Dimensional Boundary Layer Research Articles

Analysis of the two-dimensional polydisperse liquid sprays in a laminar boundary layer flow using the similarity transformation method

In this paper we analyze the model that describes the evaporation process of multi-size (polydisperse) of fuel droplets in a laminar boundary layer flow. The spray is described using a probability density function and is based on the well-known sectional approach. The spray is described in two dimensional boundary layer directions that consists of five equations: the continuity equation, the momentum equation, the energy equation, the equation of state and the spray equation. The governing equations are a system of nonlinear partial differential equations (PDE). In order to convert the PDE to ordinary differential equations, we applied the Lees-Dorodnitsyn similarity transformation and the corresponding similar solution based on the compressible stream function. We then solve the model numerically and compare our results to the sectional approach with an experimental data.

Melting heat transfer effects on stagnation point flow of micropolar fluid with variable dynamic viscosity and thermal conductivity at constant vortex viscosity

The two dimensional boundary layer flow of micropolar fluid towards stagnation point formed on a horizontal linearly stretching surface is investigated. Melting heat transfer at the surface, temperature and exponentially space dependent internal heat generation within fluid domain are considered. It is assumed that dynamic viscosity and thermal conductivity are temperature dependent while micropolar vortex viscosity is constant. These assumptions are discussed. Classical temperature dependent viscosity and thermal conductivity models were modified to suit the case of melting heat transfer following all the necessary theories. Similarity transformations are used to convert the governing equations into non-linear boundary value problem and solved numerically. Effects of various parameters on the micropolar fluid flow and heat transfer are analyzed. The results reveal that one of the possible ways to increase transverse velocity of micropolar fluid flow over melting surface is to consider variable thermo-physical property of micropolar fluid at constant vortex viscosity with a decrease in melting parameter while velocity ratio increases. For correct analysis/investigation of micropolar fluid flow with variable properties over melting surface, the new thermo-physical models are to be considered. The velocity increases with the increase of velocity ratio under the new condition compare to classical condition (constant thermo-physical property) of micropolar fluid flow over melting surface.

Lie Group Analysis for Boundary Layer Flow of Nanofluids near the Stagnation-Point over a Permeable Stretching Surface Embedded in a Porous Medium in the Presence of Radiation and Heat Generation/Absorption

This study investigates the influence of thermal radiation and heat generation/absorption on a two dimensional steady boundary layer flow near the stagnation-point on a permeable stretching sheet in a porous medium saturated with nanofluids. The governing partial differential equations with the appropriate boundary conditions are reduced to a set of ordinary differential equations via Lie-group analysis. The resultant equations are then solved numerically using Runge - Kutta fourth order method along with shooting technique. Two types of nanofluids, namely, copper-water and alumina-water are considered. The velocity and temperature as well as the shear stress and heat transfer rates are computed. The influence of pertinent parameters such as radiation parameter Nr, nanofluid volume fraction parameter , the ratio of free stream velocity and stretching velocity parameter a/c , the permeability parameter K1, suction/blowing parameter S, and heat source/sink parameter  on the flow and heat transfer characteristics is discussed. The present study helps to understand the efficiency of heat transfer transport in nanofluids which are likely to be the smart coolants of the next generation.

Similarity solutions of quasi three dimensional power law fluids using the method of satisfaction of asymptotic boundary conditions

The work presented in this paper is focused on deductive group-theoretic transformations to develop the similarity solution of steady, laminar, incompressible quasi three dimensional boundary layer flow governing power law fluid. The application of one-parameter group reduces the number of independent variables to one and consequently the system of governing, highly non-linear partial differential equations reduces to a self similar, non-linear ordinary differential equation with appropriate auxiliary conditions. The numerical solution for a power law fluid considered for small cross flow is obtained systematically using MSABC in dimensionless form.

Boundary layer flow of three-dimensional viscoelastic nanofluid past a bi-directional stretching sheet with Newtonian heating

This paper deals with steady three dimensional boundary layer flow of an incompressible viscoelastic nanofluid flow in the presence of Newtonian heating. An appropriate transformation is employed to convert the highly non linear partial differential equations into ordinary differential equations. Homotopy Analysis method (HAM) is used to find series solution of the obtained coupled highly non linear differential equations. The convergence of HAM solutions is discussed via h-curves. Graphical illustrations displaying the influence of emerging parameters on velocity, temperature and concentration profiles are given. It is observed that γ the conjugate parameter for Newtonian heating show increasing behavior on both temperature and concentration profiles. However, the temperature and concentration profiles are increasing and decreasing functions of Brownian motion parameter Nb respectively.

Dissipative Boundary Layer Flow over a Nonlinearly Stretching Sheet in the Presence of Magnetic Field and Thermal Radiation

Numerical investigation is carried out for steady two dimensional boundary layer flow of a viscous, incompressible and electrically conducting fluid over a nonlinearly stretching non-isothermal sheet in the presence of variable transverse magnetic field, thermal radiation, viscous dissipation and nonlinearly moving free stream. Similar solution of the fluid flow problem is obtained using forth-order Runge-Kutta method along with shooting technique. Influence of various pertinent parameters such as stretching parameter, stretching index, Hartmann number, Prandtl number, Eckert number and radiation parameter are displayed through graphs and tables.

Numerical Study on the Flow over a Simplified Vehicle Door Gap – an Old Benchmark Problem Is Revisited

A simplified automobile door gap model, defined at the Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems (Category 6) was investigated. After a thorough mesh study compressible and incompressible simulations were carried out and various turbulence models were tried. The influence of three dimensional effects and boundary layer thickness effects were examined too. In case of compressible simulations stability problems were encountered with the non-reflective boundary condition of CFX (beta version at the time of the simulations). It was found that for deep cavities incompressible simulations are not applicable. In spite of the diculties a good agreement between measurements and simulations was found when the flow speed was 50m/s. In case of 26.8m/s flow speed it was found that the presence of the upper channel wall, not taken into account by the previous authors simulating this problem plays an important role – a hitherto unexplained peak in the measured spectrum appeared this way in the simulation.

The transverse curvature effects of non-Newtonian flow past a slender parabolic body of revolution

The Levy Lee transformations are modified with the aim of transforming nonlinear partial differential equations of boundary value type governing the steady two dimensional incompressible boundary layer flows of non-Newtonian power-law fluids past a slender parabolic body of revolution into nonlinear ordinary differential equation with appropriate boundary conditions. The transverse curvature effect of the present flow situation is studied theoretically using group-theoretic initial value technique. It is concluded that the slope of the velocity profile is greatly influenced by transverse curvature and suction or blowing parameters.

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.

Similarity solution to three dimensional boundary layer flow of second grade nanofluid past a stretching surface with thermal radiation and heat source/sink

Development of human society greatly depends upon solar energy. Heat, electricity and water from nature can be obtained through solar power. Sustainable energy generation at present is a critical issue in human society development. Solar energy is regarded one of the best sources of renewable energy. Hence the purpose of present study is to construct a model for radiative effects in three-dimensional of nanofluid. Flow of second grade fluid by an exponentially stretching surface is considered. Thermophoresis and Brownian motion effects are taken into account in presence of heat source/sink and chemical reaction. Results are derived for the dimensionless velocities, temperature and concentration. Graphs are plotted to examine the impacts of physical parameters on the temperature and concentration. Numerical computations are presented to examine the values of skin-friction coefficients, Nusselt and Sherwood numbers. It is observed that the values of skin-friction coefficients are more for larger values of second grade parameter. Moreover the radiative effects on the temperature and concentration are quite reverse.

Approximate Analytical Solution of Magnetohydrodynamics Compressible Boundary Layer flow with Pressure Gradient and suction/injection

The aim of this work is to obtain exact analytical solution to the two dimensional laminar compressible boundary layer flow with an adverse pressure gradient in the presence of heat and mass transfer with MHD. The method applied is homotopy analysis method. It is shown that this solution agrees very well with numerical solution which is obtained by Runge-Kutta Merson method and results are shown graphically for different magnetic parameters.

EFFECTS OF HEAT SOURCE, CHEMICAL REACTION, THERMAL DIFFUSION AND MAGNETIC FIELD ON DEMIXING OF A BINARY FLUID MIXTURE FLOWING OVER A STRETCHED SURFACE

Effects of viscous dissipation, heat source, thermal diffusion and chemical reaction on demixing of a binary mixture of incompressible viscous electrically conducting fluids in two dimensional magnetohydrodynamic boundary layer flow on a vertical stretching surface are investigated. The momentum, energy and concentration equations are reduced to non-linear coupled ordinary differential equations by similarity transformations and are solved numerically by using MATLAB’s built in solver bvp4c. These numerical results are exhibited graphically from which it has been found that the effects of various parameters are to separate the components of the binary mixture by collecting the lighter and rarer component near the plate and throwing the heavier one away from it.

Investigation of a Boundary Layer Flow near the Inflection Point of a Smooth Curve

In this paper, the author investigates a generic type of the two dimensional incompressible viscous boundary layer flows near the inflection point of a smooth curve. In particular, an approximate evaluation of velocity distribution in an

Two Dimensional Boundary Layer Growth with Suction

The boundary layer equations for the unsteady fluid flow with constant suction velocity have been worked out for the impulsive motion of a circular cylinder in the form V(t)=A exp (Ct) where A and C are certain constants. The stream function has been expanded in terms of some functions X/sub 0/(s) where s is a function of y coordinate. The phase angles for various terms have been calculated, and variations shown graphically for large and small frequency of oscillations, where the oscillatory motion is obtained on replacing C by iw.

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation (absorption)

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.

Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers

AbstractThis paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime, which is valid up to the boundary and interface layers. A five-point node-centered and a four-point cell-centered tailored finite point schemes (TFPS) are introduced. The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system. Numerically, both methods can not only capture the diffusion limit, but also exhibit uniform convergence in the diffusive regime, even with boundary layers. Numerical results show that the five-point scheme has first-order accuracy and the four-point scheme has second-order accuracy, uniformly with respect to the mean free path. Therefore a relatively coarse grid can be used to capture the two dimensional boundary and interface layers.

The Time-Dependent Similarity Solutions of Boundary Layer Equations of Power-Law Fluids with Non-Isothermal Surface

Unsteady, two dimensional boundary layer flows over a heated surface of power-law fluids are investigated. Surface temperature is assumed to have o power-law variation with the time and the distance. Similarity transformation is applied to the partial differential equation system with three independent variables is reduced into an ordinary differential equations systems. Numerical solutions of non-linear differential equations are found by using a finite difference scheme. Solutions are obtained for boundary layer flow velocity and thermal boundary layer profile. Effects of flow behavior index, Prandtl number, suction-injection parameter and surface temperature exponent with the time and the distance are outlined in the figures.

Influence of convective boundary condition on double diffusive mixed convection from a permeable vertical surface

The main objective of the present paper is to obtain non-similar solutions numerically for steady two dimensional double diffusive mixed convection boundary layer flows along a vertical semi-infinite permeable surface under the influence of convective boundary condition along with surface mass transfer. The nonlinear partial differential equations governing the flow, temperature, and species concentration fields are expressed in non-dimensional form using suitable non-similar transformations. The final non-dimensional set of coupled nonlinear partial differential equations is solved by using an implicit finite difference scheme in combination with quasi-linearization technique. The effects of various governing parameters involved on the velocity, temperature and species concentration profiles are discussed in the present paper. The results show that the streamwise co-ordinate ξ significantly influences the flow, thermal, and concentration fields which indicate the importance of non-similar solutions. Results indicate that buoyancy parameter (Ri) and the ratio of buoyancy forces parameter (N) enhance the skin friction coefficient and decrease the heat transfer coefficient. Also, it is observed that the increase of suction parameter (A=1) causes the decrease in the magnitude of temperature and concentration profiles from their values for injection parameter (A=−1). In the present investigation, dual solutions are also obtained under similarity assumptions and compared with previously published work.

Three-Dimensional Flow of an Oldroyd-B Fluid with Variable Thermal Conductivity and Heat Generation/Absorption

This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B fluid with variable thermal conductivity is considered. The flow is induced due to stretching of a surface. Analysis has been carried out in the presence of heat generation/absorption. Homotopy analysis is implemented in developing the series solutions to the governing flow and energy equations. Graphs are presented and discussed for various parameters of interest. Comparison of present study with the existing limiting solution is shown and examined.

Numerical study of MHD boundary layer flow of a Maxwell fluid past a stretching sheet in the presence of nanoparticles

In the present article, two dimensional boundary-layer flows and the heat transfer of a Maxwell fluid past a stretching sheet are studied numerically. The effects of magnetohydrodynamics (MHD) and elasticity on the flow are considered. Moreover, the effects of nanoparticles are also investigated. Similarity transformations are presented to convert the governing nonlinear partial differential equation into coupled ordinary differential equations. The reduced boundary layer equations of the Maxwell nanofluid model are solved numerically. The effects of the emerging parameters, namely, the magnetic parameter M, the elastic parameter K, the Prandtl parameter Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le on the temperature and the concentration profile are discussed. Interesting results are shown graphically. The skin friction coefficient, the dimensionless heat transfer rate and the concentration rate are also plotted against the flow control parameters.