Transient heat transfer behaviors in cylindrical porous beds at relatively large Reynolds numbers

The transient behavior of heat transfer in a cylindrical porous bed was examined experimentally under various factors (flow rate, diameter of spherical solid particle, temperature of flowing fluid and physical properties of porous bed). In these factors, it was understood that especially flow rate and the diameter of the particled have important role in evaluating the transient behavior of heat transfer in the porous bed. That is, as the flow rate and the diameter of the particle under a constant diameterD of the cylindrical bed are increased, mean heat transfer coefficient between flowing fluid and the solid particles is increased and the time period to reach a thermally steady state is decreased. The useful experimental correlation equations of mean heat transfer coefficient and the time period to reach the steady state were derived with the functional relationships of Nusselt numberNu _d =f(d/D, Reynolds numberRe _d ) and Fourier numberFo =f (modified Prandtl numberPr*, d/D, Re _d ).     

A note on an improvement of heat transfer of tube banks

An experimental investigation has been conducted for exploring a possibility to improve the heat transfer of tube banks of in-line arrangement, in which the first cylinder was roughened with pyramids. Measured were the heat transfer characteristics of the first cylinder for several cylinder spacings. It is found that there exists the critical Reynolds numberRe _c , beyond which the heat transfer rate increases drastically by about 30 to 50% as compared with that for the smooth cylinder, though the increasing rate is small for the case of very narrow spacing such asC _y /d×C _x /d =1.2×1.2. In the region ofRe>Re _c , the separation point shifts downstream to θ=120° to 130° from the forward stagnation point, and it results in the decrease of the form drag.     

A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

Mixed convection heat transfer from three heated square cylinders in cross-flow at low Reynolds numbers

This paper presents the effects of cross buoyancy and Prandtl number on the flow and heat transfer characteristics around three equal isothermal square cylinders arranged in a staggered configuration within an unconfined medium. Transient two-dimensional numerical simulations are performed with a finite volume code based on the SIMPLEC algorithm in a collocated grid system. The pertinent dimensionless parameters, such as Reynolds, Prandtl and Richardson numbers are considered in the range of 1 ≤ Re ≤ 30, 0.7 ≤ Pr ≤ 100 and 0 ≤ Ri ≤ 1. The representative streamlines, vortex structures and isotherm patterns are presented and discussed. In addition, the overall drag and lift coefficients and average Nusselt numbers are determined to elucidate the effects of Reynolds, Prandtl and Richardson numbers on flow and heat transfer. The flow is observed to be steady for all the ranges of parameters considered. The drag coefficient is found to decrease with Re (for Ri = 0) and Ri at low Pr, whereas it increases with Pr at higher Ri. The lift coefficient decreases with Ri at low Pr and increases with Pr at higher Ri. The time and surface average cylinder Nusselt number is found to increase monotonically with Re as well as Pr while it remains almost insensitive to Ri at low Pr.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Binary diffusion and heat transfer in laminar mixed convection channel flows with uniform wall heat flux: extremely thin film thickness

A detailed numerical study has been performed to investigate the combined heat and mass transfer in laminar mixed convection channel flows with uniform wall heat flux. In an initial effort the liquid film on the channel wall is assumed to be extremely thin in thickness. Major dimensionless groups governing the present problem areGr _T,Gr _Mx,Pr,Sc, φ andRe. Results are specifically presented for an air-water system under various conditions. The effects of wall heating flux, the Reynolds number and the relative humidity of the moist air in the ambient on the momentum, heat and mass transfer in the flow are investigated in great detail.     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.     

Mixed convection boundary layer flow over a horizontal circular cylinder with Newtonian heating

The steady mixed convection boundary layer flow over a horizontal circular cylinder, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered in this study. The governing boundary layer equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into non-similar equations before they are solved numerically using a numerical scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient Re ^1/2 C _f and the local wall temperature θ _w (x) as well as the velocity and temperature profiles with two parameters, namely the mixed convection parameter λ and the Prandtl number Pr.     

Passive Scalar Transport in a Turbulent Cylinder Wake in the Presence of a Downstream Cylinder

This work aims to investigate how the presence of a downstream cylinder affects the passive scalar transport in a cylinder wake. The wake was generated by two tandem brass circular cylinders of the same diameter (d). The cylinder centre-to-centre spacing L/d was 1.3, 2.5 and 4.0, respectively, covering the three typical flow regimes of this flow. The upstream cylinder was slightly heated. Measurements were conducted at x/d= 10 and Re (≡ dU _∞/ν, where U _∞ is the free-stream velocity and ν is the kinematic viscosity of fluid) = 7000. A three-wire probe consisting of an X-wire and a cold wire was used to measure the velocity and temperature fluctuations, while an X-wire provided a phase reference. The phase-averaged velocity vectors and vorticity display single vortex street behind the downstream cylinder, irrespective of the flow regimes. However, the detailed flow structure exhibits strong dependence on L/d in terms of the Strouhal number, the vortex strength and its downstream evolution. This naturally affects passive scalar transport. The coherent and incoherent heat flux vectors show significant variation for different L/d.     

Dean-coupled inertial migration and transient focusing of particles in a curved microscale pipe flow

The Dean-coupled inertial migration of neutrally buoyant spherical particles that are suspended in a curved microscale pipe flow was experimentally investigated in the range of $ 6.4 \le {\text{Re}} \le 129 $ and $ 1.69 \le De \le 34.1 $ . The three-dimensional positions of the particles were measured by using digital holographic microscopy. The diameter of the microtube was 350???m, and the ratios of the tube diameter (D) to the particle diameter (d) were D/d?=?12, 23, 35, and 50. Over a critical value of the Focusing number (F _C), the particles were initially tubular-pinched at the entrance of the curved region. The detailed structures of the Segré?CSilberberg annulus as well as its deformation attributed to secondary flow were analyzed. Diverse agglomeration patterns of particles corresponding to the various flow conditions were observed. The optimal conditions that induced the particles to focus at a certain lateral position were determined.     

Effect of cylinder proximity to the wall on channel flow heat transfer enhancement

Heat-transfer enhancement in a uniformly heated slot mini-channel due to vortices shed from an adiabatic circular cylinder is numerically investigated. The effects of gap spacing between the cylinder and bottom wall on wall heat transfer and pressure drop are systemically studied. Numerical simulations are performed at Re=100$\mathit{Re}=100$, 0.1?Pr?10$0.1?\mathrm{Pr}?10$ and a blockage ratio of D/H=1/3$D/H=1/3$. Results within the thermally developing flow region show heat transfer augmentation compared to the plane channel. It was found that when the obstacle is placed in the middle of the duct, maximum heat transfer enhancement from channel walls is achieved. Displacement of circular cylinder towards the bottom wall leads to the suppression of the vortex shedding, the establishment of a steady flow and a reduction of both wall heat transfer and pressure drop. Performance analysis indicates that the proposed heat transfer enhancement mechanism is beneficial for low-Prandtl-number fluids.     

Forced convection heat transfer on a heated bottom surface of cavity with different wall-height

Experiments to obtain the heat transfer characteristics of cavity, in which the downstream wall-heightD ₂ was changed from zero toD ₁ of upstream wall-height, have been performed. The vortex flow inside cavity was varied complicatedly depending on aspect-ratio of cavity and main flow velocity, and the flow pattern for cavity ofD ₂/D ₁=0.8 was altered entirely at theRe _H of about 1.5×10⁴. Three heat transfer regions ofNu _m versusRe _H were recognized for the cavity of large aspect-ratio. A close relation between those heat transfer behavior and approaching boundary layer flow was found. Heat transfer correlation was partially obtained for every cavities.     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

Delay in response of turbulent heat transfer against acceleration or deceleration of flow in a pipe

To predict the heat transfer enhancements that result from the application of a pulsating flow in a pipe, we experimentally investigated the turbulent heat transfer variations produced in response to sudden accelerations or decelerations to flows within a pipe. To accomplish this, the Reynolds numbers with the valve open (Re₁) and close (Re₀) were systematically varied in the range of 8,000 ≤ Re₁ ≤ 34,000 and 700 ≤ Re₀ ≤ 23,000, respectively, and in-pipe spatiotemporal heat transfer variations were measured using infrared thermography simultaneously with temporal variations to the in-pipe flow properties. Based on the experimental results, it was found that the heat transfer delays that occur in response to accelerations or decelerations can be characterized using the corresponding time lag Δt and first-order time constant τ. The values of Δt and τ can be expressed as non-dimensional forms of Δt/(ν/u_τ²) and τ/(R/u_τ), respectively, where u_τ is the pipe wall friction velocity, ν is the kinematic viscosity of the fluid, and R is the pipe radius.     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

Flow around a cylinder surrounded by a permeable cylinder in shallow water

The change in flow characteristics downstream of a circular cylinder (inner cylinder) surrounded by an outer permeable cylinder was investigated in shallow water using particle image velocimetry technique. The diameter of the inner cylinder and the water height were kept constant during the experiments as d?=?50?mm and h _w ?=?25?mm, respectively. The depth-averaged free-stream velocity was also kept constant as U?=?170?mm/s which corresponded to a Reynolds number of Re_d?=?8,500 based on the inner cylinder diameter. In order to examine the effect of diameter and porosity of the outer cylinder on flow characteristics of the inner cylinder, five different outer cylinder diameters (D?=?60, 70, 80, 90 and 100?mm) and four different porosities (???=?0.4, 0.5, 0.6 and 0.7) were used. It was shown that both porosity and outer cylinder diameter had a substantial effect on the flow characteristics downstream of the circular cylinder. Turbulent statistics clearly demonstrated that in comparison with the bare cylinder (natural case), turbulent kinetic energy and Reynolds stresses decreased remarkably when an outer cylinder was placed around the inner cylinder. Thereby, the interaction of shear layers of the inner cylinder has been successfully prevented by the presence of outer cylinder. It was suggested by referring to the results that the outer cylinder having 1.6????D/d????2.0 and 0.4????D/d????0.6 should be preferred to have a better flow control in the near wake since the peak magnitude of turbulent kinetic energy was considerably low in comparison with the natural case and it was nearly constant for these mentioned porosities ??, and outer cylinder to inner cylinder diameter ratios D/d.     

Measurements of heat transfer coefficients between turbulent liquid jets and a radially finned heated disk placed at the bottom of an open vertical circular cavity

 Experiments have been performed to assess the impact of an extended surface on the heat transfer enhancement for axisymmetric, turbulent liquid jet impingement on a heated round disk. The disk, with an array of integral radial fins mounted on its surface, is placed at the bottom of an open vertical circular cavity. Hydrodynamic and heat transfer data were obtained for a dielectric fluorocarbon liquid FC-77. For a fixed circular heater of diameter D=22.23 mm, several geometric parameters were tested: the nozzle diameter (4.42≤d≤9.27 mm), the confining wall diameter of the vertical cavity (22.23≤D _c≤30.16 mm), and the nozzle-to-heater spacing (0.5≤S/d≤5.0). The FC-77 flow rates varied from =0.2 to 11.0 l/min producing Reynolds numbers in the wide interval 700≤Re _d ≤44,000. For d=4.42 mm, the heat transfer response to the separation distance S/d was small but increased gradually with increasing nozzle diameter up to d=9.27 mm. The thermal resistance R _th increased with the confining wall diameter D _c and also with the nozzle diameter d. A minimum value of the thermal resistance of R _th,min=0.4 cm² K/W was attained for a combination of d=4.42 mm, D _c=22.23 mm, S/d=1, and =7.5 l/min. Based on a simplified heat transfer model, reasonable agreement was obtained between measured values of the thermal resistance and the R _th-predictions. The total fin effectiveness ɛ_f was shown to increase with increasing nozzle diameter, but was invariant with the flow rate (or the jet exit velocity). More than a three-fold heat transfer enhancement was realized through the addition of the array of integral radial fins on the heated round disk. Received on 30 August 2000 / Published online: 29 November 2001     

Effect on the flow and heat transfer characteristics for sinusoidal pulsating laminar flow in a heated square cylinder

Two-dimensional numerical simulation is performed to understand the effect of flow pulsation on the flow and heat transfer from a heated square cylinder at Re = 100. Numerical calculations are carried out by using a finite volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid. The effects of flow pulsation amplitude (0.2 ≤ A ≤ 0.8) and frequency (0 ≤ f _p  ≤ 20 Hz) on the detailed kinematics of flow (streamlines, vorticity patterns), the macroscopic parameters (drag coefficient, vortex shedding frequency) and heat transfer enhancement are presented in detail. The Strouhal number of vortices shedding, drag coefficient for non-pulsating flow are compared with the previously published data, and good agreement is found. The lock-on phenomenon is observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, time averaged drag coefficient and heat transfer from the square cylinder is substantially augmented, and when the pulsating frequency in about the natural vortex shedding frequency, the heat transfer is also substantially enhanced. In addition, the influence of the pulsating amplitude on the time averaged drag coefficient, heat transfer enhancement and lock-on occurrence is discussed in detail.     

Convection heat transfer of closely-spaced spheres with surface blowing

A validated computer simulation model has been developed for the analysis of colinear spheres in a heated gas stream. Using the Galerkin finite element method, the steady-state Navier-Stokes and heat transfer equations have been solved describing laminar axisymmetric thermal flow past closely-spaced monodisperse spheres with fluid injection. Of interest are the coupled nonlinear interaction effects on the temperature fields and ultimately on the Nusselt number of each sphere for different free stream Reynolds numbers (20 ≤Re ≤ 200) and intersphere distances (1.5 ≤d _ij ≤ 6.0) in the presence of surface blowing (0 ≤v _b < 0.1). Fluid injection (i.e. blowing) and associated wake effects generate lower average heat transfer coefficients for each interacting sphere when the Reynolds number increases (Re>100). Heat transfer is also reduced at small spacings especially for the second and third sphere. A Nusselt number correlation for each interacting (porous) sphere has been developed based on computer experiments.     

Characterisation of gas-liquid two-phase flow in minichannels with co-flowing fluid injection inside the channel,part I: unified mapping of flow regimes

Present research highlights the potential of apparatuses with integrated minichannel packings to intensify gas-liquid-solid contacting. Especially an operation of these devices within the Taylor flow regime gained extraordinary attention due to its excellent heat and mass transfer and the segmented flow characteristics. However, criteria for flow regime transitions are mainly developed from water-similar fluids and are contradictory which hinders uniform flow regime prediction.This work presents a systematic analysis of adiabatic gas-liquid downflow in a square minichannel of 1.0 mm hydraulic diameter. In the mixing zone located within the flow channel, gas was injected into the co-flowing liquid by so-called capillary injectors with variable inner diameter (0.184, 0.317, 0.490 mm). Experiments were conducted using water, water-glycerol, and water-ethanol mixtures to cover a broad range of material properties. The gas and liquid superficial velocities were varied between 9.81·10^-4…2.72 m/s and 1.7·10⁻⁴…0.80 m/s, respectively. Taylor flow, Taylor-annular flow, annular flow, churn flow, and bubbly flow were observed. Using the Pi-theorem, 8 significant dimensionless groups dictating the flow transition were identified, namely u_{G, s}/u_{L, s}, Re_G, Re_L, We_G, We_L, Θ*, d_{In, CI}/d_h, and d_{Ou, CI}/d_h. Based on more than 1500 experimental data, criteria for the regime transitions of Taylor flow are provided. The derived flow regime map shows good agreement for all applied liquids and for the two larger injector geometries.