Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

Simulation for flow across heated square cylinders

The thermal lattice Boltzmann method is used to examine forced convection heat transfer from six inline heated square cylinders for Re = 100 at 0.5 ≤ s/d ≤ 4.0, where s is the distance between the surfaces of two cylinders and d is the cylinder size. Such a heat transfer is transient in nature for which the present work reports heat transfer regimes such as synchronous, quasiperiodic and chaotic. For 0.5 ≤ s/d ≤ 1.5 the heat transfer is synchronous, for 1.5 ≤ s/d ≤ 3.0 it is quasiperiodic and for 3.0 ≤ s/d ≤ 4.0 it is chaotic in nature at Re = 100. These regimes are confirmed through cylinder Nusselt number signals, its power spectra, and heat wake interference. The appearance of heat transfer regimes for inline heated cylinders is similar to the appearance of flow regimes for inline unheated cylinders except for the fact that transition from synchronous to quasiperiodic regime occurs at s/d = 1.5 for heat transfer and at s/d = 1.1 for flow. The synchronous heat transfer regime is characterized by a single heat wake that envelopes all cylinders while quasiperiodic heat transfer regime is characterized by the formation of thermal blobs in the gap between cylinders. A chaotic heat transfer regime is characterized by the shedding of thermal blobs and interference of thermal blobs by downstream cylinders. Regardless of spacing, the average Nusselt number encountered by cylinders is smaller than that for the isolated cylinder. The novelty of the work is that transitions occurring in the flow of heat are considered for an understanding of heat flow from bluff bodies.     

HEAT AND FLUID FLOW ACROSS A SQUARE CYLINDER IN THE TWO-DIMENSIONAL LAMINAR FLOW REGIME

The flow structure and heat transfer characteristics of an isolated square cylinder in cross flow are investigated numerically for both steady and unsteady periodic laminar flow in the two-dimensional regime, for Reynolds numbers of 1 to 160 and a Prandtl number of 0.7. The effect of vortex shedding on the isotherm patterns and heat transfer from the cylinder is discussed. Heat transfer correlations between Nusselt number and Reynolds number are presented for uniform heat flux and constant cylinder temperature boundary conditions.     

On the combined influence of Reynolds number and cylinder spacing for flow around a row of heated square cylinders

The characteristics of forced convection heat transfer across a row of heated square cylinders kept in side-by-side arrangement are numerically investigated to examine the combined effects of Reynolds number and cylinder spacing for Ri = 0, 60 ≤ Re ≤ 160, Pr = .71, and s/d = 1.0–8.0, where the space between cylinder surfaces is s and the cylinder size is d. A numerical study was carried out using the thermal lattice Boltzmann method. The goal of this work is to explore the transitions in heat transfer phenomenon that occurs behind the cylinder and to report the corresponding regimes for heat transfer namely synchronous, quasiperiodic, and chaotic. The proposed regime of heat flow is a function of Reynolds number and spacing. The synchronous heat regime is obtained for s/d ≥ 5.0 and quasiperiodic, chaotic regimes are observed for 3.0 ≤ s/d < 5.0, s/d < 3.0, respectively at Re = 100. The instantaneous isotherms, the power spectra of the corresponding Nusselt number signals, and the significance of cylinder Nusselt number frequency are used to examine these heat flow regimes. The heat transfer regimes for a row of heated cylinders and flow regimes for a row of unheated cylinders both have comparable appearances except for the fact that the heat transfer regime is synchronous at s/d ≥ 5.0 and flow is synchronous at s/d ≥ 4.0. The chaotic or quasiperiodic heat transfer regimes occur due to merging and strong interactions between thermal blobs shed from the cylinders. Heat transfer is synchronous at a higher spacing and characterized by independent thermal blobs shedded from the cylinders. It is reported that as spacing reduces and Reynolds number increases, the mean value of the Nusselt number experienced by all cylinders increases. The important outcome of the present numerical work is that for understanding heat transfer from bluff body, the transitions that occur in heat transfer are useful.     

Forced convection of flow past two tandem rectangular cylinders in a channel

This work performed the first numerical investigation on the forced convection of flow past two tandem rectangular cylinders in a channel at Re?=?100. The aspect ratio (AR) and gap ratio (GR) of the two cylinders are chosen at AR?=?1(1)4 and GR?=?1(1)8, respectively. The objective of the present work is to explore the effects of AR and GR on the characteristic flow and heat transfer quantities for the rectangular geometry that has not been studied before. The effects of the two parameters are presented by the instantaneous flow pattern, characteristic aerodynamic and heat transfer quantities, local heat transfer rate, flow patterns in the gap and near wake, and temperature distribution on the channel walls. Both time-averaged and fluctuating quantities are analyzed and presented. Numerical results reveal that for cylinders of all ARs, there are two flow regimes categorized based on the GR: the steady flow regime at GR?≤?3, where the gap flow is steady, and the unsteady flow regime at GR?≥?4. The characteristic aerodynamic and heat transfer quantities abruptly change as the flow transits from steady to unsteady regime especially for the downstream cylinder. The time-averaged and maximum fluctuating local heat transfer rate for the upstream cylinder almost does not vary with the GR, whereas they substantially vary for the downstream cylinder. The AR affects the magnitude of the quantities but not their variation trends. For flows in the unsteady regime, the recovery of the wake flow after the downstream cylinder is much more rapidly than those of steady flows due to the acceleration arising from the instability brought by the incoming shedding vortices. The violent shedding also effectively enhances heat transfer and increases the temperature of the channel walls.     

Fully-Developed Flow in a Furrowed Wavy Channel: Characterization of Unsteady Flow Regimes and Its Effect on Thermal-Hydraulic Performance

Numerical study is done at various Reynolds numbers (100–2000), for periodically fully developed flow and heat transfer in five geometrically different wavy channels. Time signal analysis is done to distinguish various unsteady flow regimes and a flow regime map is proposed; demarcating steady, two types of periodic as well as quasi-periodic, and chaotic flow regimes. Temporal variation of flow structure and Nusselt number as well as friction factor are presented – in the various unsteady regimes – and discussed for a unified cause-and-effect study. Effect of different flow regimes on the thermal-hydraulic performance of wavy as compared to plane channel is presented. Effect of Prandtl numbers (0.01–100) is also studied.     

Heat Transfer Characteristics during Mist Cooling on a Heated Cylinder

Mist cooling is expected to contribute to better steel products because it enables uniform and moderate cooling in steel-making processes. In this study, experimental data were obtained to understand the mist cooling process in a high-temperature cylinder. The wetting phenomenon on the cylinder surface was also observed with an installed CCD camera. Comparing these results with those from previous investigations, we found that our cooling curve corresponded to two distinct heat transfer regimes in mist cooling. A simplified model from the analysis was introduced to simulate the cooling curve in each heat transfer regime. The estimated cooling curves by this model agreed with the experimental data in one regime and had a similarity in the other regime.     

Periodic heat transfer in directly opposed free and forced convection flow

An experimental study of the heat transfer from small circular cylinders placed horizontal to a downward flowing air stream is reported. Based on heat-transfer measurements and flow visualization, a model for directly opposed free and forced convection was developed. Three modes of flow were observed. For very low velocities the free convection, buoyant plume dominates the heat transfer. At a “lower critical” Reynolds number, when the free and forced convections are of the same order of magnitude, a well defined periodic heat transfer was obtained. The periodic heat transfer was due to the build-up of the buoyant forces to a magnitude where they overcame the downward force of the air flow. At an “upper critical” Reynolds number the periodic heat transfer abruptly ceases. For velocities greater than the upper critical limit the forces due to the air flow dominate. A potential like, laminar sheet forms, as a shroud around the thermal layer of the hot cylinder. The average heat transfer from the cylinder decreases with increasing Reynolds number for both the case of dominant free convection and the periodic heat-transfer regime. The minimum value of the heat transfer occurred at the upper critical Reynolds number.     

Dynamics and heat transfer in a quasi-two-dimensional MHD flow past a circular cylinder in a duct at high Hartmann number

The fluid flow and heat transfer of a liquid metal past a circular cylinder in a rectangular duct (width-to-height aspect ratio of 2) under a strong transverse magnetic field is studied numerically using a quasi-two-dimensional model. Transition from steady to unsteady flow regimes is determined as a function of Hartmann number and blockage ratio, as are Strouhal number, and the heat transfer from the heated wall to the fluid. Downstream cross-stream mixing induced by the cylinder wake was found to increase heat transfer by more than a factor of two in some cases.     

Local heat transfer analysis for boiling of hydrocarbons in complex geometries: A new approach for heat transfer prediction in staggered tube bundle

This paper deals with heat transfer analysis for boiling flow in staggered tube bundle. A local analysis is performed to determine the heat transfer coefficient linked to local flow regimes by optical fibre. The first part of the paper is devoted to the literature survey of the main existing studies on the topic. We show that published heat transfer correlations deviate largely from each others and also from the experimental results that have been carried out. On these features, a new approach has been developed. It is based on the relationship between flow regimes and thermal characteristics. An experimental setup has been developed for the determination of the local heat transfer and the two-phase flow void fraction. A detailed analysis of the two-phase flow has been performed in a previous paper [1] in which two regimes were identified. In the present paper, focus is done on the heat transfer analysis in relation with the flow regime map. This new approach allows a better prediction of the heat transfer coefficient. For the bubbly flow, the heat transfer coefficient is well predicted by a classical correlation corresponding to nucleate boiling regime. For the dispersed flow, classical correlations for convective boiling are not adapted anymore for tube bundle. We evidenced that heat coefficient is mainly controlled by the vapour flow and a heat transfer law is derived using the vapour Reynolds number and vapour Prandlt number. These two heat transfer laws are used to evaluate heat transfer coefficient in the intermediate regime.     

Numerical study of different gas–solid flow regimes effects on hydrodynamics and heat transfer performance of a fluidized bed reactor

In this study, a two‐?uid Eulerian–Eulerian model has been carried out applying the kinetic theory of granular flow (KTGF) to study the hydrodynamics and heat transfer behavior of a fluidized bed reactor simultaneously. The effects of different gas–solid flow regimes on the operating conditions and heat transfer rate between the hot air and two types of low and high‐density inert particles are investigated in a fluidized bed dryer. Different gas–solid flow regimes for wood and glass particles of groups A, B, and D of Geldart's classification are simulated to introduce the most optimal flow regime in terms of heat transfer rate and operating costs. The compromise between the heating rate, the height required for the reactor, and the ratio of the final mass to the initial mass of solid particles, which specifies the need for a cyclone separator showed that the bubbling regime of Geldart B powder for low‐density particles and the turbulent regime of Geldart D powder or bubbling regime of Geldart B powder for high‐density particles are the optimal operating conditions and flow regimes. Furthermore, it was concluded that the convective heat transfer is the dominant mechanism, which increases with increasing the air velocity and decreasing the particle diameter in each group.     

Combined forced and natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper reports the results of an experimental study of heat transfer by combined forced and natural convection from a horizontal cylinder embedded in a porous medium composed of randomly packed glass spheres saturated with water. The direction of the flow of water was horizontal and normal to the longitudinal axis of the cylinder. The diameter of the cylinder, D, was 11.45mm and the equivalent diameter of the glass spheres was 3.072mm. It is shown that the condition Gr_k/Re²_D ⩽ 0.5 represents a conservative criterion for segregating heat transfer data that are predominantly governed by forced convection from those in which natural convection effects are significant. A correlation hypothesis for convection heat transfer which is based upon four assumptions, primary among which is that the flow can be (conceptually) regarded as being composed of ‘coarse’ and ‘fine’ components, is presented. This hypothesis is shown to provide a basis for successfully correlating a set of experimental heat transfer data that extends from the Darcy regime into the turbulent regime and spans the intervening Forchheimer and transition regimes. It is suggested that the correlation procedure adopted here may yield useful results if applied to other geometries such as, for example, forced convection heat transfer in ducts packed with porous media.     

Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime

The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 ? Re ? 160 and 0.7 ? Pr ? 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.     

Constructal multi-scale cylinders with natural convection

This paper shows that in a space filled with assemblies of cylinders cooled by natural convection the heat transfer density can be increased progressively by the use of cylinders of several sizes, and the optimal placement of each cylinder in the assembly. Smaller cylinders are placed closer to the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that has not yet been used for heat transfer. The paper reports the optimized flow architectures and performance for structures with one and two cylinder sizes, which correspond to structures with one and two degrees of freedom. The heat transfer rate density increases as the optimized structure becomes more complex. The optimized cylinder diameters are relatively robust, i.e., insensitive to changes in complexity and flow regime (Rayleigh number). The optimized spacings decrease monotonically as the Rayleigh number increases. The structure performance can be improved by endowing the cylinder assemblies with more degrees of freedom.     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

Direct numerical simulation of fluid flow and heat transfer in periodic wavy channels with rectangular cross-sections

Fully-developed flow and heat transfer in periodic wavy channels with rectangular cross sections are studied using direct numerical simulation, for increasing Reynolds numbers spanning from the steady laminar to transitional flow regimes. The results show that steady flow is characterized by the formation of symmetric secondary flow or Dean vortices when liquid flows past the bends. It is found that the patterns of Dean vortices may evolve along the flow direction, thus leading to chaotic advection, which can greatly enhance the convective fluid mixing and heat transfer. With increasing Reynolds numbers, the flow undergoes transition from a steady state to a periodic one with a single frequency, and subsequently to a quasiperiodic flow with two incommensurate fundamental frequencies. Within these unsteady regimes, the flow is characterized by very complex Dean vortices patterns which evolve temporally and spatially along the flow direction, and the flow symmetry may even be lost. Further increase in Reynolds number leads to chaotic flow, where the Fourier spectrum of the velocity evolution becomes broadband. The bifurcation scenario in wavy channels may thus share some common features with the well-known Ruelle–Takens–Newhouse scenario. Heat transfer simulation in all flow regimes is carried out with constant wall temperature condition and liquid water as the coolant. It is found that due to the efficient mixing in wavy channels, the heat transfer performance is always significantly more superior to that of straight channels with the same cross sections; at the same time the pressure drop penalty of wavy channels can be much smaller than the heat transfer enhancement. The present study shows that these wavy channels may have advantages over straight channels and thus serve as promising candidates for incorporation into efficient heat transfer devices.     

Transition of natural convection boundary layers—a revisit by Bicoherence analysis

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.     

Time periodic flow boiling heat transfer of R-134a and associated bubble characteristics in a narrow annular duct due to flow rate oscillation

An experiment is conducted here to investigate the effects of the imposed time periodic refrigerant flow rate oscillation in the form of nearly a triangular wave on refrigeriant R-134a flow boiling heat transfer and associated bubble characteristics in a horizontal narrow annular duct with the duct gap fixed at 2.0 mm. The results indicate that when the imposed heat flux is close to that for the onset of stable flow boiling, intermittent flow boiling appears in which nucleate boiling on the heated surface does not exist in an entire periodic cycle. At somewhat higher heat flux persistent boiling prevails. Besides, the refrigerant flow rate oscillation only slightly affects the time-average boiling curves and heat transfer coefficients. Moreover, the heated wall temperature, bubble departure diameter and frequency, and active nucleation site density are found to oscillate periodically in time as well and at the same frequency as the imposed mass flux oscillation. Furthermore, in the persistent boiling the resulting heated wall temperature oscillation is stronger for a longer period and a larger amplitude of the mass flux oscillation. And for a larger amplitude of the mass flux oscillation, stronger temporal oscillations in the bubble characteristics are noted. The effects of the mass flux oscillation on the size of the departing bubble and active nucleation site density dominate over the bubble departure frequency, causing the heated wall temperature to decrease and heat transfer coefficient to increase at reducing mass flux in the flow boiling, opposing to that in the single-phase flow. But they are only mildly affected by the period of the mass flux oscillation. However, a short time lag in the wall temperature oscillation is also noted. Finally, a flow regime map is provided to delineate the boundaries separating different boiling regimes for the R-134a flow boiling in the annular duct.