Heat transfer characteristics of staggered wing-shaped tubes bundle at different angles of attack

An experimental and numerical study has been conducted to clarify heat transfer characteristics and effectiveness of a cross-flow heat exchanger employing staggered wing-shaped tubes at different angels of attack. The water-side Re_w and the air-side Re_a were at 5 × 10² and at from 1.8 × 10³ to 9.7 × 10³, respectively. The tubes arrangements were employed with various angles of attack θ_1,2,3 from 0° to 330° at the considered Re_a range. Correlation of Nu, St, as well as the heat transfer per unit pumping power (ε) in terms of Re_a and design parameters for the studied bundle were presented. The temperature fields around the staggered wing-shaped tubes bundle were predicted by using commercial CFD FLUENT 6.3.26 software package. Results indicated that the heat transfer increased with the angle of attack in the range from 0° to 45°, while the opposite was true for angles of attack from 135° to 180°. The best thermal performance and hence the efficiency η of studied bundle occurred at the lowest Re_a and/or zero angle of attack. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.     

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.     

Effect of heater size on ultrasonic enhancement of boiling in water and surfactant solutions

Experiments were performed to study enhancement of heat transfer from the wire of d = 50 µm and the tube of d = 1.5 mm in subcooled pool boiling by ultrasonic waves. The working fluids are clean water and Alkyl (8-16) Glucoside surfactant solutions of different concentrations and bulk temperature 30 °C. The wire resistance was translated to the temperature, using the calibration data, the temperature of the tube was measured by thermocouple. The differences between effect of ultrasonic field on boiling in water for heaters of d = 50 µm and d = 1.5 mm may be summarized as follows: for boiling on the wire of d = 50 µm in subcooled water, T_b = 30 °C, enhancement of heat transfer coefficient due to applied ultrasonic field is about 70% and 20% at heat flux q = 620 kW/m² and q = 1350 kW/m², respectively. For boiling in surfactant solutions at the same boiling conditions enhancement of heat transfer coefficient is in the range of 5–10% at heat flux q = 620 kW/m² and 10–16% at heat flux q = 1350 kW/m² depending on solution concentration. For boiling on the tube of d= 1.5 mm in subcooled water, T_b= 30 ℃, enhancement of heat transfer coefficient due to applied ultrasonic field is about 50% and 45% at heat flux q = 500 kW/m² and q = 2500 kW/m², respectively. The same values are obtained for boiling in surfactant solution of concentration C = 250 ppm. For the wire of d = 50 µm the heat transfer enhancement due to acoustic vibrations in surfactant solutions is not as strong as in water. This fact may be considered as evidence of significant role of relationship between jet flow and ultrasonic field.     

Intensity of convective mass/heat transfer in a rotary regenerator rotor with the transverse needle-fins

A forced convective mass transfer coefficient was electrochemically measured for a cylindrical bundle of transverse needle-fins ?1 × 10.9, applied as the rotor porous matrix of a rotary heat regenerator. The baffle inside the rotor was present. The technique based on the ferricyanide–ferrocyanide redox reaction controlled at the cathode, in the presence of a sodium hydroxide based electrolyte, was used in this experiment. A set of the six neighbouring fins, connected in parallel, was the cathode. The distribution of the mass transfer coefficient according to different static rotor angle position and the mean mass transfer Chilton–Colburn coefficient correlation j _M  = j _M (Re) for rotation numbers, Ro: 0, 0.8, 1.6 and 2.0 were stated in the mean Reynolds number, Re, range 180–985. The comparison was made between the convective heat fluxes of the pin-fins and the sheet rotor, for Ro = 0.     

Effects of dimensions on the fluid flow and mass transfer characteristics in wavy-walled tubes for steady flow

Flow and mass transfer characteristics in axisymmetric sinusoidal wavy-walled tubes with different dimensions are investigated experimentally. The overall pressure drops are measured with U-manometer, and the measurements of mass transfer rate are performed by the electrochemical method, while the flow patterns are visualized by the aluminum dust method. The results showed that the wavelength and amplitude of the wavy-walled tubes obviously affect the fluid flow and mass transfer characteristics. With the increment of the wave factor F _w , the overall pressure drop increase and thus leads to an earlier shift of transitional flow to turbulence as well as a better mass transfer enhancement. Furthermore, mass transfer enhancement is compared with the corresponding straight-walled tube under equal pumping power condition. It is found that the greater mass transfer enhancement appears at the moderate Reynolds number, and the optimum mass transfer enhancement could be obtained in the wavy-walled tube with F _w  = 0.5. Based on the flow visualization results, the characteristics of the flow structures in wavy-walled tube with different dimensions are displayed clearly.     

On shear correction factors in the non-linear theory of elastic shells

Theoretical values of two correction factors α_s = 5/6 and α_t = 7/10 are established for the respective transverse shear stress resultants and stress couples within the general, dynamically and kinematically exact, six-field theory of elastic shells. These values do not depend on the shell material symmetry, geometry of the base surface, the shell thickness, or any kind of kinematic and/or dynamic constraints. The analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section. The appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with α_s and α_t as the respective correction factors. Four numerical examples of highly non-linear shell structures illustrate the influence of different values of α_s and α_t on the results. In particular, some influence of α_t is noticed on the placement of bifurcation points. In dynamic problem of flight of three intersecting plates analysed with Newmark-type temporal algorithm, the value of α_t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure.     

Investigation of the flopping regime with two-, three- and four-cylinder arrays

The variation of the base pressure coefficient (Cp), and the characteristics of the velocity power spectra for arrays of two-, three- and four-cylinders aligned normal to the flow are presented. For the two-cylinder array with s/d=0.750 (where s is the spacing between the top and bottom surfaces of adjacent cylinders and d is the diameter of the cylinder) and Re=2.5×10³, peaks in the power spectra of 145 and 45?Hz which correspond to Strouhal numbers of 0.35 and 0.11 have been observed. For the three-cylinder array with Re=2.5×10³, at 0.338?s/d?0.730, three quasi-stable modes are observed. For 0.730?s/d?0.850, flopping and one quasi-stable mode are observed. For 0.850?s/d?1.202, only one mode is observed. The hot-wire power spectra measured downstream of the cylinder array on the center plane between the top and center cylinder and, also on the plane at s/2 above the top cylinder has three relative peaks that correspond to a wake structure, i.e. a pattern of vortices. For the four-cylinder array, when 0.338?s/d?0.750, four quasi-stable modes are observed. First, a mode can be observed in which the average Cp value of the top cylinder is relatively high, the average Cp value of the bottom cylinder is relatively low, and the average Cp values of the two center cylinders are nearly equal. A second mode is sometimes observed that is similar to the first except that the relatively high and low average Cp values of the outer cylinders are interchanged. A third mode is observed in which the average Cp value of the upper–inner cylinder is relatively high, the average Cp value of the lower–inner cylinder is relatively low, and the average Cp values of the outer cylinders are nearly equal. A fourth mode can be observed that is similar to the third mode except that the relative high and low average Cp values of the two inner cylinders are interchanged. For 0.750?s/d?1.202, only two of these modes are observed.     

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.     

Mean flow characteristics of a 3D turbulent wall jet over an isothermal and an insulating flat surface

An experimental study was carried out on the mean aerodynamic and heat-exchange characteristics of a weaklyheated air jet flowing over an isothermal and an insulating flat surface. The jet issued from a contracting profiled rectangular nozzle (39×22 m² outlet) at 30 m/sec velocity (Re _d =~5.5×10⁴) and incidence angle α₀, π/12, π/6, π/4. It was established that as α₀ increases, so do the decay rates of the axial velocity and temperature along the jet axis as well as the jet width, while the jet thickness decreases. Parallel examination of an in sulating and an isothermal surface permitted separation of the heat-exchange process between the jet and the surrounding medium, from that between the jet and the wall surface-with the conclusion tha tin the isothermal case, the exchange with the surface intensifies as α₀ increases.     

Analytical solution of two intersecting cylindrical shells subjected to transverse moment on nozzle

In this paper a theoretical solution for two normally intersecting cylindrical shells subjected to transverse moment on the branch pipe is presented, which based on thin shell theory. The accurate shell equations, boundary conditions and calculating methods are adopted so that the solution presented can be applicable up to d/D⩽0.8 and λ=d/(DT)^1/2⩽8. The presented results are in very good agreement with experimental and numerical results for ORNL-1 Model. They are also in agreement with the results obtained by WRC Bulletin 297 when d/D is small.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

The effect of flexible tube vibration on pressure drop and heat transfer in heat exchangers considering viscous dissipation effects

The pressure drop and heat transfer coefficient in tube bundle of shell and tube heat exchangers are investigated considering viscous dissipation effects. The governing equations are solved numerically. Because of temperature-dependent viscosity the equations should be solved simultaneously. The flexible tubes vibration is modeled in a quasi-static method by taking the first tube of the row to be in 20 asymmetric positions with respect to the rest of the tubes which are assumed to be fixed and time averaging the steady state solutions corresponding to each one of these positions .The results show that the eccentricity of the first tube increases pressure drop and heat transfer coefficients significantly comparing to the case of rigid tube bundles, symmetrically placed. In addition, these vibrations not only compensate the effect of viscous dissipations on heat transfer coefficient but also increase heat transfer coefficient. The constant viscosity results obtained from our numerical method have a good agreement with the available experimental data of constant viscosity for flexible tube heat exchangers.     

Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations

We consider a family of linearly elastic shells with thickness 2?, clamped along their entire lateral face, all having the same middle surfaceS=φ(?ω) ?R ³, whereω ?R ² is a bounded and connected open set with a Lipschitz-continuous boundaryγ, andφ ∈l ³ ( $\overline \omega$ ;R ³). We make an essential geometrical assumption on the middle surfaceS, which is satisfied ifγ andφ are smooth enough andS is “uniformly elliptic”, in the sense that the two principal radii of curvature are either both>0 at all points ofS, or both<0 at all points ofS. We show that, if the applied body force density isO(1) with respect to?, the fieldtu(?)=(u _i(?)), whereu _i (?) denote the three covariant components of the displacement of the points of the shell given by the equations of three-dimensional elasticity, one “scaled” so as to be defined over the fixed domain Ω=ω×]?1, 1[, converges inH ¹(Ω)×H ¹(Ω)×L ²(Ω) as?→0 to a limitu, which is independent of the transverse variable. Furthermore, the averageξ=1/2ε _?1 ¹ u dx ₃, which belongs to the space $$V_M (\omega ) = H_0^1 (\omega ) \times H_0^1 (\omega ) \times L^2 (\omega ),$$ satisfies the (scaled) two-dimensional equations of a “membrane shell” viz., $$\mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \gamma _{\sigma \tau } (\zeta )\gamma _{\alpha \beta } (\eta ) \sqrt \alpha dy = \mathop \smallint \limits_\omega \left\{ {\mathop \smallint \limits_{ - 1}^1 f^i dx_3 } \right\}\eta _i \sqrt a dy$$ for allη=(η _i) εV _M(ω), where $a^{\alpha \beta \sigma \tau }$ are the components of the two-dimensional elasticity tensor of the surfaceS, $$\gamma _{\alpha \beta } (\eta ) = \frac{1}{2}\left( {\partial _{\alpha \eta \beta } + \partial _{\beta \eta \alpha } } \right) - \Gamma _{\alpha \beta }^\sigma \eta _\sigma - b_{\alpha \beta \eta 3} $$ are the components of the linearized change of metric tensor ofS, $\Gamma _{\alpha \beta }^\sigma$ are the Christoffel symbols ofS, $b_{\alpha \beta }$ are the components of the curvature tensor ofS, andf ⁱ are the scaled components of the applied body force. Under the above assumptions, the two-dimensional equations of a “membrane shell” are therefore justified.     

Heat transfer and skin-friction in a turbulent boundary layer under a non-equilibrium longitudinal adverse pressure gradient

The experimental data on the effect of weak and moderate non-equilibrium adverse pressure gradients (APG) on the parameters of dynamic and thermal boundary layers are presented. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re^** = 5500. The APG region was a slot channel with upper wall expansion angles from 0 to 14°. The profiles of the mean and fluctuation velocity components were measured using a single-component hot-wire anemometer. The friction coefficients were determined using two methods, namely, the indirect Clauser method and the direct method of weighting the lower wall region on a single-component strain-gage balance. The heat transfer coefficients were determined by a transient method using an IR camera. It is noticed that in the pressure gradient range realized the universal logarithmic region in the boundary layer profile is conserved. The values of the relative (divided by the parameters in zero gradient flow at the same value of Re^**) friction and heat transfer coefficients, together with the Reynolds analogy factor, are determined as functions of the longitudinal pressure gradient. The values of the relative friction coefficient reduced to c_f/c_f0 = 0.7 and those of the heat transfer to St/St₀ = 0.9. A maximum value of the Reynolds analogy factor (St/St₀)/(c_f/c_f0) = 1.16 was reached for the pressure gradient parameter β = 2.9.     

Effects of injection angle orientation on concave and convex surfaces film cooling

The present study employs a transient liquid crystal thermography to measure film cooling performance over constant curvature of concave and convex surfaces. This work investigates detailed distributions of both film cooling effectiveness and heat transfer coefficient on concave and convex surfaces with one row of injection holes inclined stream-wise at 35° at four blowing ratios (0.5, 1.0, 1.5 and 2.0) on four test pieces with different hole configurations. All test models have a row of discrete holes with a stream-wise injection angle (γ of 35° and a pitch-to-diameter ratio (P/d) of 3. The current work examines four different injection configurations, one with simple and three with 8° forward-expanded holes. Three compound angles of 0, 45 and 90° with air (ρ_c/ρ_m = 0.98) as coolants are tested under the mainstream Reynolds number (Re_d) of 2300 on concave surface, and 1700 on convex surface. Measured results of the concave surface show that both the span-wise averaged heat transfer coefficient and film cooling effectiveness increase with blowing ratios for all tested models. Higher heat transfer levels induced by large flow disturbance of compound-angle injection also lead to poorer overall film cooling performance, especially at high blowing ratio and large span-wise injection angle. Present results show that the best surface protection on the concave surface over the widest range of M can be provided by the forward-expanded holes with β = 0° (Model-B), followed by the forward-expanded holes with β = 45° (Model-C). Convex surface results show that the compound-angle injection indicates increases in both film cooling effectiveness and heat transfer at moderate and high blowing ratios. The forward-expanded hole with simple-angle injection provides the best film performance because of high film cooling effectiveness and low heat transfer coefficient at blowing ratio of 0.5.     

Fluid transfer between tubes in interacting capillary bundle models

The interacting capillary bundle model proposed by Dong et al. [Dong, M., Dullien, F.A.L., Zhou, J.: Trans. Porous Media 31, 213–237 (1998); Dong, M., Dullien, F.A.L., Dai, L., Li, D.: Trans. Porous Media 59, 1–18 (2005); Dong, M., Dullien, F.A.L., Dai, L., Li, D.: Trans. Porous Media 63, 289–304 (2006)] has simulated correctly various aspects of immiscible displacement in porous media, such as oil production histories at different viscosity ratios, the effects of water injection rate and of the oil–water viscosity ratio on the shape of the displacement front and the independence of relative permeabilities of the viscosity ratio. In the interacting capillary bundle model pressure equilibrium was assumed at any distance x measured along the bundle. Interaction between the capillaries also results in transfer of fluids across the capillaries. In the first part of this paper the process of fluid transfer between two capillaries is analysed and an algebraic expression for this flow is derived. Consistency with the assumption of pressure equilibration requires that all transfer must take place at the positions of the oil/water menisci in the tubes without any pressure drop. It is shown that fluid transfer between the tubes has no effect on the predictions obtained with the model. In the second part of the paper the interacting tube bundle model is made more realistic by assuming fluid transfer between the tubes all along the single phase flow regions across a uniform resistance, resulting in pressure differences throughout the single phase regions between the fluids present in the different tubes. The results of numerical simulations obtained with this improved interacting capillary bundle model show only small differences in the positions of the displacement front as compared with the predictions of the idealized model.     

Experimental investigations on a 1–2 heat exchanger with wire-wound tubes

This paper deals with experimental investigations on a 1–2 shell and tube heat exchanger, to study the effect of spiral turbulators on its performance. The heat exchanger has its tubes wound with copper wire, so that the winding acts as an augmenting device. Experiments were conducted with various winding wire diameters and pitches and the heat transfer coefficients were evaluated for a wide range of temperature levels and flow rates of the shell side fluid. The experimental results are discussed in detail and correlations are proposed to predict the shell side Nusselt number of the exchanger with varying winding pitches and diameters. The existence of optimum winding is also discussed in this paper. The present results are based on over 250 experimental observations made in the laminar range of flow.

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Experimentelle Untersuchungen an einem 1–2-Wärmetauscher mit drahtumwickelten Rohren

Zusammenfassung Diese Arbeit befaßt sich mit experimentellen Untersuchungen an einem 1–2-Zylindermantel/Rohrwärmetauscher und hat die Klärung des Einflusses von spiralförmigen Turbulenzpromotoren auf das Übertragungsverhalten zum Ziel. Die Rohre des Wärmetauschers sind mit Kupferdraht umwickelt, dessen Windungslagen den Austausch befördern. Die Experimente wurden mit verschiedenen Drahtdurchmessern und Steigungen durchgefürht und hieraus Wärmeübergangskoeffizienten in einem weiten Bereich der Temperaturniveaus und der Mengenströme des die Rohre umströmenden Fluids bestimmt. Die experimentellen Befunde werden eingehend diskutiert und Korrelationen zur Bestimmung der Nusselt-Zahl auf der Rohraußenseite in Abhängigkeit von Steigung und Durchmesser der Drahtwindungen angegeben. Die Ergebnisse basieren auf mehr als 250 Messungen im Bereich der Laminarströmung und belegen die Existenz einer optimalen Windungskonfiguration.

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Nomenclature A _o heat transfer surface area outside the tube, m² - A _i heat transfer surface area inside the tube, m² - d _o outer diameter of the tube, m - D inner diameter of the shell, m - D _e equivalent diameter of shell for heat transfer, m - d _w diameter of the winding wire, m - F _T LMTD correction factor [8] - h _i inside heat transfer coefficient, W/m² K - h _o outside heat transfer coefficient, W/m² K - k _o thermal conductivity of water outside tube, W/mK - L length of the shell, m - l _t tube length, m - l _w length of the winding wire, m - LMTD logarithmic mean temperature difference, K - m mass flow rate of cold fluid, kg/h - N number of tube passes - Nu _i inside Nusselt number for the tube - Nu _o outside Nusselt number for the tube - Nu _o * outside Nusselt number, average over the temperature range - n _t number of tubes per pass - P pitch of the winding wire, m - Pr _t Prandtl number, tube side - Q heat transfer rate, W - Re _t tube side Reynolds number - Re _s shell side Reynolds number for heat transfer - T corrected mean temperature difference, K [8] - Th _i inlet temperature of hot water, °C - Th _o exit temperature of hot water, °C - Ti _i inlet temperature of cold water, °C - Tc _o exit temperature of cold water, °C - U _o overall heat transfer coefficient, W/m² K     

Experimental analysis of local void fractions measurements for boiling hydrocarbons in complex geometry

The present paper is part of a research program on two-phase flows and heat transfer studies in tube bundles. An experimental study was carried out to analyse the void fraction for vertical two-phase flows. Boiling across a horizontal tube bundle for three hydrocarbons (n-pentane, propane and iso-butane) under saturated conditions is investigated. The experiments were performed on a tube bundle with 45 plain copper tubes of 19.05 mm outside diameter in a staggered configuration with a pitch to diameter ratio of 1.33. An optical probe has been developed to determine the local void fraction at the minimum cross section between the tubes.     

Effect of rib angle orientation on local mass transfer distribution around sharp 180 deg turn with rib-turbulators mounted in entire two-pass channels

The local mass transfer distributions around sharp 180 deg turn with rib-turbulators in a relatively short (L/D=4) two-pass, square channel were determined via the naphthalene sublimation technique. The rib height-to-hydraulic diameter ratio (e/D) was 0.05 and the rib pitch-to-height ratio (p/e) was 10. Experiments were conducted for five attack angles (α=90,45,60,?45, and ?60 deg), and for three Reynolds numbers (3.0×10⁴, 6.0×10⁴ and 9.0×10⁴). Results show that the rib-roughened wall Sherwood numbers after the turn are higher than those in the turn region, which, in turn, are higher than those before the turn due to the ribs installed in the turn region. While in the previous studies, the ratio Sh/Sh ₀ in the turn region was found to be lower than that in the before turn region, because of the absence of rib in the turn region. The rib angle and rib orientation have significant effect on both the local and average Sherwood number ratios. The average Sherwood number ratios (Sh _m /Sh ₀) for α = 60 deg have the highest values, then comes the case of α = 45 deg, and the Sherwood number ratios (Sh _m /Sh ₀) for α = 90 and ?45 deg are the lowest. Correlations for the average rib-roughened wall Sherwood number ratios for the before-turn, in-turn and after-turn segments are provided.     

Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers

In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 × 10⁴ < Ra < 5 × 10⁵) for different annulus gap widths (L/D _o = 0.23, 0.3, and 0.37) and different inclination of the annulus (α = 0°, 30° and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and (3) increasing Ra increases the heat transfer rate for any L/D _o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D _o and α. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.