transformed into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing values of the ratio of the free stream velocity to the stretching velocity. Velocity increases with the increasing temperature dependent fluid viscosity parameter when the free-stream velocity is less than the stretching velocity but opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. Temperature at a point of the surface is found to decrease with increasing thermal radiation.