Natural Convection Boundary Layer Research Articles

Simulation of Natural Convective Boundary Layer Flow of a Nanofluid Past a Convectively Heated Inclined Plate in the Presence of Magnetic Field

This paper deals with the numerical simulation of transient magnetohydrodynamics natural convective boundary layer flow of a nanofluid over an inclined plate. In the modeling of nanofluids, dynamic effects including the Brownian motion and thermophoresis are taken into account. Numerical solutions have been computed via the Galerkin-finite element method. The effects of angle of inclination, buoyancy-ratio parameter, Brownian motion, thermophoresis and magnetic field are taken into account and controlled by non-dimensional parameters. To compute the rate of convergence and error of the computed numerical solution, the double mesh principle is used. Similarity solutions are calculated and presented graphically for non-dimensional velocity, temperature, local rate of heat and mass transfer with pertinent parameters. The modified Nusselt number decreases with increasing inclination angle, buoyancy-ratio parameter, Brownian motion and thermophoresis parameter, whereas it increases with increasing Prandtl number. Validation of the results is achieved with earlier results for forced convective flow and non-magnetic studies. Such problems have several applications in engineering and petroleum industries such as electroplating, chemical processing of heavy metals and solar water heaters. External magnetic fields play an important role in electrical power generation, inclination/acceleration sensors, fine-tuning of the final materials to industrial specification because of their controlling behaviour on the flow characteristics of nanofluids.

Impact of surface texture on natural convection boundary layer of nanofluid

Heat transfer characteristics are investigated in natural convection flow of water-based nanofluid near a vertical rough wall. The analysis considers five different nanoparticles: silver, copper, alumina, magnetite, and silica. The concentration has been limited between 0-20% for all types of nanoparticle. The governing equations are modeled using the Boussinesq approximation and Tiwari and Das models are utilized to represent the nanofluid. The analysis examines the effects of nanoparticle volume fraction, type of nanofluid, and the wavy surface geometry parameter on the skin friction and Nusselt number. It is observed that for a given nanofluid the skin friction and Nusselt number can be maximized via an appropriate tuning of the wavy surface geometry parameter along with the selection of suitable nanoparticle. Particular to this study cooper is observed to be more productive towards the flow and heat transfer enhancement. In total the metallic oxides are found to be less beneficial as compared to the pure metals.

Anisotropic slip magneto-bioconvection flow from a rotating cone to a nanofluid with Stefan blowing effects

A mathematical model for two dimensional steady laminar natural convective anisotropic slip boundary layer flows from a rotating vertical cone embedded in ethylene glycol bionanofluid is presented. The influence of Stefan blowing is also taken into account. Four different non-particles namely Copper (Cu), Alumina (Al2O3), Copper Oxide (Cuo), Titanium Oxide (TiO2) are explored. Suitable similarity transformations are used to convert the governing equations into non-linear ordinary differential equations. These are then solved numerically, with appropriate boundary conditions, utilizing an implicit finite difference method (the BVP5C code in MATLAB). During computation Sc, Lb, Le and Lb are presented as unity, whilst Pr is taken as 151. The effects of the governing parameters on the dimensionless velocities, temperature, nanoparticle volume fraction, density of motile microorganisms as well as on the local skin friction, local Nusselt, Sherwood number and motile micro-organism number density are thoroughly examined via tables and graphs. It is found that the skin friction factor increases with tangential slip, magnetic field and Schmidt number whilst it decreases with blowing parameter and spin parameters. It is further observed that both the friction and heat transfer rates are highest for copper nanoparticles and lowest for TiO2nanoparticles. Validation of the BVP5C numerical solutions with published results for several special cases of the general model is included. The study is relevant to electro-conductive bio-nano-materials processing.

MHD natural convection of ferrofluid from a fixed vertical plate with aligned, transverse magnetic field and convective boundary condition

The present study analyzed the influence of aligned and transverse magnetic field on two dimensional natural convection boundary layer flow of a ferrofluid over a semi-infinte fixed vertical plate in the presence of convective boundary condition. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface. Two different base fluids (water and kerosene) containing magnetite (Fe3O4) as ferroparticle are considered. The governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations using similarity variables. The resultant system of equations is then solved numerically by using Keller-Box method. Numerical results for the skin friction coefficient and local Nusselt number were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effect of the inclined angle, magnetic field parameter, volume fraction, Grashof number and Biot number on the flow field were discussed. It is found that the heat transfer rate at the plate surface with Fe3O4- kerosene ferrofluid is higher than Fe3O4- water.

MHD natural convective flow of nanofluids past stationary and moving inclined porous plate considering temperature and concentration gradients with suction

PurposeThis paper aims to focus on the mathematical modeling of magnetohydrodynamic natural convective boundary layer flow of nanofluids past a stationary and moving inclined porous plate considering temperature and concentration gradients with suction effects.Design/methodology/approachThe transformed non-dimensional and coupled governing partial differential equations are solved numerically using the finite element method.FindingsThe obtained numerical results for physical governing parameters on the velocity, temperature and concentration distributions are exemplified graphically and presented quantitatively. The boundary layer thickness increased with the increasing values of Soret, Dufour and Grashof numbers, while the thickness of boundary layer decreased with increasing values of suction for both stationary and moving plate cases. The primary and secondary velocity profiles are decreasing with an angle of inclination for moving plate and inclination has no significant effect for the stationary plate. An increase of the Soret number and Dufour number tend to increase the heat and mass transfer, while an increase of suction reduces the heat and mass transfer.Originality/valueThe problem is an important contribution to the field of nanofluid science and technology and is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids. This study is relatively original in nanofluids.

The K-type and H-type transitions of natural convection boundary layers

The K-type and H-type transitions of a natural convection boundary layer of a fluid of Prandtl number 7 adjacent to an isothermally heated vertical surface are investigated by means of three-dimensional direct numerical simulation (DNS). These two types of transitions refer to different flow features at the transitional stage from laminar to turbulence caused by two different types of perturbations. To excite the K-type transition, superimposed Tollmien–Schlichting (TS) and oblique waves of the same frequency are introduced into the boundary layer. It is found that a three-layer longitudinal vortex structure is present in the boundary layer undergoing the K-type transition. The typical aligned $\wedge$-shaped vortices characterizing the K-type transition are observed for the first time in pure natural convection boundary layers. For exciting the H-type transition, superimposed TS and oblique waves of different frequencies, with the frequency of the oblique waves being half of the frequency of the TS waves, are introduced into the boundary layer. Unlike the three-layer longitudinal vortex structure observed in the K-type transition, a double-layer longitudinal vortex structure is observed in the boundary layer undergoing the H-type transition. The successively staggered $\wedge$-shaped vortices characterizing the H-type transition are also observed in the downstream boundary layer. The staggered pattern of $\wedge$-shaped vortices is considered to be caused by temporal modulation of the TS and oblique waves. Interestingly the flow structures of both the K-type and H-type transitions observed in the natural convection boundary layer are qualitatively similar to those observed in Blasius boundary layers. However, an analysis of turbulence energy production suggests that the turbulence energy production by buoyancy rather than Reynolds stresses dominates the K-type and H-type transitions. In contrast, the turbulence energy production by Reynolds stresses is the only factor contributing to the transition in Blasius boundary layers.

Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.

THERMAL RADIATION EFFECT ON MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OVER A PLATE WITH SUCTION (INJECTION) AND VARIABLE VISCOSITY

The effect of thermal radiation on steady natural convection boundary layer flow over a plate with variable viscosity and magnetic field has been studied in this paper. The effect of suction and injection is also considered in the investigation. The system of partial differential equations governing the nonsimilar flow has been solved numerically using implicit finite difference scheme along with a quasilinearization technique. The thermal radiation has significant effect on heat transfer coefficient and thermal transport in presence of viscosity variation parameter and magnetic field in case of suction and injection.

CFD solutions for magnetohydrodynamic natural convection over horizontal and vertical surfaces

This paper investigates the effects of a magnetic field on the natural convective boundary layer flow of an electrically conducting fluid adjacent to horizontal as well as vertical surfaces. This has allowed us to establish overall similarities and several subtle differences between the two cases. Previously published studies concentrated on obtaining self-similar solutions at the cost of assuming very restrictive variation of the magnetic field along the surface. In the present work, a numerical model and an in-house computer program have been developed to solve directly the non-linear boundary layer equations which can accommodate any arbitrary variation of the magnetic field. Special emphasis is given to the case of uniform magnetic field which perhaps represents the most practical case and which cannot be solved by the similarity theory. Computations show that the Nusselt number and the skin-friction coefficient decrease as the magnetic field increases. It is shown that the detailed characteristics of the velocity profiles and the values of Nusselt number and skin-friction coefficient for the case of a magnetic field which admits similarity are significantly different from those when a uniform magnetic field is applied, thus showing the importance of the present model.

Double Diffusive Natural Convection Flow Over a Wavy Surface Situated in a Non-absorbing Medium

This analysis discuss the influence of heat and mass transfer on natural convection boundary layer flow of thermally radiating wavy surface. To make the surface radiating; Stephan-Boltzmann law is used in the boundary conditions. Therefore, convection and thermal radiation interact simultaneously with the aid of Stephan-Boltzmann law and ultimately producing highly nonlinear boundary conditions. The governing coupled boundary layer equations are switched into suitable form by using primitive variable formulations over which two-point iterative finite difference scheme is applied to obtain the unknown quantities. Physical quantities like wall shear stress, rate of heat transfer and rate of mass transfer are expressed graphically by varying significant emerging parameters: surface radiation (R), radiative length parameter (ξ), buoyancy ratio parameter (N) and amplitude of the wavy surface (α). Comparison of numerical results is also done in tabular form with the earlier study of Siddiqa et al. (2013) in order to validate the results.

Numerical Study of Nonlinear Heat Transfer from a Wavy Surface to a High Permeability Medium with Pseudo-Spectral and Smoothed Particle Methods

Motivated by petro-chemical geological systems, we consider the natural convection boundary layer flow from a vertical isothermal wavy surface adjacent to a saturated non-Darcian high permeability porous medium. High permeability is considered to represent geologically sparsely packed porous media. Both Darcian drag and Forchheimer inertial drag terms are included in the velocity boundary layer equation. A high permeability medium is considered. We employ a sinusoidal relation for the wavy surface. Using a set of transformations, the momentum and heat conservation equations are converted from an (x, y) coordinate system to an ( $$x, \eta )$$ dimensionless system. The two-point boundary value problem is then solved numerically with a pseudo-spectral method based on combining the Bellman–Kalaba quasi linearization method with the Chebyschev spectral collocation technique (SQLM). The SQLM computations are demonstrated to achieve excellent correlation with smoothed particle hydrodynamic (SPH) Lagrangian solutions. We study the effect of Darcy number (Da), Forchheimer number (Fs), amplitude wavelength (A) and Prandtl number (Pr) on the velocity and temperature distributions in the regime. Local Nusselt number is also computed for selected cases. The study finds important applications in petroleum engineering and also energy systems exploiting porous media and undulating (wavy) surface geometry. The SQLM algorithm is shown to be exceptionally robust and achieves fast convergence and excellent accuracy in nonlinear heat transfer simulations.

Higher-order and length-scale statistics of velocity and temperature fluctuations in turbulent boundary layer along a heated vertical flat plate

Time-developing direct numerical simulation (DNS) was performed to clarify the higher-order turbulent behaviors in the thermally-driven boundary layers both in air and water along a heated vertical flat plate. The predicted statistics of the heat transfer rates and the higher-order turbulent behaviors such as skewness factors, flatness factors and spatial correlation coefficients of the velocity and temperature fluctuations in the natural-convection boundary layer correspond well with those obtained from experiments for space-developing flows. The numerical results reveal that the turbulent structures of the buoyancy-driven boundary layers are mainly controlled by the fluid motions in the outer region of the boundary layer, and these large-scale structures are strongly connected with the generation of turbulence in the thermally-driven boundary layers, in accordance with the actual observations for space-developing flows. Moreover, to specify the turbulence structures of the boundary layers, the cross-correlation coefficients and the characteristic length scales are examined for the velocity and thermal fields. Consequently, it is found that with a slight increase in freestream velocity, the cross-correlation coefficient for the Reynolds shear stress and turbulent heat flux increases for opposing flow and decreases for aiding flow, and the integral scales for the velocity and temperature fields become larger for opposing flow and smaller for aiding flow compared with those for the pure natural-convection boundary layer.

Heat and mass transfer effects on natural convection flow along a horizontal triangular wavy surface

An analysis is carried out to thoroughly understand the characteristics of heat and mass transfer for the natural convection boundary layer flow along a triangular horizontal wavy surface. Combine buoyancy driven boundary layer equations for the flow are switched into convenient form via co-ordinate transformations. Full non-linear equations are integrated numerically for Pr = 0.051. Interesting results for the uneven surface are found which are expressed in the form of wall shear stress, rate of heat transfer and rate of mass transfer. Solutions are also visualized via streamlines, isotherms, and isolines for concentration. Computational results certify that, shear stress, temperature gradient and concentration gradient enhances as soon as the amplitude of the wavy surface, a, increases, but complex geometry do not allow to carry simulations for a > 1.5. This factor probably ensures that sinusoidal waveform is better than triangular waveform. <br><br><font color="red"><b> This article has been corrected. Link to the correction <u><a href="http://dx.doi.org/10.2298/TSCI170525126E">10.2298/TSCI170525126E</a><u></b></font>

MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OF NANOFLUID OVER A VERTICAL CONE WITH CHEMICAL REACTION AND SUCTION/INJECTION

In this article we have presented magnetohydrodynamic (MHD) natural convection boundary layer heat and mass transfer flow over a vertical cone embedded in porous medium filled with nanofluid under the enhanced boundary conditions in the presence of thermal radiation, chemical reaction, and suction/injection. The two slip effects, Brownian motion and thermophoresis, are considered in this problem. The governing nonlinear partial differential equations which represent the momentum, energy, and diffusion are transformed into ordinary differential equations with the help of suitable similarity transformations. The transformed conservation equations together with boundary conditions are then solved numerically by using a versatile, extensively validated, variational finite element method. The influences of key parameters such as magnetic field (M), buoyancy ratio parameter (Nr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), thermal radiation (R), Lewis number (Le), suction (V0 > 0), or injection (V0 < 0) parameter and chemical reaction parameter (Cr) on velocity, temperature, and concentration evaluation in the boundary layer region are examined in detail. Furthermore, the effect of these parameters on the local skin-friction coefficient (Cf), local Nusselt number (Nux), and local Sherwood number (Shx) is also investigated. The results are compared with previously published work and found to be in admirable agreement.

Magnetohydrodynamics Flow of Non-Newtonian Fluid from a Vertical Permeable Cone in the Presence of Thermal Radiation and Heat Generation/Absorption

The nonlinear, steady state magnetohydrodynamics natural convection boundary layer flow, heat and mass transfer of an viscoelastic incompressible Jeffrey’s fluid from a vertical permeable cone with thermal radiation and heat generation/absorption effects is investigated in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The Rosseland diffusion algebraic approximation is utilized to simulate thermal radiation effects. The surface of the cones is maintained at a constant temperature and concentration with mass flux present. Excellent correlation of the present results with previous studies is obtained to validate the numerical code. The influence of Deborah number (De), ratio of relaxation to retardation times ( $$\lambda $$ ), radiation parameter (F), heat generation/absorption parameter ( $$\Delta $$ ), suction/injection parameter ( $$f_{w}$$ ), magnetic parameter (M) and dimensionless tangential coordinate ( $$\xi $$ ) on velocity, temperature and concentration evolution in the boundary layer regime are examined in detail. Also, the effects of these parameters on local skin friction, heat transfer rate and mass transfer rate are investigated.

Numerical investigation of a spatially developing turbulent natural convection boundary layer along a vertical heated plate

Large-eddy simulation (LES) on a spatially developing natural convection boundary layer along a vertical heated plate was conducted. The heat transfer rate, friction velocity, mean velocity and temperature, and second-order turbulent properties both in the wall-normal and the stream-wise direction showed reasonable agreement with the findings of past experiments. The spectrum of velocity and temperature fluctuation showed a -2/3-power decay slope and -2-power decay slope respectively. Quadrant analysis revealed the inclination on Q1 and Q3 in the Reynolds stress and turbulent heat flux, changing their contribution along the distance from the plate surface. Following the convention, we defined the threshold region where the stream-wise mean velocity takes local maximum, the inner layer which is closer to the plate than the threshold region, the outer layer which is farther to the plate than the threshold region. The space correlation of stream-wise velocity tilted the head toward the wall in the propagating direction in the outer layer; on the other hand, the correlated motion had little inclination in the threshold region. The time history of the second invariant of gradient tensor Q revealed that the vortex strength oscillates both in the inner and the outer layers in between the laminar and the transition region. In the turbulent region, the vortex was often dominant in the outer layer. Instantaneous three-dimensional visualization of Q revealed the existence of high-speed fluid parcels associated with arch-shape vortices. These results were considered as an intrinsic structure in the outer layer, which is symmetrical to the structure of canonical smooth/rough wall bounded layer flow in forced convection.

Non-Darcy Natural Convection Boundary Layer Flow Over a Vertical Cone in Porous Media Saturated with a Nanofluid Containing Gyrotactic Microorganisms with a Convective Boundary Condition

Non-Darcy Natural Convection Boundary Layer Flow Over a Vertical Cone in Porous Media Saturated with a Nanofluid Containing Gyrotactic Microorganisms with a Convective Boundary Condition

MHD Free Convection Flow and Heat Transfer of Ferrofluids over a Vertical Flat Plate with Aligned and Transverse Magnetic Field

Objective: This paper aims to examine the Magnetohydrodynamics (MHD) ferrofluid’s steady natural convection boundary layer flow over a vertical flat plate. Method: Two types of base fluids (kerosene and water) were selected to formulate a problem that incorporates embedded magnetite ferroparticle. The governing nonlinear partial differential equations are modified with similarity transformations to a system of nonlinear ordinary differential equations. Then the Keller Box method is employed to numerically solve transform equations. The different values of governing parameters features and the characteristics of heat transfer and flow are analysed and discussed. Results: The results of the experiment are illustrated graphically to show the effects of the aligned and transverse magnetic field parameter, the particle volume fraction parameter and free convection parameter on heat transfer, skin friction and velocity and temperature profiles. The results were then compared with the published papers, which were found to agree well. Conclusion: At the plate surface with Fe3O4-kerosene ferrofluid, the heat transfer rate was higher than in the case of Fe3O4-water. The heat transfer rate at the plate surface increased with the rise in ferroparticle volume fraction, the angle of magnetic field, local Grashof number and magnetic field parameter.

Scalings for unsteady natural convection boundary layers on a vertical plate at time-dependent temperature

In this paper, a scaling analysis using a simple three-region structure was used to develop scalings for the unsteady natural convection boundary layer (NCBL) of a homogeneous Newtonian fluid with Pr>1 adjacent to a finite vertical plate evenly heated with a time-varying sinusoidal temperature, where Pr is the Prandtl number. Three distinct sub-stages are identified in the heating stage, i.e., a start-up stage, a transitional stage, and a quasi-steady stage. After the heating stage, there is a very short cooling stage, in which a double thermal boundary layer structure is developed, which leads to a new, thinner thermal boundary layer adjacent to the plate co-existing with the original thermal boundary layer. A series of scalings are developed for the thermal and viscous boundary thicknesses, the maximum vertical velocity within the boundary layer, and the Nusselt number which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e., the Rayleigh number Ra, Pr, and the dimensionless natural frequency of the time-varying sinusoidal temperature at various flow development stages. These scalings are tested by full numerical solutions of the governing equations and are shown to, in general, provide an accurate description of the flow.

Natural convection flows along a 16-storey high-rise building

The flow caused by natural convection adjacent to a heated vertical wall (wall flow) is an important mechanism in the creation of wind flows in a city when the background wind is weak. The wall flows along a 16-storey building were measured in Guangzhou, China. Fourteen three-dimensional ultrasonic anemometers were installed on three floors to study the boundary layer structure. Continuous measurements were taken during three test periods. The Rayleigh numbers were approximately 1013, 1013 and 1014 at the height of the 5th, 10th and 14th floors, respectively. The diurnal changes in the velocity of the wall flows, the wall surface temperature and the ambient air temperature were analysed.Our new experimental data support the theory that the natural convection boundary layer has a three-layer structure, i.e. an inner viscous layer, a transition layer and an outer turbulent layer, as first proposed theoretically by Wells and Worster. The outer turbulent layer is governed by the law of plumes with a Gaussian profile. The vertical velocity changes with g′4/9x1/3 along the vertical wall, where g′ is the buoyancy force and x is the coordinate along the vertical wall. It was noted that only the building's roof was significantly cooler than the ambient air at night, due to the sky radiation effect, so no downward flow adjacent to the wall caused by the cooling plate effect was found in our field measurements.