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Subject to daytime heating and nighttime cooling, a horizontal temperature gradient is generated in nearshore waters owing to the gradually deepening topography offshore. The resulting natural convection has significant biological and environmental implications. The present investigation is concerned with natural convection in a reservoir model induced by a periodically varying surface temperature. A hybrid of semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to characterize the periodic flow. The present scaling focuses on the long period scenario for which a quasi-steady state is reached within a thermal forcing cycle. This is the case in natural water bodies under typical field conditions. Compared to the previously reported constant heating or cooling cases, the present scaling analysis is more complex and the developed scales depend on the period of the thermal forcing. Two critical functions of the Rayleigh number have been derived to identify the distinctness and stability of the thermal boundary layer. Distinct subregions are identified, and the scales of flow velocity and phase lag are derived for different subregions. These scaling results are verified by numerical simulations. Numerical results show that the flow response varies significantly with the length of period. For short periods, the large scale flow never reverses from cooling-induced flow. For the long period scenario, flow reversal occurs, with much more intense flow during the cooling phase than during the heating phase. The phase lag of flow response decreases with increasing period length. Finally, the present scaling results are applied to field situations, which agree well with field observations.

A three-dimensional direct numerical simulation is carried out to investigate the response of the flow past a highly confined circular cylinder to single-mode sinusoidal perturbations. The Reynolds number is fixed at 1000, and the blockage ratio (the ratio of the cylinder diameter to the distance between two lateral walls) is fixed at 0.6. Local perturbations are introduced upstream of the cylinder at normalized excitation frequencies ( fe/f0) from 0.2 to 3.4, where f0 is the vortex shedding frequency in an unperturbed flow. It is observed that the vortex shedding frequency of the perturbed flows ( fs) and the excitation frequency ( fe) are locked-on in four distinct modes including fs = 2.0 fe, fs = 1.5 fe, fs = 1.0 fe, and fs = 0.5 fe, respectively. Among them, the fundamental lock-on with fs = 0.5 fe appears over a wide range of excitation frequencies ( fe/f0 = 1.4–2.8). By contrast, only the fundamental lock-on regime of fs = 0.5 fe is observed when perturbing an unconfined flow at the same Reynolds number, highlighting the significant impact of confinement on the lock-on behavior. It is further revealed that the lock-on behavior is controlled by the responses of separated shear layers in the near wake, which switch from higher modes to lower modes with increasing excitation frequency in the confined flow.

In this study, a Particle Image Velocimetry (PIV) measurement is carried out to investigate the flow past a highly confined circular cylinder at a fixed blockage ratio of 60%. The Reynolds number (Re) in terms of the cylinder diameter and the mean incoming flow velocity is varied from 318 to 1431. It is observed that the characteristic frequency of the separated shear layers is amplified through a so-called frequency-filtering process. The instability of the separated shear layers causes two different vortex shedding modes including alternating and symmetric shedding modes, which are observed at Re = 927–1242. An intermittent switch between the two shedding modes is also observed. The theory of mixing layers is applied with modification to predict the characteristics of the separated shear layers, and the prediction shows a good agreement with the experimental data. It is found that the vortex roll-up and merging locations can be estimated by calculating the energy contents of individual frequency modes.

Natural convection arising over vertical and horizontal heated flat surfaces is one of the most ubiquitous flows at a range of spatiotemporal scales. Despite significant developments over more than a century contributing to our fundamental understanding of heat transfer in natural convection boundary layers, certain “hidden” characteristics of these flows have received far less attention. Here, we review scattered progress on less visited fundamental topics that have strong implications to heat and mass transfer control. These topics include the instability characteristics, laminar-to-turbulent transition, and spatial flow structures of vertical natural convection boundary layers and large-scale plumes, dome, and circulating flows over discretely and entirely heated horizontal surfaces. Based on the summarized advancements in fundamental research, we elaborate on the selection of perturbations and provide an outlook on the development of perturbation generators and methods of altering large-scale flow structures as a potential means for heat and mass transfer control where natural convection is dominant.

A three-dimensional liquid bridge is considered in this study to numerically investigate the effects of an external non-uniform rotating magnetic field (RMF) on the thermocapillary flow in semiconductor melt under microgravity. Simulations are carried out to examine the convection and instability features of the thermocapillary flow over a range of Marangoni numbers (Ma = 15–50) under a non-uniform RMF. The present results show that applying an external non-uniform RMF enhances the maximum tangential velocity and depresses the maximum axial velocity. As a consequence, an approximately axisymmetric flow is maintained in the melt under the effect of the non-uniform RMF, which is beneficial for growing high quality crystal. Further investigation of the thermocapillary flow subject to different non-uniform RMFs (corresponding to Taylor numbers Ta = 3.8 × 10 2 –1.86 × 10 4 and Rotating Reynolds number Re ω = 2.2 × 10 4 ) reveals that the thermocapillary convection may undergo a transition from the approximately axisymmetric steady flow to a periodically oscillatory flow for Ma above a critical value. The critical Ma generally increases with the intensity of the non-uniform RMF.

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.

We report the first definitive Nusselt number scale of thermal boundary layers from curved surfaces characterized by the proposed non-dimensional curvature parameter ξ = R 0/(H Ra −1/4), where R 0 denotes the radius of a curved surface, H denotes the corresponding finite height, and Ra denotes the global Rayleigh number of a virtual reference thermal boundary layer on a vertical flat surface. The Nusselt number scale is given by Nu ∼ ξ −1/5 Ra 1/4 in which Nu ∼ Ra 1/4 is the scale for the flat surface case, revealing that curved thermal boundary layers could present times-of-magnitude larger heat flux with the curvature parameter being ξ ≪ 1. The velocity and thickness scales are also given by V s ∼ R 0 2 / 5 R a 3 / 5 H 7 / 5 κ and Δ T ∼ R 0 1 / 5 H 4 / 5 R a 1 / 5 .

The ‘natural transition’ of a natural convection boundary layer adjacent to an isothermally heated vertical surface is investigated by means of three-dimensional direct numerical simulation (DNS). In order to trigger ‘natural transition’ numerically, spatially and temporally random perturbations are introduced into the upstream boundary layer. The propagation of the random perturbations in the streamwise direction is observed. It is found that there exist two competing wavenumbers of spanwise vortical structures, one large and the other small. The large wavenumber dominates in the upstream boundary layer, whereas the small wavenumber dominates in the downstream boundary layer. The streamwise evolution of the mean (time-averaged) streamwise vorticity observed at planes perpendicular to the heated surface in general reveals two- and three-layer longitudinal roll structures. Nonlinear processes in a transitioning natural convection boundary layer are also analysed using Bicoherence method. The transition route and mechanism are discussed based on the power spectra and Bicoherence spectra of the temperature time series obtained in the boundary layer. A spectrum filling process during the ‘natural transition’ to turbulence is also observed, which is qualitatively similar to that observed in Blasius boundary layers.

Turbulent natural convection with and without radiation transfer in two-dimensional (2D) and three-dimensional (3D) air-filled differentially heated cavities is numerically investigated using various RANS (Reynolds Averaged Navier–Stokes) turbulence models and the Discrete Ordinates radiation model. Five different two-equation eddy-viscosity models including the standard k–e model, the renormalization group (RNG) k–e model, the realisable k–e model, the standard k–ω model and the shear-stress transport (SST) k–ω model are selected for comparison. Qualitative and quantitative data are presented to demonstrate the effects of three-dimensionality, radiation transfer and the thermal boundary conditions on the horizontal surfaces on the numerical solution of the convective flow in the cavity. The present numerical results are compared against published experimental and direct numerical simulation data. It is found that the predicted thermal stratification in the interior of the cavity is improved when the simulation is extended from 2D to 3D and when the effect of radiation transfer is accounted for. The discrepancy with regard to the interior stratification between the experiment and numerical simulation is mainly caused by the negligence of radiation transfer. The thermal boundary conditions on the horizontal surfaces also have a significant impact on the numerical solution, especially when the radiation transfer is not accounted for. Further, the present results show that all the RANS models are capable of capturing the main features of the flow and the overall performance of these turbulence models in terms of predicting time-averaged quantities is acceptable. It is found that the variation of the numerical results obtained with the three k–e models is very small, whereas the discrepancy between the two k–ω models is significant. The SST k–ω model has the best overall performance and the standard k–ω model has the worst overall performance.

This paper considers linear and oscillatory behaviours of the natural convection boundary layer induced by the absorption of incoming radiation in response to constant and time-varying (ramp) thermal forcing. The considered configuration is relevant to the flow in littoral regions of lakes and reservoirs in response to the daytime thermal forcing due to solar radiation. The absorption of the incoming solar radiation is depth-dependent, following Beer’s law, whilst the residual radiation at the bottom bathymetry is absorbed and released back to the water body as a boundary flux. Therefore, a potentially unstable thermal boundary layer forms adjacent to the bottom bathymetry and the associated thermoconvective instability induces vertical mixing in the form of rising plumes (i.e. intermittent convection). The linear theory is applied to investigate the incipient evolution of the instability, and direct comparisons of linear and direct stability analyses are performed. The fastest growing mode and the corresponding temporal growth rate obtained via a quasi-static linear stability analysis are shown to be in excellent agreement with the results of the direct stability analysis based on numerical simulations of the flow. Further, the time and frequency scales of the unstable bottom thermal boundary layer are derived via a local Rayleigh number analysis. It is then demonstrated that the boundary layer response to the time-varying thermal forcing is in equilibrium with the forcing intensity at each instant of time.

The transient stability of penetrative convection induced by internal heating coupled with a Robin (or third kind) boundary condition is investigated by adopting different transient approaches. A Robin boundary condition introduces a heat exchange coefficient as an additional parameter. In the system, a destabilising boundary flux is determined by the temperature increase of the fluid adjacent to the boundary, which is in turn controlled by the internal heat source, thus the boundary flux increases gradually with time. The study shows that the stability properties of the flow are independent of the Prandtl number and the transient approach being used. Further, the results of the present study demonstrate the effect of varying the heat exchange coefficient on the critical conditions and the formation of primary convection rolls. Interestingly, the horizontal and vertical length scales of the convection rolls are found to be insensitive to the value of the heat exchange coefficient, whilst the onset time of the penetrative convection is strongly dependent on this parameter.

The separation of plumes from an adiabatic horizontal thin fin attached to a sidewall of a differentially heated cavity at quasi-steady stage is experimentally and numerically studied at three Rayleigh numbers (0.92 × 10 9 , 1.84 × 10 9 and 3.68 × 10 9 ) and over a range of fin positions. Regular plume separation is observed over the present range of parameters during the quasi-steady stage. Both experimental and numerical results reveal that the plume separation frequency increases with the Rayleigh number and decreases with the fin height measured from the leading edge. A higher Rayleigh number leads to a more unstable flow above the horizontal thin fin which in turn leads to a higher plume separation frequency. The decrease of the plume separation frequency with the increasing fin height is mainly due to the reduction of the adverse temperature gradient in the unstable layer above the thin fin as a result of the cavity-wide temperature stratification. It is further revealed that the heat transfer through the sidewall is improved by the presence of the thin fin. An optimum fin height for maximum heat transfer enhancement has been identified for the case with a Rayleigh number of 0.92 × 10 9 . For the other two higher Rayleigh number cases considered in this study, the heat transfer through the sidewall monotonically decreases with the fin height.

The present study considers the early stage of the flow development in a water-filled, three-dimensional parallelepiped cavity subject to solar radiation. The thermal structure consists of an upper stable stratification due to internal heating, provided by the direct absorption of radiation, and a bottom potentially unstable boundary layer due to the absorption and re-emission of the residual radiation by the bottom boundary. The growth of the competing thermal layers and the stability properties of the bottom thermal boundary layer are investigated by means of a scaling analysis and a direct stability analysis based on three-dimensional numerical simulation. The scaling relations are benchmarked against the numerical simulation, and the effects of the normalised water depth, the Rayleigh number and the box aspect ratio on the thermal instability are studied.

This study focuses on the marginal stability of the natural convection flow induced by the absorption of radiation. Non-uniform internal heating associated with the absorption of radiation following Beer’s law and the absorption and re-emission of residual radiation by the bottom boundary wall lead to a nonlinear base temperature profile that evolves with time. A horizontal throughflow and lateral confinement are incorporated in the analysis, and two forms of convective instability, i.e. longitudinal and transverse rolls, are investigated. It is shown that the formation of longitudinal rolls, with their axes parallel to the throughflow direction, is not affected by the presence of the throughflow. For transverse rolls, with their axes perpendicular to the throughflow direction, however, the throughflow is shown to have a stabilising effect, with the critical Rayleigh number increasing with the increasing throughflow Reynolds number. It follows that longitudinal rolls are the preferred form of instability in laterally unconfined domains for any nonzero Reynolds number and in confined domains if the Reynolds number is greater than a critical value. The value of the critical Reynolds number, which separates the preferred mode of instability, is found to rapidly reduce with increasing lateral extent and approaches zero for a normalised lateral extent greater than 2.0. The lateral confinement is also shown to have a stabilising effect for both longitudinal and transverse rolls, with the critical Rayleigh number increasing with the reducing lateral extent. It is shown that the lateral confinement only substantially affects the wave number of the rolls with their axes parallel to the confining walls but not the rolls with their axes perpendicular to the confining walls.

This study considers the natural convection flow in a water body subjected to heating by solar radiation. The investigation into this type of natural convection flow has been motivated by the fact that it is known to play a crucial role in the daytime heat and mass transfer in shallow regions of natural water reservoirs and lakes, with a resultant impact on biological activity. An analytical solution for temperature in such an internally heated system shows that the temperature stratification consists of an upper stable stratification and a lower unstable stratification. One of the important consequences of such a nonlinear temperature stratification is the limitation of the mixing driven by rising thermal plumes with the penetration length scale of the plumes determining the lower mixed layer thickness. A theoretical analysis conducted in the present study suggests that in relatively deep waters, the lower mixed layer thickness is equal to the attenuation length of the radiation, which has important implications for water quality, including the transport of pollutants and nutrients in the water body. Scalings are also obtained for the quasi-steady boundary layer. The theoretical analysis is validated against numerical simulations.

Previous studies have revealed that heat transfer through a convective thermal boundary layer can be significantly enhanced by perturbing the thermal boundary layer to advance linear to nonlinear transition. It has also been demonstrated that the enhancement of heat transfer is mostly achieved in the nonlinear regime. In this study, the transition of the thermal boundary layer adjacent to an isothermally heated vertical surface is revisited by means of Bicoherence analysis, which is a statistical approach for identifying and quantifying quadratic wave interactions. The streamwise evolution of Bicoherence spectra suggests that the thermal boundary layer can be classified into three regimes: a linear flow regime, a transitional flow regime and a nonlinear flow regime. The positions of the transition from the transitional to nonlinear regimes in the thermal boundary layer at various Rayleigh numbers, perturbation frequencies and perturbation amplitudes are determined using Bicoherence analysis. It is found that in the nonlinear flow regime, the number of resonance groups fluctuates, which indicates the occurrence of coupling and decoupling of harmonics in the boundary layer. This process may be the mechanism responsible for the resonance induced enhancement of heat transfer.

In this study the natural convection flow adjacent to a finned sidewall of a differentially heated cavity is experimentally investigated using the shadowgraph technique. Two Perspex fins of different lengths are placed horizontally at different heights along each of the cavity sidewalls. It is revealed from the shadowgraph observation of the heated sidewall that similar horizontal hot intrusions form underneath the fins and the cavity ceiling at the early stage. In the transitional stage, the thermal flows bypassing the fins are entrained towards the heated sidewall and a cavity-scale interior temperature stratification is gradually established. In the quasi-steady stage, regular oscillations are observed above the lower fin. The oscillation in the horizontal thermal flow above the lower fin results in strong mixing in the thermal boundary layer between the two fins and that downstream of the upper fin. As a consequence, heat transfer through the downstream thermal boundary layer is greatly enhanced. A corresponding numerical simulation is also conducted and a good agreement between the simulation and the experiment is achieved. It is further revealed numerically that the convective flow across the cavity is significantly enhanced due to the presence of the fins. The heat transfer is improved by up to 17.1% over the investigated Rayleigh number range. The dependency of the time averaged Nusselt number at the finned sidewall on the Rayleigh number has been quantified.

The present investigation is concerned with the transient flow response of a reservoir model to periodic thermal forcing at water surface. A previously reported concurrent PIT/PIV experiment is numerically reproduced using a Computational Fluid Dynamics (CFD) code coupled with a Discrete Phase Model (DPM). Both qualitative and quantitative agreements are achieved between the present numerical simulation and the experiment. A parametric study is also carried out using the numerical model to determine the dependence of the flow response and its stability properties on the Grashof number.

This study is concerned with particle transport in a reservoir model subject to diurnal temperature variation at the water surface. A Computational Fluid Dynamics (CFD) code coupled with a Discrete Phase Model (DPM) is adopted to examine the particle transport in the reservoir. The particle deposition and dispersion as well as the concentration of particles in various regions of the water body are examined. The present study demonstrates the importance of buoyancy-driven flows for particle deposition and dispersion in reservoirs.

The flow behavior due to natural convection of air (with a Prandtl number less than 1) inside a solar chimney with an imposed heat flux on a vertical absorber wall is investigated by a scaling analysis and a corresponding numerical simulation. Three distinct flow regimes are identified, one with a distinct thermal boundary layer and the other two without a distinct thermal boundary layer, depending on the Rayleigh number. The two regimes without a distinct thermal boundary layer are further classified into low and medium Rayleigh number sub-regimes respectively. These sub-regimes are characterized by conduction dominance in which the thermal boundary layer grows to encompass the entire width of the channel before convection becomes important. Flow development in each of these flow regimes and sub-regimes is characterized through transient scaling, and scaling correlations are developed to describe the temperature, flow velocity and mass flow rate, which characterize the ventilation performance of the solar chimney. The scaling arguments are validated by the corresponding numerical data.

Nearshore natural convection induced by differential heating across shore has significant biological and environmental implications. The present investigation is concerned with convection in a wedge-shaped reservoir sidearm induced by isothermal heating at the water surface which increases linearly over a specified time period from an initial value to a final steady value (i.e. ramped heating), extending our previous report on convection induced by constant isothermal heating. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. It is revealed that the flow domain is composed of two distinct subregions, a conductive region nearshore which finally becomes isothermal and stationary, and a convective region offshore which eventually maintains a steady flow velocity. Different scenarios are revealed through the comparison between the ramp duration P and a characteristic time t c of the induced flow. For the conductive region, the characteristic time is the time for the thermal boundary layer formed at the surface to reach the full local depth. For the convective region, it is the steady state time when convection balances conduction. For a short ramp ( P t c ), no steady state is reached within the ramping stage. For a long ramp ( P > t c ), a quasi-steady state is reached for both subregions before the ramp finishes. For the conductive region, the quasi-steady state is characterized by a steady flow velocity and the same local temperature growth rate as the water surface. For the convective region, the quasi-steady state is characterized by a change in the growth rate of the velocity. Major time and velocity scales governing the flow development in both subregions are proposed by a semi-analytical solution coupled with scaling and verified by the numerical simulation. Implication of the present study for field situations is also discussed.

In this study we investigate the transition from a steady flow to an unsteady flow induced by an adiabatic fin on the sidewall of a differentially heated cavity using numerical simulation. A range of Rayleigh numbers (10 6 –10 9 ) and various fin lengths with Prandtl number 6.63 are considered. It is found that the flow adjacent to the finned sidewall is unsteady for the cases with Rayleigh numbers higher than a critical value for a given fin length. Such an unsteady flow results from a fluid layer above the fin with an adverse temperature gradient and a through flow, which is a similar mechanism to a Rayleigh–Benard–Poiseuille (RBP) flow, though the configuration is such that it cannot be exactly a RBP flow. The transition from a steady flow to an unsteady flow is sensitive to the fin length, and the critical values of the transition for the different fin lengths are obtained. Moreover, the features of the unsteady flow induced by the fin are characterized and the mechanisms responsible for the unsteadiness are discussed.

The instability characteristics and resonance of a natural convection boundary layer adjacent to an isothermally heated vertical surface are investigated using direct stability analyses. The detailed streamwise evolution of the boundary-layer frequencies is visualized via the power spectra of the temperature time series in the thermal boundary layer. It is found that the entire thermal boundary layer may be divided into three distinct regions according to the frequency profile, which include an upstream low-frequency region, a transitional region (with both low- and high-frequency bands) and a downstream high-frequency region. The high-frequency band in the downstream region determines the resonance characteristics of the thermal boundary layer, which can be triggered by a single-mode perturbation at frequencies within the high-frequency band. The single-mode perturbation experiments further reveal that the maximum resonance of the thermal boundary layer is triggered by a perturbation at the characteristic frequency of the boundary layer. For the boundary-layer flow at $\mathit{Ra}= 3. 6\times 1{0}^{10} $ and $\mathit{Pr}= 7$, a net heat transfer enhancement of up to 44 % is achieved by triggering resonance of the boundary layer. This significant enhancement of heat transfer is due to the resonance-induced advancement of the laminar–turbulent transition, which is found to be dependent on the perturbation frequency and amplitude. Evidence from different perspectives revealing the same position of the transition are provided and discussed. The outcomes of this investigation demonstrate the prospect of a resonance-based approach for enhancing heat transfer.

The present study numerically investigates the unsteady natural convection in a triangular domain induced by ramped iso-flux cooling at the water surface. The simulations indicate that, although the ramped cooling does not alter the final state of the flow for a given steady state flux, it may change the developing path towards the final state as well as slow down the development of the flow. The ramped cooling delays or completely suppresses the onset of a Rayleigh-Benard type (RBT) instability during the developing process. As a consequence, a transitional stage characterized by the appearance and disappearance of the RBT instability at intermediate Rayleigh numbers does not occur if the ramp time is significantly long. Both qualitative and quantitative information is presented to demonstrate the effects of the ramp time on the transient behaviour of the flow at different Rayleigh numbers. A time scale for the onset time of the RBT instability under ramped cooling is also proposed and verified by the numerical results. The local instantaneous Rayleigh number at different parameters is calculated and its time history confirms the observed transient flow behaviours.

The present investigation is concerned with natural convection in a wedge-shaped domain induced by constant isothermal heating at the water surface. Complementary to the study of daytime heating by solar radiation relevant to nearshore regions of lakes and reservoirs previously reported by the same authors, this study focuses on sensible heating imposed by the atmosphere when it is warmer than the water body. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. Two flow regimes are identified depending on the comparison between the Rayleigh number and the inverse of the square of the bottom slope. For the lower Rayleigh number regime, the entire flow domain eventually becomes isothermal and stationary. For the higher Rayleigh number regime, the flow domain is composed of two distinct subregions, a conductive subregion near the shore and a convective subregion offshore. Within the conductive subregion, the maximum local flow velocity occurs when the thermal boundary layer reaches the local bottom, and the subregion eventually becomes isothermal and stationary. In the offshore convective subregion, a steady state is reached with a distinct thermal boundary layer below the surface and a steady flow velocity. The dividing position between the two subregions and the major time and velocity scales governing the flow development in both subregions are proposed by the scaling analysis and validated by corresponding numerical simulation.

The unsteady natural convection flow adjacent to the finned sidewall of a differentially heated cavity is numerically investigated through comparisons between the cases with a conducting fin and an adiabatic fin. The results show that the flow and temperature structures in the transition to a periodic flow induced by a conducting fin are considerably different from those by an adiabatic fin. Based on the present numerical results, the temporal development and spatial structures of the flow adjacent to the finned sidewall are described, and instabilities are characterized. It is found that the conducting fin improves the transient convective flows in the cavity and enhances heat transfer across the cavity (by up to 52% in comparison with the case without a fin).

In this study, stainless steel test plates with different surface roughness and textures, which are used as the heat transfer surface of a plate heat exchanger, are tested individually in calcium carbonate fouling experiments. The present experimental results clearly indicate a strong correlation between the surface roughness and the amount of crystallization fouling deposit. Through detailed image analysis, four stages of the formation of crystallization fouling are identified, and the impact of the surface morphology on the extent of crystallization fouling is described qualitatively.

This study is concerned with transient and steady state heat transfer by natural convection in a differentially heated cavity. The purpose is to evaluate a passive approach for enhancing heat transfer through the cavity. In this study, the effects of three different corner geometries (including sharp, round and straight corners) and adiabatic extensions of various dimensions on natural convection heat transfer are investigated numerically. The numerical results show marginal variations of the heat transfer rates among the three different corner shapes and a strong dependence of heat transfer enhancement on the Rayleigh number. For a given Rayleigh number, the enhancement of heat transfer by adiabatic extensions is limited.

The heat transfer through the attics of buildings under realistic thermal forcing has been considered in this study. A periodic temperature boundary condition is applied on the sloping walls of the attic to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution is seen for relatively low Rayleigh numbers. However, as the Ra gradually increases, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage.

The natural convection thermal boundary-layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary-layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady-state time, the layer reaches a quasi-steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

In this study, a discussion of the fluid dynamics in the attic space is reported, focusing on its transient response to sudden and linear changes of temperature along the two inclined walls. The transient behaviour of an attic space is relevant to our daily life. The instantaneous and non-instantaneous (ramp) heating boundary condition is applied on the sloping walls of the attic space. A theoretical understanding of the transient behaviour of the flow in the enclosure is performed through scaling analysis. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the heating-up of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

Step-by-step calibration procedures of particle image thermometry (PIT) for non-invasive and accurate temperature measurements using thermo-chromic liquid crystals (TLCs) are described in this paper. The purpose of this study is to examine the effects of various aspects of camera settings and image and data processing on the calibration of TLCs, and reveal the optimal parameter settings for achieving the best calibration curve of temperature versus color. Based on this study, an optimal window size has been proposed for median filtering to achieve the best compromise between noise removal and retaining of the true color information of the original experimental photographs; an optimal white balance settings in terms of the color temperature has been revealed for the present optical system; and finally, an optimal configuration of neural networks has been identified for obtaining the best hue–temperature correlation for further experiments.

Temperature measurements of the thermal flows in a differentially heated cavity with and without a fin on the sidewall were performed. The oscillatory behaviours in the transition from an initially isothermal state to an eventually stratified interior fluid ambient are characterized. It is revealed that, for the case without a fin, the amplitude of the oscillations in the thermal boundary layer increases as the stratification of the interior fluid increases. For the case with a fin, the temperature measurements show that the oscillations are induced by an unstable fluid layer above the fin. The spectral analysis reveals that the frequency properties of the oscillations are different between the cases with and without a fin.

Mixing and transport of terrestrially derived solutes and particulates in littoral regions depend heavily on the characteristics of flow instability. The criteria for radiation-induced instability to occur and the scope of the unstable region in near shore waters were revealed in our previously reported scaling analysis. In the present paper, the characteristics of instability of radiation-induced natural convection in shallow littoral regions are considered. Spectral analysis is conducted to reveal the frequency modes and the power of instability at various positions for different Rayleigh numbers. Results indicate that harmonic frequency modes are present at relatively low Rayleigh numbers. Both the power of instability and the prominence of higher frequency modes increase with offshore distance and the Rayleigh number for the considered shallow region. For a given offshore distance, the frequency modes of instability are the same over the local depth, but the prominence of higher frequency modes increases with depth. It is found that the scaling relation for the stable convection region specified in the previous investigation is also applicable to the time-averaged mean flow in the unstable region.

Natural convection in calm near-shore waters induced by daytime heating or nighttime cooling plays a significant role in cross-shore exchanges with significant biological and environmental implications. Having previously reported an improved scaling analysis on the daytime radiation-induced natural convection, the authors present in this paper a detailed scaling analysis quantifying the flow properties at varying offshore distances induced by nighttime surface cooling. Two critical functions of offshore distance have been derived to identify the distinctness and the stability of the thermal boundary layer. Two flow scenarios are possible depending on the bottom slope. For the relatively large slope scenario, three flow regimes are possible, which are discussed in detail. For each flow regime, all the possible distinctive subregions are identified. Two different sets of scaling incorporating the offshore-distance dependency have been derived for the conduction-dominated region and stable-convection-dominated region respectively. It is found that the scaling for flow in the stable-convection-dominated region also applies to the time-averaged mean flow in the unstable region. The present scaling results are verified by numerical simulations.

This work incorporates scaling analysis to characterise unsteady boundary-layer development for thermo-magnetic convection of paramagnetic fluids with Prandtl numbers (Pr ) greater than one. Under consideration is a square cavity with a quiescent isothermal, Newtonian fluid placed in a micro-gravity condition (g≈0g≈0), and under a uniform vertical gradient magnetic field. A distinct magnetic convection boundary layer is produced by the sudden imposition of a higher temperature on the left-hand side vertical sidewall due to the effect of the magnetic body force generated on the paramagnetic fluid. This magnetic force is proportional to the magnetic susceptibility and the gradient of the square of the magnetic induction. According to Curie’s law, the magnetic susceptibility of a paramagnetic fluid is inversely proportional to the absolute temperature. Thermal convection of a paramagnetic fluid can therefore take place even in zero-gravity environments as a direct consequence of temperature differences occurring within the fluid placed within a magnetic field gradient. Scaling predictions presented here are verified by numerical simulations It is shown that the transient flow behaviour of the resulting boundary layer can be described by three stages: a start-up stage, a transitional stage and a steady state. Special attention in this work is paid to the dependency of the flow development upon the Prandtl number, varied over the range of 5–100, thus representing various fluids. Also, the effect of the magnetic momentum parameter, m, and the quantity γRa, upon the flow development obtained in numerical simulations confirms the accuracy of new scaling predictions for paramagnetic fluids.

Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity, which includes a lower intrusion under the fin, a starting plume bypassing the fin and a thermal flow entrained into the vertical thermal boundary layer downstream of the fin in a typical case, are investigated using a scaling analysis and direct numerical simulations. The obtained scaling relations show that the thickness and velocity of the transient natural convection flows around the fin are determined by different dynamic and energy balances, which can be either a buoyancy-viscous balance or a buoyancy-inertial balance, depending on the Rayleigh number, the Prandtl number and the fin length. A time scale of the transition from a buoyancy-viscous flow regime to a buoyancy-inertial flow regime is obtained. The major scaling relations quantifying the transient natural convection flows are also validated by direct numerical simulations. In general, there is a good agreement between the scaling predictions and the corresponding numerical results.

A scaling analysis is presented for the transient boundary layer established on a vertical wall following non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time. The scaling analysis is verified by comparison with numerical solutions of the full equations of motion and energy. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady state before the temperature growth is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time, and the fluid acceleration also changes character. If the wall temperature growth period is sufficiently short, the boundary layer commences differently, but after the wall temperature growth is completed, the boundary layer develops as though the start up had been instantaneous. In both cases, the ultimate steady state is the same as if the start up had been instantaneous; however the different transient nature may have implications for the stability of the boundary layer or of the subsequent development of the flow in a cavity of which the wall is one boundary.

The coupled thermal boundary layers adjacent to a partition in a differentially heated cavity are numerically investigated. The cavity is filled with water, which is initially quiescent but with an imposed temperature difference between the two sides of the vertical partition. The numerical results show that the development of natural convection flows in the partitioned cavity undergoes three main stages: an initial stage, a transitional stage and a steady stage. The transient features of the coupled thermal boundary layers adjacent to the partition as well as the overall natural convection flow in the partitioned cavity are described, and heat transfer through the coupled thermal boundary layers and the partitioned cavity is examined.

The effect of a strong magnetic field on the average heat transfer rate and flow profiles of joint gravitational and thermo-magnetic convection of a paramagnetic fluid in a cubic enclosure heated from below and cooled from above was experimentally investigated. The working fluid consisted of 80% mass glycerol aqueous solution with a concentration of 0.8 mol/kg gadolinium nitrate hexahydrate making it paramagnetic. The cubic enclosure of 32-mm sides was located in the 10-cm bore of a horizontally oriented 5-Tesla super-conducting magnet at a position where the magnetic force distribution was relatively uniform. Under this configuration, the magnetic field imposed in the horizontal direction acted perpendicularly to gravity. It was found that the heat transfer rate through the cube increased with the increase of the magnetic induction. Furthermore, steady and transient state flow visualizations were carried out with a 10-Tesla super-conducting magnet to show a change in the temperature field when magnet-thermo convection dominated. Visualization was made using thermo-chromic liquid crystal slurry added to the working fluid and illuminated in a vertical cross-section of the cube.

The present numerical investigation is concerned with the transient flow response in a reservoir model to periodic heating and cooling at the water surface. The numerical modelling reveals a stable stratification of the water body during the heating phase and an unsteady mixing flow in the reservoir during the cooling phase. It is shown that thermal instabilities play an important role in breaking up the residual circulation and initiating a reverse flow circulation in deep waters when the thermal conditions switch from heating to cooling. Further, if cooling is sufficiently strong, a clear undercurrent is formed, bringing cold water to the deep region of the reservoir. Moreover, heating from the water surface results in a stable large-scale convective roll which is clearly observed in the simulations. Understanding of the flow mechanisms pertinent to this problem is important for predicting the transport of nutrients and pollutants across reservoirs.

The present study is concerned with radiation-induced natural convection in a water-filled triangular enclosure with a sloping bottom, which is directly relevant to buoyancy-driven flows in littoral regions. An improved scaling analysis is carried out to reveal more detailed features of the flow than a previously reported analysis. Two critical functions of the Rayleigh number with respect to the horizontal position are derived from the scaling for identifying the distinctness and stability of the thermal boundary layer. Four flow scenarios are possible, depending on the bottom slope and the maximum water depth. For each flow scenario, the flow domain may be composed of multiple subregions with distinct thermal and flow features, depending on the Rayleigh number. The dividing points between neighbouring subregions are determined by comparisons of the critical functions of the Rayleigh number with the global Rayleigh number. Position-dependent scales have been established to quantify the flow properties in different subregions. The different flow regimes for the case with relatively large bottom slopes and shallow waters are examined in detail. The present scaling results are verified by numerical simulations.

The average heat transfer rate of joint gravitational and magnetic convection of a paramagnetic fluid (an 80% mass aqueous solution of glycerol with 0.8 mol/kg concentration of gadolinium nitrate hexahydrate) in a cubic enclosure heated from below and cooled from above is experimentally measured for five different strengths of the magnetic field. The cubic enclosure of 0.032-m sides is placed in the bore of a 5-Tesla super-conducting magnet below the solenoid centre at a position where the magnetic force distribution is relatively uniform. The magnetic field imposed in the vertical direction acts against gravity and the heat transfer rate decreases with the increase of the magnetic induction. Furthermore, steady and transient states flow visualizations are carried out with a 10-Tesla super-conducting magnet to show a stable stratification obtained in the form of magneto-thermal.

The transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity is numerically investigated. The numerical results are compared with a previously reported experiment. It is demonstrated that the transient flow obtained numerically shows features consistent with the experimental flow. Based on the present numerical results, the temporal development and spatial structures of the thermal flow around the fin are described, and the separation of the thermal flow above the fin is discussed. It is found that the presence of the fin changes the flow regime and results in the transition of the thermal flow to a periodic flow. The present numerical results also indicate that the unstable temperature configuration above the fin results in intermittent plumes at the leeward side of the fin, which in turn induce strong oscillations of the downstream boundary layer flow. It is demonstrated that the oscillations of the boundary layer flow significantly enhance the heat transfer through the finned sidewall (by up to 23%).

The present work is concerned with magnetic convection of a paramagnetic fluid in a cubic enclosure heated and cooled from the sidewalls. The influence of a 10-T transverse magnetic field on the convection mode of a paramagnetic fluid and the heat transfer rate was investigated numerically and experimentally, and compared with gravitational natural convection. The present study clearly shows that natural convection can be enhanced and the direction of the convective flow can be changed when using a strong magnetic field in terrestrial conditions.

The unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity is visualized using a shadowgraph technique and measured using fast-response thermistors. Experiments show that the transition of the unsteady thermal flow around the fin from initiation by sudden heating to a quasi-steady state undergoes a number of stages including the formation of a horizontal gravity current under the fin and a starting plume bypassing the fin, entrainment into the downstream thermal boundary layer, and separation and oscillations of the thermal flow above the fin. We present a series of flow visualization images to describe the transition of the unsteady thermal flow, and obtain the unsteady velocity scales of the fronts of the lower intrusion and starting plume as functions of the time and Rayleigh number, which are verified by the results of the flow visualization experiments. In the transition to the quasi-steady state, separation and oscillations of the thermal flow above the fin are observed. It is demonstrated that these oscillations, which are sensitive to the geometry of the fin, trigger instability of the downstream thermal boundary layer flow and thus enhance convection. It is found that the frequency of the oscillations is a linear function of the Rayleigh number.

This study is concerned with transient natural convection in a water-filled isosceles triangular enclosure subject to cooling at the inclined surfaces and simultaneous heating at the base. The unsteady flows over a range of Grashof numbers are visualized using a shadowgraph technique, and corresponding numerical simulations are carried out using a Finite Volume Method. Both the experiments and numerical simulations have revealed that the transient flow development in the enclosure due to abrupt heating and cooling through the boundaries can be classified into three distinct stages, that is, an early stage, a transitional stage, and a steady/quasi-steady stage. The major flow features at each of the three stages are described and the Grashof number effects on the flow development and heat transfer are discussed. It is found that, for a fixed aspect ratio of 0.5, a transition of the unsteady flow from symmetric to asymmetric structures occurs for Grashof numbers above 2.95 × 104. Moreover, the present heat transfer calculations indicate that the average Nusselt number over the inclined and horizontal surfaces approximately scales with Gr0.2.

A cube was filled with an aqueous solution of glycerol with the addition of gadolinium nitrate hexahydrate to make the working fluid paramagnetic. A very small amount of liquid crystal slurry was then added in order to visualize the local temperature inside the enclosure. One vertical wall of the cube was uniformly heated by nichrome wire from a DC power supply while the opposite one was cooled by cold water flowing from a thermostatic circulator. The system was placed close to the solenoid of a superconducting magnet which was horizontally oriented. Two cases were considered in the experiment: the first with the cooled wall close to the solenoid and the second with the heated wall close to the magnet's electric multi-wires. Natural convection was investigated for both cases: first without a magnetic field and second with various strengths of magnetic force acting on the system. The experimental results showed clearly suppression and enhancement of natural convection. Corresponding numerical computations were carried out for comparison with the experimental data. For this purpose, isotherms of the experimental data were extracted from the color images using the Particle Image Thermometry method and were compared with the numerical results.