Steady Boundary Layer Flow Research Articles

Analysis of Forced Convection Boundary Layer Flow and Heat Transfer Past a Semi-Infinite Static and Moving Flat Plate Using Nanofluids-by Haar Wavelets

The paper presents, the steady state two-dimensional forced convection boundary layer flow of heat transfer past a semi-infinite static flat plate (Blasius problem) and moving flat plate (Sakiadis problem) in the water based nanofluid with various nanoparticles. The self-similar solution exists for the boundary layer equations and using suitable similarity variables, the governing equations have been converted into coupled nonlinear ordinary differential equations (NODEs) with an infinite domain. The governing problems over an infinite interval were solved using semi-numerical technique which makes the use of power of Haar wavelets coupled with collocation method. The solutions obtained using wavelet methods have been confirmed to be more accurate as compared to other previously published results. The several physical interesting results of the problem are concentrated and verified through numerical schemes. Three different types of nonmetallic or metallic nanoparticles such as alumina (Al2O3), copper (Cu) and titania (TiO2) in the base fluid of water with Prandtl number Pr = 6.2, to study the effect of solid volume fraction parameter Φ of the nanofluids. The effect of local skin friction coefficients, Nusselt number, velocity and temperature profiles are plotted for various values of nanoparticle volume fractions and for different nanoparticles are analyzed in detail, the numerical results are presented in terms of Tables. It predicts that, the solid volume fraction affects the fluid flow and heat transfer characteristics.

Numerical simulation for the steady nanofluid boundary layer flow over a moving plate with suction and heat generation

In the study, the steady, laminar, incompressible, convective flow of a viscous fluid over a moving plate is investigated theoretically by adopting different types of nanoparticles. Radiation, internal heat generation and viscous dissipation effects are considered in the energy modeled equation. The governing flow equations for the momentum and temperature are reduced to dimensionless form via similarity transformations. The solutions to the resultant equations alongside with the transformed boundary conditions are numerically obtained using MATLAB package bvp4c. Validation with earlier studies are done for the non-internal heat generation case for two distinct nanoparticles of type Cu-water and Al-water. Extensive visualization of flow rate and heat distributions for various emerging parameters are examined. Temperature is consistently enhanced with a rising Eckert number of both types of nanofluids, whereas it is strongly reduced with rising values of radiation term. Heat transfer coefficient is consistently increased with a nanoparticle volume fraction of high convective heat in the medium.

Mixed convection flows of tangent hyperbolic fluid past an isothermal wedge with entropy: A mathematical study

AbstractThe nonlinear, steady, and mixed convective boundary layer flow and heat transfer of an incompressible tangent hyperbolic non‐Newtonian fluid over an isothermal wedge in the presence of magnetic field are analyzed numerically using the implicit Keller‐Box finite‐difference technique. The entropy analysis due to MHD flow of a tangent hyperbolic fluid past an isothermal wedge and viscous dissipation is also included. The numerical code is validated with previous Newtonian studies available in the literature. Graphical and tabulated results are analyzed to study the behavior of the fluid velocity, temperature, concentration, shear stress, heat transfer rate, entropy generation number, and Bejan number for various emerging thermophysical parameters, namely Weissenberg number (We), power‐law index (n), mixed convection parameter (λ), pressure gradient parameter (m), Prandtl number (Pr), Biot number (γ), Hartmann number (Ha), Brinkmann number (Br), Reynolds number (Re), and temperature gradient (Π). It is observed that velocity, entropy, Bejan number, and surface heat transfer rate are reduced with the increase in the Weissenberg number, but temperature and local skin friction are increased. An increase in pressure gradient enhances velocity, entropy, local skin friction, and surface heat transfer rate, but reduces temperature and Bejan number. An increase in an isothermal power‐law index (n) is observed to increase velocity, Bejan number, and surface heat transfer rate, but it decreases temperature, entropy, and local skin friction. An increase in the magnetic parameter (Ha) is found to decrease temperature, entropy, surface heat transfer rate, and local skin friction, and it increases velocity and Bejan number. The research is applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water‐soluble solution thermal treatment.

Steady Boundary Layer Flow of Casson Fluid over a Nonlinear Stretched Sheet in Presence of Viscous Dissipation Using the Spectral Relaxation Method

Steady Boundary Layer Flow of Casson Fluid over a Nonlinear Stretched Sheet in Presence of Viscous Dissipation Using the Spectral Relaxation Method

Convergence acceleration for high-order shock-fitting methods in hypersonic flow applications with efficient implicit time-stepping schemes

The research on hypersonic boundary layer transition is a recent focal point in fluid dynamics. One of the effective numerical methods for transition study is the high-order shock-fitting method, which is especially suitable for dealing with shock-related interactions and removing post-shock oscillations as compared with shock-capturing methods. Currently, explicit time-stepping schemes are mainly used for shock-fitting methods. In comparison, implicit schemes have received less attention due to the extra complexity arising from dynamic shock and moving mesh, even though they can accelerate the convergence speeds for steady flows by up to an order of magnitude. In this paper, two implicit time-stepping methods, GMRES (generalized minimum residual) and LR (line-relaxation), are realized for the efficient calculation of steady flow fields using the 5th-order shock-fitting method. The gas models include both calorically perfect gas and 5-species thermal-chemical non-equilibrium gas required for high-speed and high-enthalpy flows. The results of test cases showed that the convergence rates of GMRES+LR and LR are 4 to 20 times faster than the explicit/semi-implicit Runge-Kutta schemes. Therefore, the usage of implicit GMRES and LR as time-stepping schemes raises the computational efficiency for obtaining steady boundary layer flows, which helps the important high-order shock-fitting methods play a greater role in the study of hypersonic boundary layer stability and transition.

Numerical Simulation of Water Based Ferrofluid Flows along Moving Surfaces

The steady two-dimensional boundary layer flow past a stretching flat sheet in a water-based ferrofluid is investigated. The spatially varying magnetic field is created by two line currents. The similarity method is applied to transform the governing equations into a system of coupled ordinary differential equations. Numerical investigations are performed for ferrofluids, the suspensions of water, and three types of ferroparticles (magnetite, cobalt ferrite, and Mn-Zn ferrite). The impact of the solid volume fraction, the surface stretching parameter, and the ferromagnetic coefficient on the dimensionless velocity and temperature profiles, the skin friction coefficient, and the local Nusselt number are analysed for the three types of ferrofluid.

Magnetohydrodynamic chemically reactive Sisko liquid flow through a stretching surface with nonlinear thermal radiation

Present article reveals results of steady 2D magnetohydrodynamic boundary layer flow of a chemically reactive Sisko liquid due to a stretching surface with nonlinear thermal radiation. The governing equations are computed with R-K 4th order method with BVP4C technique. Numerical evaluations have been accomplished for disparate values of physical constraints with abet of delineates. Additionally, the coefficient of drag force, local Nusselt and Sherwood numbers have been evaluated for disparate parameters and scrutinized for engineering interest.

Heat and mass transfer effect on a radiative second grade MHD flow in a porous medium over a stretching sheet

A study on heat and mass transfer of a steady laminar boundary layer flow of an electrically conducting fluid of second grade in a porous medium subject to a uniform magnetic field past a semi-infinite stretching sheet with power law surface temperature or power law surface heat flux. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of the pertinent flow parameters. The asymptotic expansions of the solutions for large Prandtl number are also given for the two heating conditions. The temperature distribution decreases with the increase in thermal radiation parameter in case of PST and PHF. The rate of mass transfer at the solid surface increases in the presence of magnetic field and decreases with heavier diffusing species.

Nonlinear Convection Flow of Micropolar Nanofluid due to a Rotating Disk with Multiple Slip Flow

In this analysis, steady, laminar, and two-dimensional boundary layer flow of nonlinear convection micropolar nanofluid due to a rotating disk is considered. The mathematical formulation for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variables, the governing nonlinear boundary value problems were reduced into coupled high-order nonlinear ordinary differential equations with numerically solved. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of different parameters on skin friction coefficients f″0 and G′0, wall duo stress coefficients H1′0, -H2′0, and -H3′0, the Nusselt number -θ′0, and Sherwood number Ω′0, as well as the velocities, temperature, and concentration are analysed and discussed through tables and plotted graphs. The findings indicate that an increase in the values of thermal and solutal nonlinear convection parameters allow to increase the value of velocities f′η and Gη near surface of the disk and reduce at far away from the disk as well as thermal and solutal Grashof numbers tolerate to increase in the value of radial velocity f′η near surface of the disk.

MHD Nonlinear Mixed Convection Flow of Micropolar Nanofluid over Nonisothermal Sphere

In this paper, two-dimensional steady laminar boundary layer flow of a nonlinear mixed convection flow of micropolar nanofluid with Soret and magnetic field effect over a nonisothermal sphere is evaluated. The mathematical formulation for the flow problem has been made with appropriate similarity transformation and dimensionless variables, and the main nonlinear boundary value problems were reduced into mixed high-order nonlinear ordinary differential equations. Solution for velocity, microrotation, temperature, and concentration has been obtained numerically. The equations were calculated using method bvp4c from Matlab software for various quantities of main parameters. The effects of various parameters on skin friction coefficient f″0, wall duo stress coefficient -G′0, and convection mass transfer coefficient -Φ′0 are analysed and presented through the graphs and tables. The convergence test has been maintained. For the number of points greater than the suitable mesh number of points, the precision is not influenced but the set time is increased. Moreover, a comparison with a previous paper, obtainable in the literature, has been presented and an excellent agreement is obtained. The findings indicate that an increase in the values of nonisothermal parameters (m, P), magnetic Ma, thermal and solutal nonlinear convection (λ, s) parameter, and Soret number is to enhance the temperature difference between the boundary layer and ambient fluid to diffuse which increases the velocity profile f′ζ and their boundary layer thicknesses near the surface of the sphere.

Triple Solutions and Stability Analysis of Mixed Convection Boundary Flow of Casson Nanofluid over an Exponentially Vertical Stretching/Shrinking Sheet

In this paper, we studied the 2D steady laminar boundary layer flow and heat transfer of Casson based nanofluid over an exponentially vertical stretching and shrinking sheet using one phase model. The thermal radiation and heat source/sink parameters are incorporated in the heat transfer equation and the slip parameters for the velocity and temperature are considered in the boundary conditions. The similarity variables have been used to convert the governing equations as a system of partial differential equations to the ordinary differential equations. The transformed equations are then solved by applying shooting technique, shootlib in Maple software. The numerical solutions for the governing equations indicate that the triple solutions arise when high suction is imposed for both stretching/shrinking sheet at certain ranges of the pertinent parameters. To examine the stability of the solutions, stability analyses is done by using BVP4c in Matlab software. The first solution is found to be a stable solution and physical realizable while the remaining solutions are not stable. The inclusion of three different nanoparticles shows that Copper – Casson nanofluid has the highest heat transfer rate compared to Aluminum-Casson and Graphite Oxide-Casson nanofluid.

Numerical Solution of MHD Nanofluid Over a Stretching Surface with Chemical Reaction and Viscous Dissipation

The main objective of this paper is to focus on a numerical study of chemical reaction and viscous dissipation effects on the steady state boundary layer flow of MHD nanofluid past the horizontally stretching sheet with the existence of nanoparticles. A proper similarity transformation is utilized to convert the boundary layer equations into the nonlinear and coupled ordinary differential equations. These ODEs are sorted out numerically by applying the shooting mechanism. Graphical representations are also included to explain the effect of evolving parameters against the above-mentioned distributions. Significance of different physical parameters on dimensionless velocity, temperature and concentration are elaborated through graphs and tables. For increasing values of Eckert number, the temperature profile increases whereas the chemical reaction parameter increases, the boundary layer thickness decreases.
 Chemical Engineering Research Bulletin 21(2019) 36-45

Analytical and Numerical Investigation of Second Grade Magnetohydrodynamics Flow over a Permeable Stretching Sheet

In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.

MHD slip flow and convective heat transfer due to a moving plate with effects of variable viscosity and thermal conductivity

PurposeThe steady two-dimensional laminar boundary layer flow, heat and mass transfer over a flat plate with convective surface heat flux was considered. The governing nonlinear partial differential equations were transformed into a system of nonlinear ordinary differential equations and then solved numerically by Runge–Kutta method with the most efficient shooting technique. Then, the effect of variable viscosity and variable thermal conductivity on the fluid flow with thermal radiation effects and viscous dissipation was studied. Velocity, temperature and concentration profiles respectively were plotted for various values of pertinent parameters. It was found that the momentum slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the momentum slip.Design/methodology/approachNumerical Solution is applied to find the solution of the boundary value problem.FindingsVelocity, heat transfer analysis is done with comparing earlier results for some standard cases.Originality/value100

Effects of Viscous Dissipation on Mixed Convection Boundary Layer Flow Past a Vertical Moving Plate in a Nanofluid

Adaptation from the thermal management applied in modern engine cooling system and central processing unit (CPU) in performance computer devices, present study solved the problem of steady mixed convection boundary layer flow and heat transfer on a moving vertical plate in a nanofluid with the presence of viscous dissipation and constant wall temperature. The mathematical model which is in non-linear partial differential equations is solved numerically by similarity transformation approach with the Keller-box method. The characteristics and effects of pertinent parameters considered which are Prandtl number, Lewis number, Eckert number, Brownian motion parameter, thermophoresis parameter, mixed convection parameter, concentration mixed convection parameter and plate velocity parameter are analyzed and discussed. In conclusion, there exist dual solutions in opposing flow for moving parameter range 0.18 0.48.    Further, the increase of mixed convection parameter in assisting flow results to the increase in the Nusselt number and skin friction coefficient.

Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

Mixed Convection Flow Of Viscoelastic Nanofluid Past A Horizontal Circular Cylinder In Presence Of Heat Generation

The steady two-dimensional mixed convection boundary layer flow of viscoelastic nanofluid past a horizontal circular cylinder with convective boundary condition in presence of heat generation has been studied numerically. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as a nanoparticle with the Prandtl number Pr = 6.2. The Tiwari and Das model has been considered in this study. The governing partial differential equations are reduced to a system of ordinary differential equations by introducing similarity transformations. The nonlinear similarity equations are solved numerically by applying the Keller-box method. The numerical results are presented graphically for different values of the parameters including the heat generation parameter, nanoparticles volume fraction, and Biot number. A systematic study is discussed to analyze the effect of these parameters on the velocity and temperature profiles as well as the skin friction and heat transfer coefficient. The thermal boundary layer shows the changes in variation behavior when the nanoparticles volume fraction, heat generation and Biot number are increased. Heat transfer coefficient is increasing function of heat generation parameter. Nanoparticles volume fraction on heat transfer coefficient have opposite effect when compared with heat generation parameter.

Mass Transfer Characteristics of MHD Casson Fluid Flow past Stretching/Shrinking Sheet

The paper analyzes steady laminar boundary layer flow of low-conductivity Casson fluid over a stretching/shrinking sheet subjected to a transverse magnetic field in the presence of suction/injection when the fluid far away from the surface is at rest. This flow problem is mathematically modelled and the non-Newtonian fluid under consideration obeys the rheological equation of state by the Casson model. A similarity transformation converts the governing nonlinear partial differential equations into nonlinear ordinary differential equations, which are solved analytically. Using the stream function and velocity components, these results are analyzed in dependence on the Casson fluid parameters, Chandrasekhar number, and mass transpiration parameters.

Similarity Solution and Numerical Analysis of the Steady Nanofluid Layer Induced by Gyrotactic Microorganisms Containing Wall Temperature Variations

The problem of free convective steady boundary layer flows over a solid horizontal flat plate nested in a porous medium filled with a nanofluid containing gyrotactic microorganisms is considered. The exponent of the temperature, the nanoparticle volume fraction and the density of motile microorganisms are introduced to make the quantities dimensionless. The impacts of the considered exponent and bioconvection parameters on the dimensionless temperature, velocity, nanoparticle concentration and density of motile microorganisms along with Nusselt, Sherwood and motile microorganism numbers are tabulated and shown graphically. For a regular fluid and also for the isothermal case, the results are compared with the existing data and excellent compatibility is found.

Impact of slip effects on unsteady Sisko nanoliquid heat and mass transfer characteristics over stretching sheet filled with gold nanoparticles

AbstractWe have presented a comparison between steady and unsteady magnetohydrodynamic boundary layer flow, heat transfer features of Au–kerosene‐based nanoliquid over a stretching surface by taking variable viscosity, variable thermal conductivity, and slip boundary conditions in this study. Appropriate similarity translations are engaged to reduce nonlinear partial differential equations into a set of ordinary differential equations. These equations along with boundary conditions are elucidated numerically by finite‐element technique. Influence of several pertinent parameters on velocity, temperature, and concentration scatterings, in addition to that, the values of Nusselt number, skin‐friction coefficient, and Sherwood number are scrutinized in detail and the outcomes are exhibited through plots and tables. It is perceived that the values of Nusselt number, skin‐friction coefficient, and Sherwood number intensify in both steady–unsteady cases as the values of volume fraction parameter rise.