The influence of tube bundle geometry on cross-flow boiling heat transfer and pressure drop

An experimental investigation was performed to compare the boiling heat transfer coefficients and two-phase pressure drops from a square inline and a staggered tube bundle having the same tube pitch-to-diameter ratio (P/D = 1.30) and from two square inline tube bundles having different pitch-to-diameter ratios (P/D = 1.30 and 1.70). Except at the highest heat fluxes the heat transfer coefficients generally were higher in the staggered tube bundle than in the inline tube bundle and higher in the larger P/D tube bundle than in the smaller. As the heat flux increased, the differences decreased. The differences were attributed to the tradeoff between nucleation and convection. The staggered tube bundle had higher pressure drops than the inline bundle except at low mass velocities; the larger pressure drop in the staggered bundle was attributed to the combination of a larger void fraction and a larger friction multiplier, with the frictional component dominating at higher mass velocities. Comparing the inline tube bundle pressure drops, it was concluded that the larger P/D bundle had a larger void fraction than the smaller P/D tube bundle; no conclusions could be drawn regarding the relative magnitude of the two-phase fraction multiplier.     

Free- and forced-convection film condensation from a horizontal elliptic tube with a vertical plate and horizontal tube as special cases

A simple mathematical model is developed for the study of the mixed-convection film condensation with downward flowing vapors onto a horizontal elliptic tube. Analytical analysis for both the local condensate film thickness and heat transfer characteristics under simultaneous effects of interfacial vapor shear and pressure gradient has been performed by adopting a unified geometry parameter, eccentricity e. The present results for two limit cases, e = 0 (circular tube) and e = 1.0 (vertical plate) are in an excellent agreement with the earlier works. For very slow vapor flow, the present result for dimensionless mean heat transfer coefficient reduces to the same form as in the earlier works, , whose value is 0.728 for e = 0 and 0.943 for e = 1.0. As for very fast vapor flow, the dimensionless mean heat transfer coefficient, increase with increasing eccentricity under the effects of pressure gradient caused by potential flow and surface tension.     

Heat transfer in tube assemblies under conditions of laminar axial,transverse and inclined flow

This paper considers laminar flow heat transfer in tube assemblies. The main interest is focused on the virtually unexplored cases of heat transfer under conditions of fully-developed flow inclined to the axes of the tubes and of purely transverse developing flow. The limiting cases of purely axial or purely transverse fully-developed flow are also examined. In all cases, the thermal boundary condition on the tubes is constant heat flux. Governing differential equations are expressed in terms of curvilinear-orthogonal coordinates and solved using finite-differences. Results are compared with available theoretical and experimental data. The effect of the transverse component of the flow on the temperature distribution is found to remain very strong even in nearly-axial flows and therefore considerably higher heat transfer coefficients are exhibited by a nearly-axial flow than a purely axial one.     

On natural convection from a vertical plate with a prescribed surface heat flux in porous media

This paper presents a theoretical and numerical investigation of the natural convection boundary-layer along a vertical surface, which is embedded in a porous medium, when the surface heat flux varies as (1 +x ²)), where is a constant andx is the distance along the surface. It is shown that for > -1/2 the solution develops from a similarity solution which is valid for small values ofx to one which is valid for large values ofx. However, when -1/2 no similarity solutions exist for large values ofx and it is found that there are two cases to consider, namely < -1/2 and = -1/2. The wall temperature and the velocity at large distances along the plate are determined for a range of values of .Notation g Gravitational acceleration - k Thermal conductivity of the saturated porous medium - K Permeability of the porous medium - l Typical streamwise length - q _w Uniform heat flux on the wall - Ra Rayleigh number, =gK(q _w /k)l/(v) - T Temperature - Too Temperature far from the plate - u, v Components of seepage velocity in the x and y directions - x, y Cartesian coordinates - Thermal diffusivity of the fluid saturated porous medium - The coefficient of thermal expansion - An undetermined constant - Porosity of the porous medium - Similarity variable, =y(1+x ) ^/3/x ^1/3 - A preassigned constant - Kinematic viscosity - Nondimensional temperature, =(T – T )Ra^1/3 k/qw - Similarity variable, = =y(log_e x)^1/3/x ^2/3 - Similarity variable, =y/x ^2/3 - Stream function     

Heat transfer enhancement in a turbulent natural convection boundary layer along a vertical flat plate

An experimental study on heat transfer enhancement for a turbulent natural convection boundary layer in air along a vertical flat plate has been performed by inserting a long flat plate in the spanwise direction (simple heat transfer promoter) and short flat plates aligned in the spanwise direction (split heat transfer promoter) with clearances into the near-wall region of the boundary layer. For a simple heat transfer promoter, the heat transfer coefficients increase by a peak value of approximately 37% in the downstream region of the promoter compared with those in the usual turbulent natural convection boundary layer. It is found from flow visualization and simultaneous measurements of the flow and thermal fields with hot- and cold-wires that such increase of heat transfer coefficients is mainly caused by the deflection of flows toward the outer region of the boundary layer and the invasion of low-temperature fluids from the outer region to the near-wall region with large-scale vortex motions riding out the promoter. However, heat transfer coefficients for a split heat transfer promoter exhibit an increase in peak value of approximately 60% in the downstream region of the promoter. Flow visualization and PIV measurements show that such remarkable heat transfer enhancement is attributed to longitudinal vortices generated by flows passing through the clearances of the promoter in addition to large-scale vortex motions riding out the promoter. Consequently, it is concluded that heat transfer enhancement of the turbulent natural convection boundary layer can be substantially achieved in a wide area of the turbulent natural convection boundary layer by employing multiple column split heat transfer promoters. It may be expected that the heat transfer enhancement in excess of approximately 40% can be accomplished by inserting such promoters.     

Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers

A numerical investigation of the mixed convection heat transfer from vertical helically coiled tubes in a cylindrical shell at various Reynolds and Rayleigh numbers, various coil‐to‐tube diameter ratios and non‐dimensional coil pitches was carried out. The particular difference in this study compared with other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid‐to‐fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell‐side mass flow rate on shell‐side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell‐side of the heat exchanger reasonably demonstrates the desired relation. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical study of natural convection flow in a vertical slot

The stability of convective motion, generated by a lateral temperature difference across a vertical slot, is studied numerically over a range ofGr=5000 to 1.5 × 10⁵,Pr=0.01 to 10, andA=8,16 and 20. Various cellular flow structures and temperature patterns are illustrated. Several branches of solutions characterized by different numbers of the cells in the flow patterns as well as by both steady and unsteady multicellular patterns are found for low-Prandtl-number fluid in the vertical slot. Meanwhile, the behaviors of the temperature variation and heat transfer are also discussed. The project supported by the National Natural Science Foundation of China (59776011) and by the Returnee from Abroad Funding of Academia Sinica.     

Heat transfer and pressure drop characteristics of turbulent flow in a circular tube fitted with regularly spaced twisted-tape elements

The results of an experimentalnvestigation of turbulent flow heat transfer and pressure drop characteristics in a circular tube fitted with regularly spaced twisted-tape elements connected by thin circular rods are reported. The characteristics are governed by Reynolds number, Prandtl number, twist ratio, space ratio, and rod-to-tube diameter ratio. Correlations for friction factor and Nusselt number are also reported. It is shown that on the basis of both constant pumping power and constant heat duty, regularly spaced twisted-tape elements do not perform better than full-length twisted tapes.     

Mass and heat transfer by natural convection in a vertical cavity

This paper reports a fundamental study of laminar natural convection in a rectangular enclosure with heat and mass transfer from the side, when the bouyancy effect is due to density variations caused by either temperature or concentration variations. In the first part of the study scale analysis is used to determine the scales of the flow, temperature and concentration fields in boundary layer flow for all values of Prandtl and Lewis numbers. In particular, scale analysis shows that in the extreme case where the flow is driven by bouyancy due to temperature variations, the ratio of mass transfer rate divided by heat transfer rate scales as $\text{Le}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ only if (Pr > 1, Le < 1) or (Pr < 1, Sc < 1), and as $\text{Le}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ if (Pr > 1, Le > 1) or (Pr < 1, Sc > 1). In the second part of the study, the boundary layer scales derived in the first part are used to determine the heat and mass transport characteristics of a vertical slot filled with fluid. Criteria for the existence of distinct thermal and concentration boundary layers in the slot are determined. Numerical solutions for the flow and concentration fields in a slot without distinct thermal boundary layers are reported. These solutions support further the method of scale analysis employed in the first part of the study     

Self-induced thermocapillary convection in film boiling heat transfer from a vertical surface in saturated conditions and viscous regimen

Self-induced thermocapillary convection and its significance with regard to film boiling heat transfer from a vertical saturated surface is discussed. Utilizing a simplified geometrical model, an analytical expression (multiplier factor) for the vapor film thickness and heat transfer coefficient corrected by thermocapillary phenomena was derived. The above equation is a new theoretical viewpoint for the enhancement in the heat transfer coefficient observed in the experimental data in the viscous regime and agree qualitatively with available experimental measurements made on R113 coolant.     

Turbulent natural convection scaling in a vertical channel

Using direct numerical simulation (DNS) data, this study appraises existing scaling laws in literature for turbulent natural convection of air in a differentially heated vertical channel. The present data is validated using past DNS studies, and covers a range of Rayleigh number, Ra between 5.4 × 10⁵ and 2.0 × 10⁷. We then appraise and compare the various scaling laws proposed by Versteegh and Nieuwstadt, 1999, Hölling and Herwig, 2005, Shiri and George, 2008, George and Capp, 1979 with the profiles of the mean temperature defect, mean streamwise velocity, normal velocity fluctuations, temperature fluctuations and Reynolds shear stress. Based on the arguments of an inner (near-wall) and outer (channel centre) region, the data is found to support a minus one-third power law for the mean temperature in an overlap region. Using the inner and outer temperature profiles, an implicit heat transfer equation is obtained and we show that a correction term is non-negligible for the present Ra range when compared with explicit equations found in literature. In addition, we determined that the mean streamwise velocity and normal velocity fluctuations collapse in the inner region when using the outer velocity scale. We also find that the temperature fluctuations scale in inner coordinates, in contrast to the outer scaling behaviour reported in the past. Lastly, we show evidence of an incipient proportional relationship between friction velocity, u_τ, and the outer velocity scale, u_o, with increasing Ra.     

An analytical model for the determination of stability boundaries in a natural circulation single-phase thermosyphon loop

In this paper, an extension of previous analyses of natural circulation in a simple single-phase loop is presented. Assuming more general correlations for the friction factor and the heat transfer coefficient, an analytical model describing the system is obtained and a parametric representation of its dynamic behaviour is achieved. On this basis, stability maps can be drawn. A preliminary validation of the analytical model has been carried out by using an independent program developed for the analysis of stability in natural circulation loops. The aim of the present work is to provide a simple analytical tool devoted to the stability analysis of a reference single-phase loop. This model can be applied in a relatively wide range of conditions and regimes to provide benchmark solutions for thermal-hydraulic codes and related nodalisations.     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

Effect of a helical wire on mixed convection heat transfer to carbon dioxide in a vertical circular tube at supercritical pressures

Reactor core of a SCWR (supercritical water-cooled reactor) employs a tight lattice in order to efficiently remove heat from nuclear fuels. In the narrow sub-channels of a tight lattice reactor core, a helical wire instead of a complicated conventional spacer has been used as a turbulence generator and a space-keeper between the fuel rods.A series of experiments were performed in order to investigate an effect of a helical wire on heat transfer to upwardly flowing CO₂ in a electrically-heated circular tube with an inner diameter of 6.32 mm, where a helical wire with an outer diameter of 1.3 mm was tightly inserted inside the tube. The tube inner diameter corresponds to the equivalent hydraulic diameter of a sub-channel of a KAERI’s fuel assembly concept. The mass fluxes ranged from 400 to 1200 kg/m² s; the heat fluxes ranged from 30 to 90 kW/m²; and the pressures were 7.75 and 8.12 MPa. The corresponding Reynolds numbers at the test section inlet ranged from 1.8 × 10⁴ to 7.5 × 10⁴. The heat transfer rate reached almost twice the value obtained from the experiment with a plain tube of the same size near the pseudocritical temperature and the effect of a wire was attenuated as the temperature moved away from the pseudocritical temperature. The wall temperature distribution along the span between the contact points was a concave downward parabola. Near the pseudocritical temperature, the wall temperature showed relatively higher values, indicating a stagnant fluid around the wire. On the other hand, the wall temperature at the contact point showed a relatively lower value, indicating a fin function of a wire.     

Numerical heat transfer in a cavity with a solar control coating deposited to a vertical semitransparent wall

A transient two‐dimensional computational model of combined natural convection, conduction, and radiation in a cavity with an aspect ratio of one, containing air as a laminar and non‐participating fluid, is presented. The cavity has two opaque adiabatic horizontal walls, one opaque isothermal vertical wall, and an opposite semitransparent wall, which consists of a 6‐mm glass sheet with a solar control coating of SnS–Cu_xS facing the cavity. The semitransparent wall also exchanges heat by convection and radiation from its external surface to the surroundings and allows solar radiation pass through into the interior of the cavity. The momentum and energy equations in the transient state were solved by finite differences using the alternating direction implicit (ADI) technique. The transient conduction equation and the radiative energy flux boundary conditions are coupled to these equations. The results in this paper are limited to the following conditions: 10⁴≤Gr≤10⁶, an isothermal vertical cold wall of 21°C, outside air temperatures in the range 30°C≤T₀≤40°C and incident solar radiation of AM2 (750 W m⁻²) normal to the semitransparent wall. The model allows calculation of the redistribution of the absorbed component of solar radiation to the inside and outside of the cavity. The influences of the time step and mesh size were considered. Using arguments of energy balance in the cavity, it was found that the percentage difference was less than 4 per cent, showing a possible total numerical error less than this number. For Gr=10⁶ a wave appeared in the upper side of the cavity, suggesting the influence of the boundary walls over the air flow inside the cavity. A Nusselt number correlation as a function of the Rayleigh number is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Effects of anisotropy on the free convection from a vertical plate embedded in a porous medium

The effects of anisotropy on the steady laminar boundary-layer free convection over a vertical impermeable surface are analysed by using the method of integral relations. If the permeability in the direction orthogonal to the plate is greater than the permeability along the plate, then there is an increase in the temperature field.     

Heat transfer and pressure loss of a very shallow fluidized-bed heat exchanger Part 2. Experiment with multirow tube banks

Experiments were carried out on heat transfer and pressure-loss characteristics of a low-pressure-loss fluidized-bed heat exchanger with an extremely small ststic bed height of glass beads. This heat exchanger was composed of a tube bankd in a staggered arrangement and a multislit distributor designed especially to reduce the pressure loss. The effect of the cross-sectional shape of the distributor, the particle size of the glass beads, the static bed height, and the number of rows on heat transfer performance were examined. The heat transfer and pressure-loss characteristics are compared with experimental data in terms of fan power consumption and the compactness of the heat exchanger.     

Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium

An analysis is presented for the calculation of heat transfer due to free convective flow along a vertical plate embedded in a porous medium with an arbitrarily varying surface heat flux. By applying the appropriate coordinate transformations and the Merk series, the governing energy equation is expressed as a set of ordinary differential equations. Numerical solutions are presented for these equations which represent universal functions and several computational examples are provided.     

最大偏心圆环空间自然对流传热的数值分析

采用正切圆坐标变换 ,对不同直径比以及上、下、侧面三种偏心位置 ,偏心率达到最大值± 1的变壁温水平圆柱环形封闭空间内空气的自然对流传热进行了数学模拟 ,求出的二维空间温度分布与实验拍摄相应的温度干涉条纹图片吻合良好。计算结果同时给出流线分布及内、外壁面的局部传热系数、热流量。并与现有的偏心率小于 1的有关资料作对比分析。数值计算的范围是 :2 .0× 1 0 2 ≤ Ra≤ 3 .0× 1 0 5,1 .3≤ Do/Di≤ 3 .8,Pr=0 .70 6,|ε|=1 .