Natural Convection Boundary Layer Research Articles

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

The non-Oberbeck–Boussinesq effects on the stability of a vertical natural convection boundary layer are investigated using the linearised disturbance equations for air flows up to a temperature difference of $\Delta T=100\,{\rm K}$ . Based on the linear stability results, the neutral curve is shown to be sensitive to the choice of reference temperature. When evaluated using the film temperature $T_f$ , a lower film Grashof number is required to trigger the linear instability for larger $\Delta T$ . The relative contributions of shear and buoyant production to the perturbation kinetic energy budget reveals that the marginally unstable modes are amplified based on different mechanisms: for lower wavenumbers at relatively small Grashof number, the instability is driven by buoyancy; whereas for higher wavenumbers and larger Grashof number, the flow becomes unstable due to a shear instability. The use of reference temperature is found to scale the shear- and buoyant-driven instabilities differently so that no single reference temperature definition would collapse the neutral curves. The linear stability result further demonstrates that at a given Grashof number a higher temperature difference would give a larger amplification rate of the perturbation, which then leads to an earlier onset of the nonlinearities when evaluated at $T_f$ . Finally, by comparing the amplification rates obtained from direct numerical simulation and the linear stability results, the extent of the linear regime is determined for $\Delta T = 100\,{\rm K}$ .

On the natural transition of the natural convection boundary layer under a constant heat flux condition

This study investigates the thermo-fluidic characteristics of a natural convection boundary layer over a vertical plate heated under a constant heat flux condition. We used particle image velocimetry to observe the surface convection velocity at the proximity of the plate, which is submerged in a water chamber with Rayleigh number, Ra=7×109 and Prandtl number, Pr = 8.1. The velocity distributions indicated the presence of distinct stripe-like flow structures in the early transition (upstream) region and that of distinct negative–positive Λ-shaped flow structures in the downstream region. In addition, the temporal variation of spanwise and streamwise velocity components was presented. Furthermore, proper orthogonal decomposition (POD) analysis was used to reduce the complexity of the flow structure and retain the most salient characteristics of the flow field. Our results confirmed the existence of a very weak inceptive oscillation in the behaviour of POD time coefficients in the upstream region.

Characteristics of MHD Jeffery Fluid Past an Inclined Vertical Porous Plate

This paper is concerned with the study of an unsteady, MHD natural convective boundary layer flow of a viscous, incompressible and electrically conducting, non-Newtonian Jeffery fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of thermal radiation, heat absorption and thermal diffusion, heat and mass transfer. . The permeability of the porous medium and the suction velocity are considered to be an exponentially decreasing function of time. The fundamental governing equations for this investigation are solved numerically using the perturbation technique. The results are presented graphically and in tabular form for various controlling parameters. The behavior of different physical parameters is shown graphically. The numerical values of Skin friction, Nusselt number, and Sherwood number are presented in a tabular form. Obtained outcomes are compared with earlier studies in the special case and strong agreement is noted. From graphical representation, it is concluded that velocity and temperature distribution increases with the mixed convection parameter and buoyancy force parameter. An increasing value of magnetic field parameter, slip parameter, and Jeffery parameter tends to reduced velocity and also raising the values of Prandtl number, radiation parameter and heat absorption parameter tends to downfallen temperature profiles. This study may be useful in several industrial applications, for example, polymer production, manufacturing of ceramics or glassware and food processing, and so forth.

Scaling laws for natural convection boundary layer of a Pr > 1 fluid on a vertical solid surface subject to a sinusoidal temperature in a linearly-stratified ambient fluid

The understanding of the transient behavior of natural convection boundary layer (NCBL) on a heated vertical solid surface under various heating conditions is of fundamental significance and application importance. In this study, scalings for the parameters representing the behavior of unsteady NCBL flow of a linearly-stratified Pr > 1 fluid on a semi-infinite vertical solid surface heated with a time-varying sinusoidal temperature at different development stages are developed with a scaling analysis, in terms of Ra, Pr, s, and fn, which are the Rayleigh number, Prandtl number, stratification number, and frequency of the sinusoidal temperature, respectively. These scalings are validated and quantified with a series of numerical simulations over wide ranges of Ra, Pr, s, and fn. The frequency of the fluctuations experienced by the NCBL behavior at the transitional stage, due to the stratification of the ambient fluid, is also analyzed, and it is shown that the previously obtained scaling for the unsteady NCBL case with the constant heat flux heating condition is basically applicable for the current case, Ra and fn have additional effects as well due to the time-varying nature of the applied temperature.

Convection boundary layers with transpiration: Non-similar solutions and scaling

We present a new formulation and novel scaling relations for natural convection boundary layers on horizontal surfaces with weak transpiration velocities Vi, for intermediate Schmidt numbers (or Prandtl numbers Pr) 1<Sc<20. Using characteristic scales derived from integral boundary layer equations, we define a new similarity variable η=(y/x)(Rex/Grx)1/4/Sc1/5 that has Vi within it, where Rex and Grx are the local Reynolds and Grashof numbers based on Vi and the concentration difference ΔC, respectively. Using η, and the dimensionless transpiration velocity ξ=(Rex/Grx1/5)5/4 as a non-similarity variable, we obtain novel, reduced, non-similar boundary layer equations. Numerical solution of these reduced boundary layer equations using a local non-similarity approach gives us the profiles of horizontal velocity and concentration, boundary layer thicknesses, wall shear stress, and mass flux as functions of Sc, for various ξ in the range ξ<1. Using normalizing functions, we then obtain scaling relations for these parameters; we observe extended similarity where the non-similarity parameter ξ itself appears in the obtained similarity scaling relations.

Magneto-convective hybrid nanofluid slip flow over a moving inclined thin needle in a Darcy-Forchheimer porous medium with viscous dissipation

PurposeThe purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.Design/methodology/approachThe first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.FindingsIt is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al2O3 and Fe3O4 are nanoparticles, H2O − C2H6O2 (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.Practical implicationsThe results can be very helpful to improve the energy efficiency of thermal systems.Social implicationsThe hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.Originality/valueThis study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

Scaling high Rayleigh number natural convection boundary layer statistics: A vertical water tunnel experiment

A high Rayleigh number natural convection boundary layer adjacent to the vertical heated wall was investigated at a large-scale facility. The global Rayleigh number (Rax) measured by the temperature difference between the wall and ambient water and the distance from the bottom of the heated wall reached 1013. Experimental results confirm that the global Nusselt number Nux is scaled by power 1/3 of Rax, which is similar to the well-known asymptote of the previously achieved Rax. The velocity field obtained using particle image velocimetry (PIV) indicated that the buoyancy-dominant outer-layer scaling suggested by Wells and Worster [A geophysical-scale model of vertical natural convection boundary layers, J. Fluid Mech. 609, 111–137 (2008)] was not only applicable to scale the lower-order velocity statistics but was also valid as a reasonable measure of the spatial correlation, probability distribution, and quadrant contribution features in the outer layer. The dynamical behavior of fluid motion captured by PIV supported a robust momentum transfer to positive wall-normal direction, which was sustained by the Q1 and Q3 quadrants. In addition, merging the existing literature and current data suggested that near-wall function can be applied at a moderate Rax; the universality of this wall-function model was confirmed around z×∼0.7 (where z× represents the near-wall scaled wall-normal distance, Kiš and Herwig [The near wall physics and wall functions for turbulent natural convection, Int. J. Heat Mass Transfer 55, 2625–2635 (2012)]). At a larger buoyancy regime, it was expected to follow a canonical boundary layer flow.

Magnetohydrodynamic Effects on the Flow of Nanofluids Across a Convectively Heated Inclined Plate Through a Porous Medium with a Convective Boundary Layer

The study explores the problem of Magnetohydrodynamic natural convection boundary layer flow of a nanofluid past a convectively heated inclined porous channel. The governing partial differential equations have been transformed through appropriate similarity functions into nonlinear ordinary differential equations. The emerging equations were solved numerically using both a sixth-order Runge-Kutta-Fehlberg and the shooting technique. The influences of pertinent parameters such as plate inclination angle, magnetic field, buoyancy ratio, and the convective heating term on the temperature, velocity, and concentration profiles were investigated graphically. Key findings indicate that an increase in magnetic field and permeability leads to a decline in the fluid’s velocity while the temperature and nanoparticle concentration are significantly enhanced. The results obtained are in close correlation with existing body of knowledge discussed in the literature.

Controlling instability waves on vertical natural convection using a buoyant impinging jet

Natural convective heat transfer is typically enhanced by installing fin arrays and other devices that increase the surface area; however, large surfaces present various problems in their implementation. In contrast, the impact of a jet on a natural convection boundary layer has been reported to produce periodically alternating T- and L-flows, whose disturbance may yield flow resonance with the periodic flows present in the transition length of the natural convection boundary layer. The control of instability waves, including flow resonance, is expected to have applications in enhancing convective heat transfer over large surfaces. This study focuses on the jet temperature (between ambient temperature 296 K and wall temperature 316 K), and jet velocity (Reynolds number 95 ≤ Re ≤ 150). Based on frequency analysis, the instability waves downstream of the heated wall are classified into three categories: resonance, convective instability, and turbulence. The analysis reveals that when resonance and turbulence take place, the heat transfer is enhanced compared to natural convection, however, when convective instability takes place, heat transfer depends on the jet temperature. Furthermore, we show that an appropriate choice of jet temperature and velocity can control the instability waves over the natural convection boundary layer.

LES of natural convection along a side-heated vertical wall in a water cavity applied for the scale of Small Modular Reactor ([formula omitted

The passive safety concept of Small Modular Reactors (SMR) is based on the transfer of residual heat from the reactor to a water pool. Since the height of the reactor vessel reaches approximately 15 m, this leads to a strong heat exchange between the wall and the water by the way of natural convection. The maximum Rayleigh number (Ra) reaches 1014 or 1015. Reliable heat transfer correlations exist only up to Ra≈1012, still along with uncertainties in the extrapolation to higher Rayleigh number values. To improve the understanding of natural convection at high Rayleigh number values, the turbulent natural convection boundary layer (TNCBL) along a 15 m high, side-heated vertical wall in a water tank is simulated by employing the Large Eddy Simulation method with the CEA in-house code Triocfd (Angeli et al., 2015). The numerical results in terms of heat transfer correlation, mean temperature and mean velocity, second moment variables show a reasonable agreement with available experimental data in the range of Ra < 1012. It is observed in the simulation that the powers of the heat transfer correlations in the laminar (Nuy=0.56Gry∙Pr0.25) and the turbulent regimes (Nuy=0.114Gry∙Pr1/3) correspond well to the classical regimes at Ra<2×1012. A slight deviation from the classical exponent (1/3) is found at higher Rayleigh number (2×1012 <Ra<1.8×1015), namely Nuy=0.114(Gry∙Pr)0.33 . Through the analysis of turbulent kinetic energy budget, it is found that turbulent contribution from shear stress increases continuously with the increase of Rayleigh number. However, the turbulence contribution from buoyancy keeps increasing until Ra≈6.6×1013, then decreases gradually at higher Rayleigh number. The behavior of the maximum buoyant force shifts slowly from the inner boundary layer to the outer boundary layer may indicate the potential transition of the buoyancy-dominated regime to the shear stress dominated regime, thus confirming previous theoretical prediction (Wells Andrew and Worster, 2008). The increasing scale of the streak-like turbulent structures with the increase of Rayleigh number are clearly demonstrated through visualization process.

Large-scale motions in a turbulent natural convection boundary layer immersed in a stably stratified environment

This study investigates the coherence of turbulent fluctuations in a turbulent vertical natural convection boundary layer immersed in a stably stratified medium (turbulent buoyancy layer). A turbulent buoyancy layer of a fluid having a Prandtl number of $0.71$ at a Reynolds number of $800$ is numerically simulated using direct numerical simulation. The two-point correlations reveal that the streamwise velocity fluctuations are coherent over large streamwise distances, with the length scale of the streamwise coherence being greater than the boundary layer thickness. This is due to large-scale motions (LSMs), similar to the LSMs observed in canonical wall-bounded turbulence despite the stark differences in flow dynamics. Both high-speed (positive) and low-speed (negative) streamwise velocity fluctuations form LSMs, with their streamwise length scales increasing with increasing wall-normal distance. High-speed LSMs are composed of upwash flow with high temperatures, while low-speed LSMs are composed of downwash flow with low temperatures. Both high-speed and low-speed LSMs meander appreciably in the streamwise direction, with the degree of meandering being correlated with the sign of the spanwise velocity fluctuations. The LSMs exhibit coherence across significant wall-normal distances and contribute significantly to the turbulence production in the outer layer. Examining the one-dimensional energy spectra of the turbulent buoyancy layer shows that the LSMs are the dominant energy-containing motions, implying that the length scale of the energy-containing range is of the order of boundary layer thickness. Notably, wall-normal velocity, spanwise velocity and buoyancy fluctuations do not form LSMs with streamwise length scales comparable to streamwise velocity fluctuations.

The effects of thermal radiation, internal heat generation (absorption) on unsteady MHD free convection flow about a truncated cone in presence of pressure work

The aim of present paper is to analyse the effect of radiation, internal heat generation (absorption) on unsteady laminar natural convective boundary layer flow over a truncated cone considering pressure work and magnetic field due to the variation in fluid flow behavior in various physical conditions. Suitable transformation is used to form system of coupled non linear partial differential equations is to governing the flow and heat transfer. These equations have been solved numerically by using an implicit finite difference scheme along with quasilinearization technique. According to numerical findings, the pressure work, internal heat generation (absorption), radiation, and magnetic field have a significant impact on both skin friction and heat transfer. Further, skin friction is found to decrease 12.13%, 30.3% and 41.67% for various values (from 0.0 to 0.5) of pressure work, magnetic field and heat generation (absorption) alongside the cone surface whereas heat transfer rate rises 17.19%, 17.65% and 73.51% respectively due to unsteadiness in the flow. It is observed that the thickness of boundary layer enhances for various values (from 0.0 to 0.5) of heat generation and radiation parameter but diminishes for pressure work and Prandtl number.

The turbulence development of a vertical natural convection boundary layer

Results from direct numerical simulations of a vertical natural convection boundary layer (NCBL) with $Pr=0.71$ reveal that the turbulence development of such a thermally driven convective flow has two distinct stages: at relatively low Grashof number, the bulk flow is turbulent while the near-wall region is laminar-like or weakly turbulent; at sufficiently high Grashof number, the entire flow becomes turbulent in the sense of von Kármán (cf. Grossmann &amp; Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56, for the ultimate turbulent regime). Investigations on the turbulence statistics show that the near-wall Reynolds shear stress is negligible in the weakly turbulent regime but will grow in magnitude as the flow transitions to the ultimate regime at higher Grashof number. Similar behaviour is also seen in the streamwise turbulence intensity, where it develops from a mono-peak profile into a dual-peak structure as the Grashof number increases. At higher Grashof number, the near-wall energetic site is shown to have an energy distribution similar to that of a canonical wall-bounded turbulence (e.g. Hutchins &amp; Marusic, Phil. Trans. R. Soc.A, vol. 365, 2007, pp. 647–664), with a peak centred at fixed location and wavelength ( $y^+=18$ and $\lambda ^+_x=1000$ ) in viscous coordinates. Investigation on the spanwise spectra also suggests that the turbulent near-wall streaks emerge only at sufficiently high Grashof number, with constant spacing $\lambda _z^+\approx 130$ . The extent of the weakly turbulent regime is identified using the maximum velocity location $\delta_m$ and a laminar length scale $\delta_u$ . The development of near-wall turbulence is also investigated by examining the turbulence kinetic energy budget. In the weakly turbulent regime, the near-wall turbulence is sustained predominantly by the pressure transport in addition to the shear production. At higher Grashof number, the flow becomes fully turbulent, and both turbulent transport and shear production become stronger, while the pressure transport is decreased. These results also reveal that the production–dissipation ratio $P/\varepsilon$ of the NCBL would follow a fundamentally different trend to the canonical wall-bounded flows, which further supports that the near-wall turbulence generation is affected by the bulk flow.

Effect of shear on local boundary layers in turbulent convection

In Rayleigh Bénard convection, for a range of Prandtl numbers $4.69 \leqslant Pr \leqslant 5.88$ and Rayleigh numbers $5.52\times 10^5 \leqslant Ra \leqslant 1.21\times 10^9$ , we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers on the hot plate. The velocity distribution in a horizontal plane within the boundary layers at each $Ra$ , at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities $V_{bl}$ ; (B) bimodal with the first peak between $V_{bl}$ and $V_{L}$ , the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately $V_{L}$ . Type A distributions occur more at lower $Ra$ , while type C occur more at higher $Ra$ , with type B occurring more at intermediate $Ra$ . We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as $V_{L}$ scales with $Ra$ . We then show that the areas of such regions that have velocities of the order of $V_{L}$ increase exponentially with increase in $Ra$ and then saturate. The velocities in the remaining regions, which contribute to the first peak of the bimodal type B distributions and the single peak of type A distributions, are also affected by the shear. We show that the Reynolds number based on these velocities scale as $Re_{bs}$ , the Reynolds number based on the boundary layer velocities forced externally by the shear due to the LSF, which we obtained as a perturbation solution of the scaling relations derived from integral boundary layer equations. For $Pr=1$ and aspect ratio $\varGamma =1$ , $Re_{bs} \sim Ra^{0.375}$ for small shear, similar to the observed flux scaling in a possible ultimate regime. The velocity at the edge of the natural convection boundary layers was found to increase with $Ra$ as $Ra^{0.35}$ ; since $V_{bl}\sim Ra^{1/3}$ , this suggests a possible shear domination of the boundary layers at high $Ra$ . The effect of shear, however, decreases with increase in $Pr$ and with increase in $\varGamma$ , and becomes negligible for $Pr\geqslant 100$ at $\varGamma =1$ or for $\varGamma \geqslant 20$ at $Pr=1$ , causing $Re_{bs}\sim Ra_w^{1/3}$ .

RANS thermal modelling of a natural convection boundary layer at low Prandtl number

The present work evaluates the performance of different RANS turbulence models in a natural convection boundary layer at three different Prandtl numbers: 0.71, 0.2 and 0.025. An assessment on the prediction of the boundary layer is presented in function of the wall fluxes, mean and turbulent flow fields. It is observed that the chosen turbulence model to close the momentum equation is relevant in order to capture the flow field at low Prandtl numbers. This is due to the strong interaction between the momentum and thermal fields in natural convection. From the thermal point of view, the analogy between the turbulent momentum and turbulent thermal diffusivities presents serious issues to correctly predict the flow field independently of the Prandtl number. Advanced models that employ algebraic or transport equations of the turbulent heat fluxes introduces the needed physics to correctly predict the natural convection boundary layer.

Using of large eddy simulation model for a spatially developing turbulent natural convection boundary layer in water along a side-heated vertical wall with high Rayleigh number ([formula omitted

To further understand the turbulent natural convection in the residual heat removal process of a nuclear reactor in accidental condition, a spatially developing natural convection boundary layer along a side-heated vertical plane in water is simulated with Large Eddy Simulation (LES) strategy. The maximum modified Rayleigh number (Ra*=Ra×Nu) reaches 8×1014 with the uniform heat flux input (≈10000W/m2). In particular, the buoyancy driven flow is simulated by an incompressible flow solver with Boussinesq approximation. The Wall Adaptive Local Eddy (WALE) model is selected as the sub-grid scale model for the LES simulation. After comparing with available measurements, it is found that reasonable agreement has been achieved in wall temperature distribution along the heated wall, heat transfer rate as well as mean temperature, mean velocity and turbulent statistics in the boundary layer. The detailed vortex structure and velocity spectra in the boundary layer corresponding to different regime are clearly demonstrated. It is shown that the transition process in the boundary layer can be accurately presented with the refined mesh (x+≈0.1) in the near wall region. To be more specific, the appeared ordered vortex street in the transition stage and the estimated critical Rayleigh number for turbulence inception correspond well to previous experimental observations. The significant effect of early transformation of two-dimensional (2D) linear Tollmien–Schlichting waves on the heat transfer is also proved. It is expected that current study can enhance the understanding of turbulent boundary layer at high heat flux and high Rayleigh number.

VISUALIZATION AND MEASUREMENT OF NATURAL CONVECTION BOUNDARY LAYER BY PARTICLE IMAGE VELOCIMETRY

VISUALIZATION AND MEASUREMENT OF NATURAL CONVECTION BOUNDARY LAYER BY PARTICLE IMAGE VELOCIMETRY

Unified scale laws for transient convective boundary layers: From flat to curved boundary layers

Transient natural convection boundary layer flow is studied at Pr&gt;1 and the curvature effect is specifically and fundamentally explored. Important scale laws, i.e. boundary layer thickness \ensuremath{\delta}t and characteristic velocity ${u}_{z}$ of the transient and steady states and the cut-off time ${t}_{s}$ of the initial growth, are proposed and validated. We find that for cylinder radius much larger than the boundary layer thickness, the present scaling relations reduce to those of the classic flat boundary layer. The most curved boundary layer we examine is 26 times thicker than the cylinder radius. We show that the present scaling set is accurate for all flow conditions bounded by the two limiting scenarios.

Les of a Space-Developing Natural Convection Boundary Layer in Water Along a Vertical Wall with High Heat Flux

Les of a Space-Developing Natural Convection Boundary Layer in Water Along a Vertical Wall with High Heat Flux

Scaling laws for natural convection boundary layer of a Pr &gt; 1 fluid on a vertical solid surface subject to a sinusoidal heating flux in a linearly stratified ambient

AbstractThe understanding of the transient behavior of the natural convection boundary layer on a heated vertical solid surface is crucial for numerous applications. In this study, scaling analysis is performed to derive the scaling laws for the major parameters that characterize the transient behavior of natural convection boundary layer of a Prandtl number larger than 1 fluid on a vertical solid surface subject to a sinusoidal heating flux in a linearly stratified ambient. It is found that the developed scaling laws are in good agreement with the direct numerical simulation results over wide ranges of Prandtl number, stratification parameter, and frequency of the sinusoidal heat flux.