Incompressible Laminar Boundary Layer Research Articles

Embedded large eddy simulation of boundary layer transition behind a micro-ramp

Boundary layer transition induced by surface roughness elements plays an important role in aerodynamic and aero-thermodynamic design of subsonic/supersonic/hypersonic vehicles. However, the effect of three-dimensional isolated roughness element in the process of promoting/suppressing boundary layer transition is far from being fully understood, particularly in the incompressible laminar flow. In the present study, the laminar-to-turbulent transition induced by a three-dimensional isolated micro-ramp element immersed in an incompressible laminar boundary layer is investigated numerically. The embedded large eddy simulation (ELES) combining the intermittency transition model and the wall-modeled large eddy simulation (WMLES) S − Ω model is employed for the first time. Numerical results on the time-averaged/instantaneous flow field and the statistical flow fluctuations are analysed and validated thoroughly by the existing experimental measurements. It is found that the interaction of the secondary and the tertiary streamwise vortices causes a high level of wall shear and an inflectional velocity distribution in the near-wall region. An additional eddy system that develops nonlinearly from the unstable inflectional flow may trigger the boundary layer transition. The present study validates that the ELES combined with the WMLES S − Ω model is an efficient simulation tool for industrial wall-bounded flows allowing effective compromise between flexibility, cost, and accuracy.

Simulating the propagation of boundary-layer disturbances by solving boundary-value and initial-value problems

Abstract The article deals with the downstream propagation of small–amplitude disturbances of viscous incompressible laminar boundary layers, using the linearized equations for disturbance amplitudes. Two different methods are proposed. The first one solves a two-dimensional boundary-value problem, using a buffer-domain technique to mimic the outflow boundary condition. The second one solves a streamwise initial-value problem, using a spectral parabolization at each integration step. Both methods show good performance in simulating the propagation of the Tollmien–Schlichting waves and the Görtler vortices and can be applied to compute the spatial optimal disturbances.

The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method

The current study investigates the laminar flow of boundary layer using a porous surface shrinking exponentially under varying magnetic field, suction/injection, radiation on velocity and thermal slips. The dimensionless nonlinear differential equations were also defined in terms of governing partial differential equations and applying similarity transformations. The equations were analytically solved following the homotopy analysis method (HAM). An excellent agreement is observed in comparison with theavailable literature in special case (Skin friction coefficient). In the current study, an analytic solution is obtained for the laminar incompressible MHD boundary layer viscous fluid flow problem on the exponentially electrically conducting porous shrinking surface. The impact of different parameters like injection/suction, Prandtl number, radiation, velocity slip, thermal slip, as well as the magnetic field on different velocity and temperature values have been presented graphically, and have been discussed in detail. The f″(0) skin friction rises with higher suction parameter s(>0) values, magnetic parameter M but it decreases when the slip parameter value is increased. Whereas heat transfer rate −θ′(0) rises with an increasing M, s and λ..

MHD flow and heat transfer of micropolar nanofluid on a linearly stretching/shrinking porous surface

In this paper, there is considered incompressible steady two-dimensional laminar MHD boundary layer flow, heat and mass transfer characteristics of micropolar nanofluid across a linearly stretching/shrinking porous surface. The effects of the magnetic, thermal slip, mass slip and heat source sink parameters are also considered. By applyingn appropriate similarity variables, the system of governing partial differential equations associated to micropolar nanofluid flow is transformed into a system of non - linear ordinary differential equations. The resulting equations are numerically solved in the Maple software by using shooting technique. The impact of the different applied parameters on skin friction, couple stress, Nusselt and the Sherwood numbers along the related profiles are determined for both stretching and shrinking cases of the surfaces. It was observed that with an increase in suction and magnetic parameters, the fluid velocity decreased. An increment in the thermal slip, the fluid temperature decreased and nanoparticles concentration decreases as the mass slip parameter is enhanced. An increase in concentration decreases but temperature increases. While, concentration and temperature both increase due to increase in thermophoresis parameter, and concentration also increases by increase in rate of chemical reaction. Thus, suction at the boundary and magnetic parameter acted as flow controlling parameter. It is believed that this type of investigation is very much helpful for the manufacturing of complex fluids and also for cleaning oil from surfaces.

Unsteady Magnetohydrodynamic (MHD) Cu–Al2O3/Water Hybrid Nanofluid Flow and Heat Transfer from an Exponentially Accelerated Plate

The present study intends to explore heat transfer characteristics of the unsteady natural convective flow of Cu–Al2O3/water hybrid nanofluid due to exponentially accelerated vertical plate. 2D Laminar viscous incompressible boundary layer fluid flow is considered in the presence of MHD and accelerating parameter. The governing partial differential equations with appropriate boundary conditions are solved using the Crank-Nicolson numerical technique. Plots for skin friction coefficient, velocity, temperature, Nusselt number concerning Magnetic parameter (M), Accelerating parameter (a), Grashof number (Gr), Volume fraction (Φ2), and time are disclosed. The study imparted that Cu–Al2O3 hybrid nanoparticles with water as base fluid facilitate a higher heat transfer rate and soaring Nusselt number compared to nanofluid Cu/water. Furthermore, we found an elevated skin friction coefficient in nanofluid Cu/water than in hybrid nanofluid Cu–Al2O3/water in all non-dimensional parameters.

Numerical study of gyrotactic bioconvection in stretching flow of a variable viscosity nanofluid with buoyancy and power-law wall effects

Modern aerospace is increasingly embracing bio-inspired designs. Intelligent coatings are being developed which amalgamate nanotechnological and also biological features including, bio-rheology, anti-corrosion/fouling features and strategic embedded of micro-organisms which respond to specific stimuli including light, heat, chemical concentration, electrical or magnetic fields. This article develops a mathematical model for steady, 2-D, incompressible laminar boundary layer flow and gyrotactic bioconvection in a variable viscosity nanofluid along a convectively heated stretched plate. The model is driven by the investigation of innovative bio-inspired nanocoatings. The behavior of nanoparticles and microorganisms, which is non-isothermal and non-isosolutal, has been taken into account. The Buongiorno two-component nanoscale model is employed which permits simultaneous mass and heat (nano-particle) transfer. A boundary layer framework is deployed. The transformed boundary value problem is solved numerically by using finite difference method with central differencing, tridiagonal matrix manipulation and Iterative algebraic solution procedure. Validation with former studies for selected special cases of the generalized model is conducted. Further validation of the general model solutions is achieved with a generalized differential quadrature (GDQ) algorithm. The major inspections of the current work are the flow is accelerated with greater viscosity parameter and bioconvection Rayleigh number. Future investigations will explore more complex non-Newtonian constitutive models.

Characteristics of boundary-layer transition driven by diverse streamwise vortices

The present direct numerical simulations investigate the dynamics of diverse streamwise vortices in a zero-pressure gradient incompressible laminar boundary layer and the onset of turbulence. Due to the critical role of streamwise vortices in bypass transitions, we compare the transition mechanisms induced by a single vortex and vortex pairs. We initially examine the evolution of a single vortex by employing streamwise vortex profiles at two wall-normal locations. The single streamwise vortex will prompt a more rapid eruption from the bottom part of the boundary layer if moved nearer to the wall, as observed in the experimental study by Manu et al. [“Evolution of isolated streamwise vortices in the late stages of boundary-layer transition,” Exp. Fluids 48, 431–440 (2010)]. In the late stages of boundary-layer transition, the vortex–wall interaction emerges to be particularly pronounced. The second set of simulations triggers flow transition by imposing counter-rotating vortex pairs at the inlet of the computational domain. Streamwise vortex pairs with net upward flows cause intense, sporadic ejections of near-wall fluids into the boundary-layer edge, providing the first signs of inflectional instability in all considered cases. Instead of vortex–wall interactions, flow structures created by vortex pairs penetrate deeply into the inviscid region, resulting in substantial unsteady viscous-inviscid interactions. When counter-rotating vortices accompany to form a net downward flow, the initial formation of each vortex is analogous to that of a single vortex. The instability frequency and wavelength of the transitional flow produced by a vortex introduced in the middle of the boundary layer are lower than those imposed near the wall. The transitional flow generated by the vortex pair exhibits longer-wavelength instability than the single vortex cases.

Analytical and numerical solutions of heat and mass transfer of boundary layer flow in the presence of a transverse magnetic field

AbstractThe present investigation aims to study the effect of a transverse magnetic field with the presence of an adverse pressure gradient on the two‐dimensional laminar incompressible boundary layer flow over a flat plate. Using appropriated similarity transformations, the partial differential equations governing the studied problems are transformed into the ordinary nonlinear differential equations. Thereafter, these equations are solved numerically and analytically using the fourth‐order Runge‐Kutta method featuring shooting technique and the Adomian decomposition method, respectively. Obtained results reveal an excellent agreement between analytical and numerical data for temperature and concentration profiles.

A novel hybridity model for TiO2-CuO/water hybrid nanofluid flow over a static/moving wedge or corner

In this study, we are going to investigate semi-analytically the steady laminar incompressible two-dimensional boundary layer flow of a TiO2-CuO/water hybrid nanofluid over a static/moving wedge or corner that is called Falkner-Skan problem. A novel mass-based approach to one-phase hybrid nanofluid model that suggests both first and second nanoparticles as well as base fluid masses as the vital inputs to obtain the effective thermophysical properties of our hybrid nanofluid, has been presented. Other governing parameters are moving wedge/corner parameter (λ), Falkner-Skan power law parameter (m), shape factor parameter (n) and Prandtl number (Pr). The governing partial differential equations become dimensionless with help of similarity transformation method, so that we can solve them numerically using bvp4c built-in function by MATLAB. It is worthwhile to notice that, validation results exhibit an excellent agreement with already existing reports. Besides, it is shown that both hydrodynamic and thermal boundary layer thicknesses decrease with the second nanoparticle mass as well as Falkner-Skan power law parameter. Further, we understand our hybrid nanofluid has better thermal performance relative to its mono-nanofluid and base fluid, respectively. Moreover, a comparison between various values of nanoparticle shape factor and their effect on local heat transfer rate is presented. It is proven that the platelet shape of both particles (n1 = n2 = 5.7) leads to higher local Nusselt number in comparison with other shapes including sphere, brick and cylinder. Consequently, this algorithm can be applied to analyze the thermal performance of hybrid nanofluids in other different researches.

Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

AbstractThe present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.

Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization

Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems, porous bearings, porous layer insulation, biomechanics, geomechanics etc. Motivated by such applications, in this article a numerical investigation of entropy generation effects on the heat and momentum transfer in unsteady laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly heated vertical cylinder embedded in a porous medium is presented. Darcy’s law is employed to simulate bulk drag effects at low Reynolds number for an isotropic, homogenous porous medium. Heat line visualization is also included. The mathematical model is derived and normalized using appropriate transformation variables. The resulting time-dependent non-linear coupled partial differential conservation equations with associated boundary conditions are solved with an efficient unconditionally stable implicit finite difference Crank Nicolson scheme. The time histories of average values of momentum and heat transport coefficients, entropy generation and Bejan number, as well as the steady-state flow variables are computed for several values of non-dimensional parameters arising in the flow equations. The results indicate that entropy generation parameter and Bejan number are both elevated with increasing values of Casson fluid parameter, Darcy number, group parameter and Grashof number. To analyze the heat transfer process in a two-dimensional domain, plotting heat lines provides an excellent approach in addition to streamlines and isotherms. The dimensionless heat function values are shown to correlate closely with the overall rate of heat transfer. Bejan’s heat flow visualization implies that the heat function contours are compact in the neighbourhood of the leading edge of the boundary layer on the hot cylindrical wall. It is observed that as the Darcy number increases, the deviations of heat lines from the hot wall are reduced. Furthermore the deviations of flow variables from the hot wall for a Casson fluid are significant compared with those computed for a Newtonian fluid and this has important implications in industrial thermal materials processing operations.

An innovative mass-based model of aqueous zinc oxide–gold hybrid nanofluid for von Kármán’s swirling flow

In this research, we have investigated analytically the incompressible laminar steady three-dimensional boundary layer flow of an aqueous ZnO–Au hybrid nanofluid over an impermeable rotating disk with the constant radial stretching rate. The novel attitude to single-phase hybrid nanofluid model corresponds to considering nanoparticles mass as well as base fluid mass to computing the solid equivalent volume fraction, the solid equivalent density and also the solid equivalent specific heat at constant pressure. Here, other governing parameters are stretching strength parameter \((C)\), shape factor parameter \((n)\) and Prandtl number \((Pr).\) The basic nonlinear governing PDEs are transformed into a set of dimensionless nonlinear ODEs using well-known von Karman similarity transformations, which are then solved numerically using a finite difference code from MATLAB. It is worth mentioning that validation results demonstrate a good agreement with previously published reports. Results indicate that with the increase in stretching strength parameter and second nanoparticle’s mass, both dimensionless temperature distribution and thermal boundary layer thickness decrease. Moreover, when 15 g of both first and second nanoparticles is dispersed into 100 g pure water (equivalent with \(\phi = 3.33\)% as the total nanoparticles volume fraction), the heat transfer rate increases more than 40% in comparison with the regular fluid. Besides, the results demonstrate that the heat transfer rate enhances about 2.18% with nanoparticles of platelet shape \((n_{1} = n_{2} = 5.7)\) instead of spherical ones. Finally, the present new algorithm sufficiently can be used for analysis flow and heat transfer characteristics of hybrid nanofluids in various problems with great confidence.

Melting Heat Transfer and MHD Boundary Layer Flow of Eyring-Powell Nanofluid Over a Nonlinear Stretching Sheet with Slip

The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.

Theoretical investigation of entropy generation effects in nanofluid flow over an inclined stretching cylinder

Laminar incompressible boundary layer flow and heat transfer of nanofluid over an inclined stretching cylinder is considered and the entropy effects are theoretically examined during the phenomena. The problem is mathematically modelled and nonlinear partial differential equations are attained. With the help of suitable similarity transformations, these partial differential equations are transformed into nonlinear ordinary differential equations which are numerically solved by utilising shooting technique with fourth-fifth order Runge-Kutta method. The results obtained are compared with the previously existing literature by considering certain limiting cases. The influence of physical parameters on flow, heat transfer and concentration of nanoparticles are analysed qualitatively with the use of graphs and tables. Furthermore, the impact of various physical parameters on local entropy generation number and averaged entropy generation number are also presented through graphs. A detailed comprehensive study has been carried out of the problem.

Theoretical investigation of entropy generation effects in nanofluid flow over an inclined stretching cylinder

Laminar incompressible boundary layer flow and heat transfer of nanofluid over an inclined stretching cylinder is considered and the entropy effects are theoretically examined during the phenomena. The problem is mathematically modelled and nonlinear partial differential equations are attained. With the help of suitable similarity transformations, these partial differential equations are transformed into nonlinear ordinary differential equations which are numerically solved by utilising shooting technique with fourth-fifth order Runge-Kutta method. The results obtained are compared with the previously existing literature by considering certain limiting cases. The influence of physical parameters on flow, heat transfer and concentration of nanoparticles are analysed qualitatively with the use of graphs and tables. Furthermore, the impact of various physical parameters on local entropy generation number and averaged entropy generation number are also presented through graphs. A detailed comprehensive study has been carried out of the problem.

Hampering Görtler vortices via optimal control in the framework of nonlinear boundary region equations

The control of streamwise vortices in high Reynolds number boundary layer flows often aims at reducing the vortex energy as a means of mitigating the growth of secondary instabilities, which eventually delays the transition from laminar to turbulent flow. In this paper, we aim at utilizing such an energy reduction strategy using optimal control theory to limit the growth of Görtler vortices developing in an incompressible laminar boundary layer flow over a concave wall, and excited by a row of roughness elements with spanwise separation of the same order of magnitude as the boundary layer thickness. Commensurate with control theory formalism, we transform a constrained optimization problem into an unconstrained one by applying the method of Lagrange multipliers. A high Reynolds number asymptotic framework is utilized, wherein the Navier–Stokes equations are reduced to the boundary region equations, in which wall deformations enter the problem through an appropriate Prandtl transformation. In the optimal control strategy, the wall displacement or the wall transpiration velocity serves as the control variable, while the cost functional is defined in terms of the wall shear stress. Our numerical results indicate, among other things, that the optimal control algorithm is very effective in reducing the amplitude of the Görtler vortices, especially for the control based on wall displacement.

Unsteady mixed convection over an exponentially decreasing external flow velocity

A very recent study of Patil et al. (2017) on the effects of steady mixed convection flow with an exponentially decreasing free stream velocity motivates this research investigation. The present analysis reveals the mixed convection impact over an exponentially decreasing free stream velocity in an unsteady incompressible laminar boundary layer flow involving the effects of suction or blowing and heat generation or absorption. By utilizing the appropriate non-similar transformations, the complex dimensional governing boundary layer equations are simplified into dimensionless equations. In order to prevail the mathematical convolutions in attaining the non-similar solutions at the leading edge of the streamwise coordinate as well as non-similarity variable ξ, the coalition of implicit finite difference scheme and the Quasi-linearization technique is used with the suitable step sizes along the streamwise and time directions. The effects of various dimensionless physical parameters over the momentum and thermal fields are examined. The range of the parameters studied in this analysis are taken as α(-0.5⩽α⩽1.0), ξ(0⩽ξ⩽1), τ(0⩽τ⩽1), ε(0.000001⩽ε⩽0.1), Ri(-3⩽Ri⩽10), Re(10⩽Re⩽250), A(-1⩽A⩽1) and Q(-1⩽Q⩽1). Further, the present numerical investigation is focussed towards unsteady flow and heat transfer characteristics.

Influence of mixed convection in an exponentially decreasing external flow velocity

This article explores the influence of mixed convection in a steady incompressible laminar boundary layer flow for an exponentially decreasing free stream velocity in presence of surface mass transfer and heat source or sink. The nonlinear partial differential equations governing the flow and thermal fields are expressed in dimensionless form with the help of suitable non-similar transformations. The mathematical complexities in obtaining non-similar solutions at the leading edge of the streamwise coordinate as well as non-similarity variable ξ have overcome by using the implicit finite difference scheme in conjunction with Quasi-linearization technique by choosing an appropriate finer step sizes along the streamwise direction. The effects of various dimensionless physical parameters on velocity and thermal fields are analysed.

Group analysis and numerical solution of slip flow of a nanofluid in porous media with heat transfer

The steady laminar viscous incompressible free convective boundary layer flow of a nanofluid past a chemically reacting horizontal plate situated in porous medium taking into account heat generation/absorption and the thermal slip boundary condition is studied numerically. Similarity transformations are generated by Lie group analysis. Using the similarity transformations, the transport equations are reduced to a branch of coupled similarity equations which are solved by Runge-Kutta-Fehlberg fourth-fifth order numerical method. Our analysis reveals that true similarity solution will exist provided thermal slip factor is inversely proportional to two third power of the axial distance. Effect of the governing parameters on the dimensionless velocity, temperature, nanoparticle volume fraction has been presented. Excellent agreement between our results and published is obtained. A sample of numerical results for the reduced Nusselt number and the Sherwood number is provided in a table for various values of the parameters. The reduced Nusselt number is increased with the Lewis number and reaction parameter whilst it is decreased with the order of chemical reaction, thermal slip and generation parameters. Further, the reduced Sherwood number is enhanced with the Lewis number, generation and reaction parameters whilst it is suppressed with thermal slip and order of chemical reaction parameters.

Homotopy Analysis of the Radiation Effect on MHD Flow with Heat and Mass Transfer due to a Point Sink

An analytical solution of the magnetohydrodynamic, steady, and incompressible laminar boundary layer flow in the presence of heat and mass transfer as well as magnetic field on a cone due to a point sink by using the homotopy analysis method (HAM) has been studied under the radiative fluid properties. The HAM produces an analytical solution of the governing self-similar nonlinear two-point boundary layer equations. The effects of the suction/injection, magnetic, and radiation parameters over the obtained solution have been discussed. The effects of Prandtl number on temperature and Schmidt number on concentration profiles have also been studied. It has been observed that the temperature profiles exhibit an increasing trend with radiation in case of injection while an opposite trend is observed in case of suction. The results obtained in the present study have also been compared numerically as well as graphically with the corresponding results obtained by using other methods. An excellent agreement has been found between them. The analytical solution obtained by the HAM is very near to the exact solution for a properly selected initial guess, auxiliary, and convergence control parameters and for higher orders of deformations.