Effect of fin pattern on the air-side performance of herringbone wavy fin-and-tube heat exchangers

In the present study, new experimental data on the air-side performance of fin-and-tube heat exchangers having herringbone wavy fin configuration are presented. Different from most previous studies, the present experiments have been performed to determine the effects of fin patterns and edge corrugations on the air-side performance of the heat exchangers. The experimental apparatus consists essentially of a well-insulated open wind tunnel and herringbone wavy fin-and-tube heat exchangers made from aluminium wavy finned, copper tube. Two types of wavy fin patterns commonly in industrial use are investigated. Air and hot water are used as working fluids in air-side and tube-side, respectively. From the experimental results, it is found that the fin pattern has a significant effect on the heat transfer and flow characteristics. The corrugation at the fin edge enables the Colburn factor to decrease but it has almost no effect on the friction factor.     

An experimental investigation on the airside performance of fin-and-tube heat exchangers having sinusoidal wave fins

The heat transfer and friction characteristics of the heat exchangers having sinusoidal wave fins were experimentally investigated. Twenty-nine samples having different waffle heights (1.5 and 2.0 mm), fin pitches (1.3–1.7 mm) and tube rows (1–3) were tested. Focus was given to the effect of waffle configuration (herringbone or sinusoidal) on the heat transfer and friction characteristics. Results show that the sinusoidal wave geometry provides higher heat transfer coefficients and friction factors than the herringbone wave geometry, and the difference increases as the number of row increases. The j/f ratios of the herringbone wave geometry, however, are larger than those of the sinusoidal wave geometry. Compared with the herringbone wave geometry, the sinusoidal wave geometry yielded a weak row effect, which suggests a superior heat transfer performance at the fully developed flow region for the sinusoidal wave geometry. Possible reasoning is provided considering the flow characteristics in wavy channels. Within the present geometric variations, the effect of waffle height on the heat transfer coefficient was not prominent. The effect of fin pitch was also negligible. Existing correlations highly overpredicted both the heat transfer coefficients and friction factors. A new correlation was developed based on the present data.     

Development of colburn ‘j’ factor and fanning friction factor ‘f’ correlations for compact heat exchanger plain fins by using CFD

A numerical model has been developed for plain fin of plate fin heat exchanger. Plain fin performance has been analyzed with the help of CFD by changing the various parameters of the fin, Colburn ‘j’ and fanning friction ‘f’ factors are calculated. These values compared with the standard values. The correlations have been developed between Reynolds number Re, fin height h, fin thickness t, fin spacing s, Colburn factor ‘j’ and friction factor ‘f’.     

Experimental and numerical investigation on air-side performance of fin-and-tube heat exchangers with various fin patterns

Air-side heat transfer and friction characteristics of five kinds of fin-and-tube heat exchangers, with the number of tube rows (N = 12) and the diameter of tubes (D_o = 18 mm), have been experimentally investigated. The test samples consist of five types of fin configurations: crimped spiral fin, plain fin, slit fin, fin with delta-wing longitudinal vortex generators (VGs) and mixed fin with front 6-row vortex-generator fin and rear 6-row slit fin. The heat transfer and friction factor correlations for different types of heat exchangers were obtained with the Reynolds numbers ranging from 4000 to 10000. It was found that crimped spiral fin provides higher heat transfer and pressure drop than the other four fins. The air-side performance of heat exchangers with the above five fins has been evaluated under three sets of criteria and it was shown that the heat exchanger with mixed fin (front vortex-generator fin and rear slit fin) has better performance than that with fin with delta-wing vortex generators, and the slit fin offers best heat transfer performance at high Reynolds numbers. Based on the correlations of numerical data, Genetic Algorithm optimization was carried out, and the optimization results indicated that the increase of VG attack angle or length, or decrease of VG height may enhance the performance of vortex-generator fin. The heat transfer performances for optimized vortex-generator fin and slit fin at hand have been compared with numerical method.     

Three-dimensional numerical study and field synergy principle analysis of wavy fin heat exchangers with elliptic tubes

Three dimensional numerical studies were performed for laminar heat transfer and fluid flow characteristics of wavy fin heat exchangers with elliptic/circular tubes by body-fitted coordinates system. The simulation results of circular tube were compared with the experiment data, then circular and elliptic (e = b/a = 0.6) arrangements with the same minimum flow cross-sectional area were compared. A max relative heat transfer gain of up to 30% is observed in the elliptic arrangement, and corresponding friction factor only increased by about 10%. The effects of five factors on wavy fin and elliptic tube heat exchangers were examined: Reynolds number (based on the smaller ellipse axis, 500  4000), eccentricity (b/a, 0.6  1.0), fin pitch (F_p/2b, 0.05  0.4), fin thickness (F_t/2b, 0.006  0.04) and tube spanwise pitch (S₁/2b, 1.0  2.0). The results show that with the increasing of Reynolds number and fin thickness, decreasing of the eccentricity and spanwise tube pitch, the heat transfer of the finned tube bank are enhanced with some penalty in pressure drop. There is an optimum fin pitch (F_p/2b = 0.1) for heat transfer, but friction factor always decreases with increase of fin pitch. And when F_p/2b is larger than 0.25, it has little effects on heat transfer and pressure drop. The results were also analyzed from the view point of field synergy principle. It was found that the effects of the five factors on the heat transfer performance can be well described by the field synergy principle.     

A tube-by-tube reduction method for simultaneous heat and mass transfer characteristics for plain fin-and-tube heat exchangers in dehumidifying conditions

This study proposed a new method, namely a tube-by-tube reduction method to analyze the performance of fin-and-tube heat exchangers having plain fin configuration under dehumidifying conditions. The mass transfer coefficients which seldom reported in the open literature, are also presented. For fully wet conditions, it is found that the reduced results for both sensible heat transfer performance and the mass transfer performance by the present method are insensitive to change of inlet humidity. Unlike those tested in fully dry condition, the sensible heat transfer performance under dehumidification is comparatively independent of fin pitch. The ratio of the heat transfer characteristic to mass transfer characteristic (h_c,o/h_d,o C_p,a) is in the range of 0.6~1.0, and the ratio is insensitive to change of fin spacing at low Reynolds number. However, a slight drop of the ratio of (h_c,o/h_d,o C_p,a) is seen with the decrease of fin spacing when the Reynolds number is sufficient high. This is associated with the more pronounced influence due to condensate removal by the vapor shear. Correlations are proposed to describe the heat and mass performance for the present plate fin configurations. These correlations can describe 89% of the Chilton Colburn j-factor of the heat transfer (j_h) within 15% and can correlate 81% of the Chilton Colburn j-factor of the mass transfer (j_m) within 20%.     

Experimental study of the airside performance of tube row spacing in finned tube heat exchangers

Almost all of the studies in dehumidifying coils are experimental studies. In this study, effect of tube regulation space on heat and mass transfer and friction factor for heat exchangers made from aluminum fins and cooper tubes are identified experimentally. External surface heat transfer coefficient, Colburn factor and friction factor was calculated by the help of the computer program by using experimental values done. After the diagrams investigated, with the decreasing of tube row spacing the external surface heat transfer in the dry surface and friction factor increased. If wet and dry surfaces are compared, Colburn and friction factor in wet surfaces is larger than Colburn and friction factor in dry surfaces.     

Wing-type vortex generators for fin-and-tube heat exchangers

The effect of wing-type vortex generators on heat transfer and pressure drop of a fin-and-tube heat exchanger element was investigated. Local heat transfer was measured by liquid crystal thermography on the fin in the Reynolds number range of 600–2700. Flow losses were estimated from the measured pressure drop of an element. Delta winglets were used as vortex generators. Four fin-and-tube configurations were tested, an inline and a staggered arrangement, each with plain fins and with fins with a pair of vortex generators behind each tube. For the inline tube arrangement the vortex generators increase the heat transfer by 55–65% with a corresponding increase of 20–45% in the apparent friction factor. Results indicate that the vortex generators have the potential to reduce considerably the size and mass of heat exchangers for a given heat load.     

The effects of span position of winglet vortex generator on local heat/mass transfer over a three-row flat tube bank fin

The naphthalene sublimation method was used to study the effects of span position of vortex generators (VGs) on local heat transfer on three-row flat tube bank fin. A dimensionless factor of the larger the better characteristics, JF, is used to screen the optimum span position of VGs. In order to get JF, the local heat transfer coefficient obtained in experiments and numerical method are used to obtain the heat transferred from the fin. A new parameter, named as staggered ratio, is introduced to consider the interactions of vortices generated by partial or full periodically staggered arrangement of VGs. The present results reveal that: VGs should be mounted as near as possible to the tube wall; the vortices generated by the upstream VGs converge at wake region of flat tube; the interactions of vortices with counter rotating direction do not effect Nusselt number (Nu) greatly on fin surface mounted with VGs, but reduce Nu greatly on the other fin surface; the real staggered ratio should include the effect of flow convergence; with increasing real staggered ratio, these interactions are intensified, and heat transfer performance decreases; for average Nu and friction factor (f), the effects of interactions of vortices are not significant, f has slightly smaller value when real staggered ratio is about 0.6 than that when VGs are in no staggered arrangement. A cross section area of flow passage [m²] - A _mim minimum cross section area of flow passage [m²] - a width of flat tube [m] - b length of flat tube [m] - B _pT lateral pitch of flat tube: B _pT = S ₁/T _p - d _h hydraulic diameter of flow channel [m] - D _naph diffusion of naphthalene [m²/s] - f friction factor: f = pd _h/(Lu ² _max/2) - h mass transfer coefficient [m/s] - H height of winglet type vortex generators [m] - j Colburn factor [–] - JF a dimensionless ratio, defined in Eq. (23) [–] - L streamwise length of fin [m] - L _PVG longitudinal pitch of vortex generators divided by fin spacing: L _pVG = l _VG/T _p - l _VG pitch of in-line vortex generators [m] - m mass [kg] - m mass sublimation rate of naphthalene [kg/m²·s] - Nu Nusselt number: Nu = d _h/ - P pressure of naphthalene vapor [Pa] - p non-dimensional pitch of in-line vortex generators: p = l _VG/S ₂ - Pr Prandtl number [–] - Q heat transfer rate [W] - R universal gas constant [m²/s²·K] - Re Reynolds number: Re = ·u _max·d _h/ - S ₁ transversal pitch between flat tubes [m] - S ₂ longitudinal pitch between flat tubes [m] - Sc Schmidt number [–] - Sh Sherwood number [–]: Sh = hd _h/D _naph - Sr staggered ratio [–]: Sr = (2Hsin – C)/(2Hsin) - T _p fin spacing [m] - T temperature [K] - u _max maximum velocity [m/s] - u average velocity of air [m/s] - V volume flow rate of air [m³/s] - x,y,z coordinates [m] - z sublimation depth[m] - heat transfer coefficient [W/m²·K] - heat conductivity [W/m·K] - viscosity [kg/m²·s] - density [kg/m³] - attack angle of vortex generator [°] - time interval for naphthalene sublimation [s] - fin thickness, distance between two VGs around the tube [m] - small interval - C distance between the stream direction centerlines of VGs - p pressure drop [Pa] - 0 without VG enhancement - 1, 2, I, II fin surface I, fin surface II, respectively - atm atmosphere - f fluid - fin fin - local local value - m average - naph naphthalene - n,b naphthalene at bulk flow - n,w naphthalene at wall - VG with VG enhancement - w wall or fin surface     

Convection and heat transfer of elliptical tubes

Convection heat transfer (including natural and forced convection) of elliptical tubes had been studied system-atically. The experienced formula of heat transfer had been given. It presents fin efficiency of rectangular finned elliptical tube and optimized fin geometry (i.e. length/width ratio) and fin spacing for rectangular fin.

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Konvektion und Wärmeübergang an elliptischen Rohren

Zusammenfassung Konvektion und Wärmeübergang (sowohl bei freier als auch bei erzwungener Konvektion) an elliptischen Rohren wurden systematisch untersucht. Es wird eine aus dem Experiment abgeleitete Beziehung für den Wärmeübergang angegeben, die den Gütegrad elliptischer Rohre mit Rechteckrippen unter optimierter Rippengeometrie (Längen- zu Breitenverhältnis und Rippenabstand) beinhaltet. Stichworte: Konvektiver Wärmeübergang, Rippengütegrad, Elliptische Rohre mit Rechteckrippe.

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Nomenclature A length of a rectangular fin - A _F area of a fin - A _f overall fin area of per length - A _r tube surface of per length - B width of a rectangular fin - Gr Grashof number - N fin number of per length - Nu =hl/ Nusselt number - Pr Prandtl number - Ra =Gr·Pr Rayleigh number - Re =wl/ Reynolds number - S ₁ transverse tube pitch - S ₂ longitudinal tube pitch - w fluid velocity - a long axis of a ellipse - b short axis of a ellipse - c =a/b shape factor - d _e equivalent diameter - g acceleration of gravity - h heat exchange coefficient - l characteristic length - t fin spacing Greek symbols coefficient of thermal expansion - fin thickness - _fm area average fin efficiency - coefficient of fluid thermal conductivity - _f fin's thermal conductivity - kinematic viscosity     

Air-side performance of louver-finned flat aluminum heat exchangers at a low velocity region

The heat transfer and pressure drop characteristics of heat exchangers having louver fins were experimentally investigated. The samples had small fin pitches (1.0–1.4 mm), and experiments were conducted up to a very low frontal air velocity (as low as 0.3 m/s). Below a certain Reynolds number (critical Reynolds number), the fall-off of the heat transfer coefficient curve was observed. The critical Reynolds number was insensitive to the louver angle, and decreased as the louver pitch to fin pitch ratio (L _p /F _p ) decreased. Existing correlations on the critical Reynolds number did not adequately predict the data. The heat transfer coefficient curves crossed over as the Reynolds number decreased. Possible explanation is provided considering the louver pattern between neighboring rows. Different from the heat transfer coefficient, the friction factor did not show the fall-off characteristic. The reason was attributed to the form drag by louvers, which offsets the decreased skin friction at low Reynolds numbers. The friction factor increased as the fin pitch decreased and the louver angle increased. A new correlation predicted 92% of the heat transfer coefficient and 94% of the friction factor within ±10%.     

Further understanding of twisted tape effects as tube insert for heat transfer enhancement

Tube inserts are used as heat transfer enhancement tool for both retrofit and new design of shell and tube heat exchangers. This paper discusses and reviews the characteristics and performance of twisted tapes. The theory and application are also addressed. Industrial case study was selected to illustrate the behaviour effect that the twisted tapes impose at various laminar, transition and turbulent flow regions. This effect was demonstrated by changing the inside tube diameter and twist ratio through evaluating selected exchanger design parameters such as: local heat transfer coefficient, friction factor and pressure drop. Testing the exponent powers for Re and Pr at both laminar and turbulent regions were carried out. General design considerations are outlined for the use of twisted tapes in shell and tube heat exchangers.     

Comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface

This paper presents the comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface in duct. Experiments were performed to investigate the effect of duct height on heat transfer enhancement of a surface affixed with arrays (7 × 7) of short rectangular plate fins of a co-angular and a co-rotating type pattern in the duct. An infrared imaging system with the camera of TVS 8000 was used to measure the temperature distributions to calculate the local heat transfer coefficients of the representative fin regions. Pressure drop and heat transfer experiments were performed for both types of fin pattern varying the duct to fin height ratio (H _d/H _f) of 2.0–5.0. The friction factor calculated from the pressure drop shows that friction factor decreases with increasing the duct to fin height ratio (H _d/H _f) regardless of fin pattern and this is expected because the larger friction occurs for smaller duct to fin height ratios. Detailed heat transfer distribution gives a clear picture of heat transfer characteristics of the overall surface as well as the influence of the duct height. In addition, different flow behavior and flow structure developed by both patterns were visualized by the smoke flow visualization technique.     

Chaotic advection induced heat transfer enhancement in a chevron-type plate heat exchanger

The present work examines the role of chaotic mixing as a means of heat transfer enhancement in plate heat exchangers. In order to demonstrate the chaotic behavior, sensitivity to initial conditions and horseshoe maps are visualized. The Nusselt number and the friction factor were computed in the range of reynolds number, 1 < Re < 10. The Nusselt number increases considerably in chaotic models whereas the friction factor increases only marginally.     

Investigations on the flow through a staggered tube bundle at Reynolds numbers up toRe=107

In a range of Reynolds numbers 10⁵<Re<10⁷ investigations were made on the flow through a staggered heat exchanger model consisting of five rows. The surfaces of the tubes were polished. The transversal pitch of the tube arrangement wasa=s _t/D=2.0, the longitudinal oneb=s _l/D=1.4. The distribution of the local static pressure and skin friction was experimentally determined around the tubes in several positions of the bundle. Furthermore the total pressure drop p was measured.Results: 1. The dependency of the total pressure coefficient uponRe-number is caused by a shifting of the separation point of the boundary layer. At the criticalRe-numberRe _crit=5×10⁵ the coefficient shows a minimum. The beginning of the supercritical range is indicated by an intermediate maximum of the -distribution atRe=2×10⁶. 2. From the local quantities the momentum loss of each row can be computed. Regarding the pressure drop the entrance effect is restricted to the first row. The coinciding values of the 2., 3. and 4. row represent the pressure drop curve for a heat exchanger consisting of large number of rows. 3. The percentage of the friction drag was determined to have a maximal value of 5%. It diminishes with increasingRe-number down to 0.7% atRe=10⁷. 4. The comparison of the actual results with those of other authors shows, that an increase of the roughness height of the tube surface causes smaller values of criticalRe-numbers. At the same time a rise in was observed in the supercriticalRe-range. In the subcritical flow régime the influence of roughnesses is negligible.

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Zusammenfassung Im Bereich der Reynoldszahl 10⁵<Re<10⁷ wurde die Strömung durch ein fünfreihiges versetztes Rohrbündel mit der Querteilunga=s _t/D=2,0 und der Längsteilungb=s _l/D=1,4 untersucht. Die Rohroberflächen des Wärmetauschermodells waren poliert. Es wurden der örtliche statische Druck sowie die Verteilung der lokalen Wandschub-spannung als Funktion des Umfangswinkels in verschiedenen Positionen des Bündels gemessen. Ferner wurde der Druckabfall p über das gesamte Bündel bestimmt.Ergebnisse: 1. DieRe-Abhängigkeit des Gesamtdruckbeiwertes wird durch ein Wandern des Ablösepunktes der Grenzschicht bewirkt. BeiRe=5×10⁵ ergibt sich im -Verlauf ein Minimum. Ein Zwischenmaximum beiRe=2×10⁶ deutet an, daß der überkritische Strömungszustand erreicht ist. 2. Aus den örtlichen Meßwerten läßt sich durch Integration der Druckverlustanteil der einzelnen Rohrreihen berechnen. Daraus ersieht man, daß der Einlaufvorgang bezüglich des Druckverlustes auf die erste Reihe beschränkt bleibt. Die zusammenfallenden Werte der 2., 3. und 4. Reihe ergeben die Grenzkurve für den -Verlauf eines Bündels mit hohen Rohrreihenzahlen. 3. Der Reibungsanteil am Gesamtwiderstand beträgt maximal 5%. Er nimmt mit steigenderRe-Zahl bis auf etwa 0,7% beiRe=10⁷ ab. 4. Vergleicht man die vorliegenden Meßergebnisse mit denen anderer Autoren, so erkennt man, daß sich mit zunehmender relativer Rauhigkeit die kritischeRe-Zahl verringert. Gleichzeitig ergibt sich im überkritischen Strömungsbereich eine Vergrößerung des Druckverlustbeiwertes. Unterhalb der kritischenRe-Zahl ist der Rauhigkeitseinfluß vernachlässigbar.

     

Hypersonic tail-fin heat transfer

The flow and heat transfer on the windward surface of tail fins has been experimentally investigated for Mach numbersM =5 and 8 and Re_L=(0.6–1.1)·10⁶ (L is the length of the central chord of the wing on which the fins are mounted). Two lines of flow divergence and, consequently, two zones of enhanced heat transfer on the surface of the fin have been detected. The angle of inclination of the fin to the wing surface, the angle of attack of the wing and the radius of the wing-fin junction were varied.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 18–25, March–April, 1993.The authors wish to thank S. D. Fonov and T. A. Ershova for the digital analysis of the photographs obtained by the thermal indicator coating and laser knife-edge methods.     

Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature

An analysis is presented for fully developed laminar convective heat transfer in a pipe provided with internal longitudinal fins, and with uniform outside wall temperature. The fins are arranged in two groups of different heights. The governing equations have been solved numerically to obtain the velocity and temperature distributions. The results obtained for different pipe-fins geometries show that the fin heights affect greatly flow and heat transfer characteristics. Reducing the height of one fin group decreases the friction coefficient significantly. At the same time Nusselt number decreases inappreciably so that such reduction is justified. Thus, the use of different fin heights in internally finned pipes enables the enhancement of heat transfer at reasonably low friction coefficient.Nomenclature A_f dimensionless flow area of the finned pipe, Eq. (8) - a_f flow area of the finned pipe - C_p specific heat at constant pressure - f coefficient of friction, Eq. (12) - H₁, H₂ dimensionless fin height h₁/r_o h₂/r_o - h₁, h₂ fin heights - average heat transfer coefficient at solid-fluid interface - KR fin conductance parameter, k_s/k_f - k_f thermal conductivity of fluid - k_s thermal conductivity of fin - l pipe length - mass flow rate - N number of fins - Nu Nusselt number, Eqs. (15) and (16) - P pressure - Q total heat transfer rate at solid fluid interface - Q_f1, Q_f2 heat transfer rate at fin surface - q_w average heat flux at pipe-wall, Q/(2 r_ol) - R dimensionless radial coordinate r/r_o - Re Reynolds Number, Eq. (13) - r radial coordinate - r_o radius of pipe - r₁, r₂ radii of fin tips - T temperature - T_b bulk temperature - U dimensionless velocity, Eq. (2) - U_b dimensionless bulk velocity - u_z axial velocity - z axial coordinate - angle between the flanks of two adjacent fins - half the angle subtended by a fin - angle between the center-lines of two adjacent fins - angular coordinate - dynamic viscosity - density - dimensionless temperature, Eq. (6) - _b dimensionless bulk temperature     

The effect of support position and turbulence intensity on the flow near the surface of a sphere

The flow near the surface of a sphere was studied, using a flow visualization technique, for Reynolds numbers from about 4×10⁴ to 2.5×10⁵. It was concluded that the presence of a crossflow support substantially disturbed the flow near the surface of the sphere, especially at supercritical Reynolds numbers. Photographs of the flow patterns around spheres with crossflow supports, and with rear supports, have been presented. Also, measurements were made which show the way in which the turbulence intensity of the free stream influenced the angle of separation at various Reynolds numbers.

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Zusammenfassung Die Strömung nahe der Oberfläche einer Kugel wurde untersucht, indem die Stromlinien sichtbar gemacht wurden. Die Untersuchungen wurden durchgeführt für Reynoldszahlen von etwa 4×10⁴ bis 2,5×10⁵. Die Ergebnisse zeigten, daß die Anwesenheit einer Halterung quer zur Strömung diese in der Nähe der Kugeloberfläche wesentlich störte, besonders bei überkritischen Reynoldszahlen. Photographien des Strömungsverlaufes um die Kugel sowohl mit einer Halterung quer zur Stromrichtung als auch mit einer anderen hinter der Kugel werden gezeigt. Außerdem wurden Messungen durchgeführt, die zeigen, in welcher Weise die Intensität der Turbulenz der freien Strömung den Ablösungswinkel bei verschiedenen Reynoldszahlen beeinflußt.

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Nomenclature C _D drag coefficient (total drag/dynamic head × projected area) - C _Dc critical drag coefficient. IfC _D<D _Dc, the flow pattern is considered subcritical. - h distance (s. Fig. 1) - Nu Nusselt number - R radius of the sphere - Re Reynolds number - Re _c Reynolds number at whichC _D=C _Dc - Tu turbulence intensity component in the direction of the freestream flow - _s average angle from the stagnation point to the separation circle measured in the horizontal plane - _sc critical separation angle. If _s<_sc, the flow pattern is considered subcritical. In this investigation _sc 92°     

Data reduction for air-side performance of fin-and-tube heat exchangers

The present study focuses on the data reduction method to obtain the air-side performance of fin-and-tube heat exchangers. The data reduction methodology for air-side heat transfer coefficients in the literature is not based on a consistent approach. This paper recommends standard procedures for dry surface heat transfer in finned-tube heat exchangers having water on the tube-side. Inconsistencies addressed include the -NTU relationships, calculation of the tube-side heat transfer coefficient, calculation of fin efficiency, and whether entrance and exit loss should be included in the reduction of friction factors. Use of the recommended standardized methodology will provide more meaningful data for use in the development of correlations, or for performance comparison purposes.     

Heat transfer and friction in turbulent vortex flow

Summary This paper presents experimentally measured heat transfer and friction coefficients for air and water flowing through a pipe with several types of inserts designed to induce a swirl in the flow. It was observed that inside-surface heat transfer coefficients in swirling flow can, under favourable conditions, be at least four times as large as heat transfer coefficients at the same mass flow rate in purely axial flow. At the same time the pumping power per unit rate of heat transfer can be reduced. The increase in heat transfer coefficients was found to depend on the degree of swirl and on the density or temperature gradient. However, at comparable Reynolds numbers and swirling motions the heat transfer coefficients for air were found to be smaller than the coefficients for water. The reason for this difference is not definitely known, but the phenomenon is qualitatively compatible with that causing the cooling effect in Ranque-Hilsch vortex tubes. The observed phenomena are analyzed qualitatively and it is shown that they are primarily the result of a centrifugal force which induces a radial inward motion of warmer fluid and a radial outward motion of cooler fluid. The application of vortex flow to boiling heat transfer and other high heat flux systems is discussed briefly.

Nomenclature

Symbols c _p Specific heat at constant pressure, BTU/(lb)(deg F) - D _H Hydraulic diameter, (ft) - D Tube diameter, (ft) - f ₀ Fanning friction factor for axial flow, - f Fanning friction factor for swirling flow, - g Acceleration due to gravity, ft/(sec)² - G Mass velocity, lb/(sec) (sq ft) - h _i Inside surface coefficient of heat transfer, BTU/(hr)(sq ft)(deg F) - k Thermal conductivity, BTU/(hr)(sq ft)(deg F/ft) - L Characteristic length used in Grashof numbers, ft - p Frictional pressure drop in a duct, lbs/sq ft - r Radius of tube, ft - t Temperature potential in Grashof number, deg F - U _i Over-all coefficient of heat transfer based on inside tube area, BTU/(hr)(sq ft)(deg F) - V Axial velocity, ft/sec - Coefficient of thermal expansion, (deg F)^–1 - Absolute viscosity, (lbs)/(ft)(hr) - Density, lbs/(ft)³ - Angular velocity of fluid, rad/sec Dimensionless Parameters Nu ₀ Nusselt Number in axial flow, h _i D _H /k - Nu Nusselt Number in swirling flow, h _i D _H /k - Re Reynolds Number, VD _Hp / - Pr Prandtl Number, c _p /k - j Colburn j-Factor, (Nu/RePr)Pr ^2/3 Member of Technical Staff, Bell Telephone Laboratories, Murray Hill, N. J. formerly Baldwin Research Fellow, Lehigh University.