Heat transfer and pressure drop in tubes with short turbulators

The results of investigations concerning heat transfer and pressure drop in a tube with short single-turn turbulators in form of a twisted tape are presented here. The experiments were carried out in the range: 1300≤Re≤8000 4,3≤Pr≤7,0, 2,9≤S/d≤4,4 with water as the test fluid. The results were compared with those obtained when investigating heat transfer and flow resistance in a tube with a turbulator installed all along the tube. It was demonstrated that in certain conditions, assuming thatQ=idem,F=idem andS=idem, the power demand for pumping medium can be reduced.     

Heat transfer and pressure drop in fluidized bed cooling tower

Experimental investigation has been carried out on a counter flow three-phase fluidized bed cooling tower (FBCT) with different static bed heights. The efficient static bd height for the present tower is found to be between 11 cm and 13 cm. The pressure drop observed is in the order of 0.6 mm of water column per cm of static bed height within the range of parameters investigated.

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Wärmeübergang und Druckverlust in einem Fließbett-Kühlturm

Zusammenfassung An einem Fließbett-Kühlturm unterschiedlicher Statischer Betthöhen, der von einem in drei Phasen vorliegenden Fluid im Gegenstrom beaufschlagt wird, wurde eine experimentelle Untersuchung durchgeführt. Die wirksamen statischen Betthöhen ergaben sich bei diesem Turm zu 11 und 13 cm, der gemessene Druckverlust lag bei etwa 0,6 mm Wassersäule je Zentimeter statischer Betthöhe und zwar im gesamten Variationsbereich der Versuchsparameter.

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Nomenclature p pressure drop across the bed in mm of water column - L liquid flow rate, kg/hr - G gas flow rate, kg/hr - V static bed height – m - T ₁ cold water temperature, °C - T ₂ hot water temperature, °C - i _i specific enthalpy of saturated air, kJ/kg - i _g specific enthalpy of the bulk of the air locally, kJ/kg - K mass transfer coefficient, kg/m² – hr - a cooling area per unit volume, m²/m³     

Heat transfer and pressure drop measurements in rib-roughened rectangular ducts

In the present study, the thermal and hydraulic performance of three rib-roughened rectangular ducts is investigated. The aspect ratio of the ducts was 1 to 8, and the ribs were arranged staggered on the two wide walls. Three rib configurations were tested: parallel ribs and V-shaped ribs pointing upstream or downstream of the main flow direction. For all cases, the rib height-to-hydraulic diameter ratio was 0.06, with an attack angle of 60° and a pitch-to-height ratio of 10. The Reynolds number range was from 1000 to 6000. Liquid crystal thermography was employed in the heat transfer experiment to demonstrate detailed temperature distribution between a pair of ribs on the ribbed surfaces. The secondary flows caused by the inclined ribs create a significant spanwise variation of the heat transfer coefficients on the rib-roughened wall with high heat transfer coefficient at one end of the rib and low value at the other. In the streamwise direction between two consecutive ribs, the temperature distribution shows a sawtooth fashion because of flow reattachment. Based on the local heat transfer coefficients, the average Nusselt numbers were estimated as weighted mean values. Isothermal pressure drop data were taken and presented as Fanning friction factors. The ducts are compared to each other by considering both heat transfer and friction factor performance.     

Heat/mass transfer and pressure drop in a triangular-rib-roughened rectangular channel

In this paper, the heat/mass transfer analogy was used to investigate the heat transfer and pressure drop in a square channel with triangular ribs on its two opposite walls. Reynolds number varied from 1 × 10⁴ to 7 × 10⁴; the dimensionless heights of the triangular ribs H/W were 0.04, 0.07, and 0.1; and their dimensionless pitches S/W were 0.45, 0.63, 1.0, 1.37, 1.55, and 2.1. Experimental results showed that the heat transfer coefficients of the wall with triangular rib were about 1 to 2.3 times larger than those of a smooth-channel wall, and the pressure drops along this roughened channel were about 1 to 10 times larger than those for a smooth channel. Correlations of heat transfer and pressure drop were obtained, which are useful for practical designs.     

Heat transfer and pressure drop studies in a circular tube fitted with straight full twist

Experimental investigation of heat transfer characteristics of circular tube fitted with straight full twist insert has been presented. The heat transfer coefficient increases with Reynolds number and decreasing spacer distance with maximum being 2 in. spacer distance for both the type of twist inserts. Also, there is no appreciable increase in heat transfer enhancement in straight full twist insert with 2 in. spacer distance. Experiments were carried out in turbulent flow using straight full twist insert with 4 in. spacer and similar trend of increasing Nusselt number with Reynolds number was observed. Performance evaluation analysis was made and the maximum performance ratio was obtained for each twist insert corresponding to the Reynolds number of 2550.     

Heat transfer and pressure drop in fractal microchannel heat sink for cooling of electronic chips

In this paper, the improved design of fractal branching channel net that can meet the demand for cooling of rectangular electronic chip with arbitrary ratio of length to width is presented. A theory model is proposed that can be used to estimate the performance of heat transfer and pressure drop approximately. It is found that the optimal total branching level is 7 and the ratio of length to width is 1.87 at the fixed cooling surface for fractal microchannel heat sink.     

Flow structure, heat transfer and pressure drop in varying aspect ratio two-pass rectangular smooth channels

Two-pass channels are used for internal cooling in a number of engineering systems e.g., gas turbines. Fluid travelling through the curved path, experiences pressure and centrifugal forces, that result in pressure driven secondary motion. This motion helps in moving the cold high momentum fluid from the channel core to the side walls and plays a significant role in the heat transfer in the channel bend and outlet pass. The present study investigates using Computational Fluid Dynamics (CFD), the flow structure, heat transfer enhancement and pressure drop in a smooth channel with varying aspect ratio channel at different divider-to-tip wall distances. Numerical simulations are performed in two-pass smooth channel with aspect ratio W_in/H = 1:3 at inlet pass and W_out/H = 1:1 at outlet pass for a variety of divider-to-tip wall distances. The results show that with a decrease in aspect ratio of inlet pass of the channel, pressure loss decreases. The divider-to-tip wall distance (W_el) not only influences the pressure drop, but also the heat transfer enhancement at the bend and outlet pass. With an increase in the divider-to-tip wall distance, the areas of enhanced heat transfer shifts from side walls of outlet pass towards the inlet pass. To compromise between heat transfer and pressure drop in the channel, W_el/H = 0.88 is found to be optimum for the channel under study.     

Heat transfer and pressure drop of a transversely finned concentric annulus with longitudinal flow

The characteristics of heat transfer and pressure drop have been experimentally studied for the fully developed concentric annular flow with transverse fins normal to the flow direction by the naphthalene sublimation technique. Correlations for calculating the heat transfer coefficient with different inner diametersD ₀ of the outer tube are presented. A characteristic Reynolds number has been proposed, by which the predominant role of the transverse fins can be evaluated. It has been indicated that the inner diameterD ₀ has much more effect on pressure drop than on heat transfer. The effect ofD ₀ on the overall performance is also compared under the same flow velocity or flow rate. It has been found that the effect of developing flow on heat transfer is significant and should be taken into account during experiment.

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Wärmeübergang und Druckverlust in einem querberippten konzentrischen Ringkanal bei Längsströmung

Zusammenfassung Mit Hilfe der Naphthalin-Sublimationstechnik werden die Wärmeübergangs- und Druckverlustcharakteristiken in quer zur voll ausgebildeten Strömung bei berippten Ringkanälen experimentell ermittelt und Korrelationen zur Berechnung des Wärmeübergangskoeffizienten bei variablen InnendurchmesserD ₀ des umschließenden Rohres angegeben. Ferner wird eine charakteristische Reynolds-Zahl vorgeschlagen, über die sich der dominierende Einfluß der Querrippen erfassen läßt. Es zeigte sich, daß der InnendurchmesserD ₀ den Druckverlust wesentlich mehr beeinflußt als den Wärmeübergang. Auch wurde die Abhängigkeit des Gesamt-Übertragungsverhaltens vonD ₀ bei gleicher Strömungsgeschwindigkeit bzw. Volumenstromdichte ermittelt. Es zeigte sich, daß die Ausbildung des Strömungsprofils bei Einlaufströmung den Wärmeübergang signifikant beeinflußt und deshalb im Experiment zu berücksichtigen ist.

     

Heat transfer enhancement and pressure drop in viscous liquid flows in isothermal tubes with twisted-tape inserts

Heat transfer enhancement in viscous liquid flows by means of twisted-tape inserts has been investigated in this study. Internal flows in horizontal tubes with uniform wall temperature have been considered. This is representative of typical conditions encountered in practical applications in the chemical and process industry. Experimental data were obtained for water and ehtylene glycol with snug-fit tape inserts of three different twist ratios,y=3.0, 4.5, and 6.0; the tape thickness in each case was 0.483 mm. The data cover a wide range of flow parameters: 3.5Pr<100, and=">Re<35,000, for=" both=" heating=" and=" cooling=" conditions.=" the=" results=">Nu _m andf are strongly influenced by the tape geometry and fluid flow conditions, and can be functionally represented byNu _m=(Re, Pr, _b/_w,L/d, H/d, /d) andf=(Re, H/d, /d).In dieser Untersuchung wurde die Verbesserung des Wärmeübergangs in viskosen Flüssigkeitsströmungen mittels eines Spiralband-Einsatzes erforscht. Es wurden Strömungen in horizontalen Rohren mit einheitlicher Wandtemperatur betrachtet. Diese sind repräsentativ für typische Bedingungen, die in praktischen Anwendungen in der chemischen und weiterverarbeitenden Industrie anzutreffen sind. Für Wasser und Äthylen-Glykol wurden experimentelle Daten für eingepaßte Band-Einsätze mit drei unterschiedlichen Verdrehungsverhältnisseny=3.0, 4.5 und 6.0 erhalten; die Breite des Bandes betrug jeweils 0.483 mm. Die Daten decken einen weiten Bereich von Strömungsparametern ab: 3.5Pr<100 und=">Re<35,000 für=" die=" beiden=" betriebsbedingungen=" heizen=" und=" kühlen.=" die=" ergebnisse=">Nu _m undf sind stark abhängig von der Bandgeometrie und den Strömungsbedingungen und können zweckmäßig durchNu _m=(Re, Pr, _b/_w,L/d, H/d, /d) undf=(Re, H/d, /d) dargestellt werden.Dedicated to Prof. Dr.-Ing. U. Grigull's 80th birthday     

Heat transfer and pressure drop of R-134a condensation in a coiled,double tube

An experimental study was carried out to investigate condensation heat transfer and pressure drop characteristics of R-134a in a coiled double tube oriented with its helix axis in the vertical direction. Measurements were obtained at inlet pressure of 815 kPa for refrigerant mass flux ranging from 95 to 710 kg/m²s and cooling water Reynolds number varying from 1000 to 14000. Presented results illustrate the effects of refrigerant mass flux and average condensation temperature difference on the condensation heat transfer coefficient and pressure drop. Comparison with relevant data from other sources indicates a reasonable agreement. An empirical correlation was obtained for predicting condensation heat transfer coefficient. The present study may be considered of a practical and theoretical interest for the design of the helical double-tube condensers using R-134a as the working fluid. M. El-Sayed Mosaad is on leave from Mechanical Engineering Department, Mansoura University, Egypt.     

Heat transfer and pressure drop for purely viscous non-Newtonian fluids in turbulent flow through rectangular passages

Experimental measurements of friction factor and heat transfer for the turbulent flow of purely viscous non-Newtonian fluids in a 21 rectangular channel are compared with results previously reported for the circular tube geometry. Comparisons are also made with available analytical and empirical predictions.It is found that the rectangular duct fully established friction factor measurements are within ± 5% of the Dodge-Metzner prediction if the Kozicki generalized Reynolds number is used. A modified form of the simpler explicit equation proposed by Yoo, [i.e.f=0.079n ^0.675(Re ^*)^–0.25], is found to yield predictions for both the rectangular duct and the circular tube geometries with approximately the same accuracy as the Dodge-Metzner equation.Fully developed Stanton numbers for the rectangular duct are in good agreement with the circular tube data over a range ofn from 0.37 to 0.88 for a given Prandtl number,Pr _a , when compared at a fixed value of the Reynolds number based on the apparent viscosity evaluated at the wall shear stress. In general, the experimental data are within ± 20% of Yoo's equation,St=0.0152Re _a ^–0.155 Pr _a ^–2/3 . A new equation is proposed to bring the prediction for circular pipes as well as rectangular channels into better agreement with generally accepted Newtonian heat transfer results.

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Wärmeübergang und Druckverlust für viskose nicht-Newtonsche Fluide in turbulenter Strömung durch rechteckige Kanäle

Zusammenfassung Es werden Messungen des Reibungsfaktors und des Wärmeübergangs bei turbulenter Strömung viskoser nicht-Newtonscher Fluide in einem rechteckigen Kanal mit dem Seitenverhältnis 21 verglichen mit früheren Ergebnissen, die an runden Rohren gewonnen wurden. Weiterhin werden Vergleiche mit aus der Literatur verfügbaren analytischen und empirischen Beziehungen gemacht.Es zeigte sich, daß die Messungen des Reibungsfaktors im rechteckigen Kanal bei vollausgebildeter Strömung auf ± 5% mit der Vorhersage von Dodge-Metzner übereinstimmen, wenn die von Kozicki verallgemeinerte Reynolds-Zahl verwendet wird. Eine modifizierte Form der einfachen von Yoo vorgeschlagenen einfachen Gleichung in explizierter Form (f=0,079n ^0,675(Re ^*)^–0,25) bewies, daß sie sowohl für den rechteckigen Kanal als auch das runde Rohr die Werte mit fast der gleichen Genauigkeit wie die Methode von Dodge-Metzner vorhersagen kann.Die Stanton-Zahlen für den rechteckigen Kanal bei vollausgebildeter Strömung sind in guter Übereinstimmung mit den Werten für das runde Rohr in einem Bereich vonn= 0,37 – 0,88 für eine gegebene Prandtl-Zahl, wenn man den Vergleich bei einem vorgegebenen Wert der Reynolds-Zahl anstellt, die auf die scheinbare Viskosität — abgeleitet aus der Wandschubspannungbezogen ist. Generell läßt sich sagen, daß die Werte auf ± 20% mit der Gleichung von Yoo (St=0,0152Re _a ^–0,155 )Pr _a ^–2/3 ) übereinstimmen. Es wird eine neue Gleichung vorgeschlagen, welche sowohl die Werte für runde Rohre als auch die für rechteckige Kanäle in bessere Übereinstimmung bringt mit den in der Literatur üblichen Ergebnissen für den Wärmeübergang an Newtonsche Fluide.

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Nomenclature a constant in Eq. (8) - A area of cross-section of channel [m²] - b constant in Eq. (8) - c _p specific heat of test fluid [J kg^–1 K^–1] - d capillary tube diameter [m] - D _h hydraulic diameter, 4A/P[m] - f Fanning friction factor, _w/(g9 V²/2) - h axially local (spanwise averaged) heat transfer coefficient,q _w /(T_wi-T_b) [Wm^–2 K^–1] - k _f thermal conductivity of test fluid [Wm^–1K^–1] - K consistency index of power law fluid - n power law index - Nu fully established, local (spanwise averaged) Nusselt numberh D _h /k _f - P perimeter of channel [m] - Pr _a Prandtl number based on apparent viscosjity, c _p /k _f - Pr ^* defined as (Re _a Pr _a )/Re ^* - q _w wall heat flux [Wm^–2] - Re _a Reynolds number based on apparent viscosity, VD _h/ - Re Metzner's generalized Reynolds number in Eq. (2) - Re ^* Reynolds number defined in Eq. (8) - St Stanton number,h/( V c_p) - T _b local bulk temperature of the fluid [K] - T _wi local inside wall temperature [K] - T _wo local outside wall temperature [K] - V bulk flow velocity [m s^–1] - x distance from the inlet of channel along flow direction [m] Greek symbols shear rate [s^–1] - apparent viscosity [Pa s] - density of test fluid [kg m^–3] - shear stress [Pa] - _w shear stress at the wall [Pa] Dedicated to Prof. Dr.-Ing. U. Grigull's 75th birthday     

Numerical analysis of pressure drop oscillations in parallel channels

In this study pressure drop oscillations in two parallel channels are analyzed taking into account the thermal capacity of the pipes. A different limit cycle than the one that takes place in a single channel system is found. During the instability one channel always follows the typical pressure drop oscillations limit cycle while the other channel oscillates always in the superheated vapor region. This behavior leads to very high wall temperatures at the outlet of the heated pipe. This undesirable situation with one channel operating in the superheated vapor region takes place also for the maldistributed stable solutions.     

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.     

Heat transfer,pressure drop and flow patterns during flow boiling of R407C in a horizontal microfin tube

The heat transfer, pressure drop and flow patterns during flow boiling of R407C in a horizontal microfin tube have been investigated. The microfin tube is made of copper with a total fin number of 55 and a helix angle of 15°. The fin height is 0.24 mm and the inner tube diameter at fin root is 8.95 mm. The test tube is 1 m long. It is heated electrically. The experiments have been performed at saturation temperatures between −30°C and +10°C. The mass flux was varied between 25 and 300 kg/m²/s, the heat flux from 20,000 W/m² down to 1,000 W/m². The vapour quality was kept constant at 0.1, 0.3, 0.5, 0.7 at the inlet and 0.8, 1.0 at the outlet, respectively. The measured heat transfer coefficient is compared with the correlations of Cavallini et al., Shah as well as Zhang et al. Cavallini’s correlation contains seven experimental constants. After fitting these constants to our measured values, the correlation achieves good agreement. The measured pressure drop is compared to the correlations of Pierre, Kuo and Wang as well as Müller-Steinhagen and Heck. The best agreement is achieved with the correlation of Kuo and Wang. Almost all values are calculated within an accuracy of ±30%. The flow regimes were observed. It is shown, that changes in the flow regime affect the heat transfer coefficient significantly.     

Experimental distribution of phases and pressure drop in a two-phase offset strip fin type compact heat exchanger

Uniform distribution of fluids is crucial to obtain high performance in compact heat exchangers. Maldistribution has been studied by many authors, especially for parallel channels heat exchangers. But theoretical models and experimental studies for predicting flow maldistribution in offset strip fins exchangers are scarce. Offset strip fins, besides their higher thermal hydraulic performances, favour lateral distribution due to their geometry. In this work, an experimental investigation has been carried out for this type of heat exchanger. The experimental set-up consists in a flat vertical compact heat exchanger (1 m × 1 m area and 7.13 mm thickness) equipped with offset strip fins with a hydraulic diameter of 1.397 mm. Air and water are the working fluids. The flow rates of each phase in seven zones regularly distributed at the outlet have been measured as well as the pressures at the inlet, the outlet and two intermediate positions. These measurements were completed with visualisations using a high-speed camera.     

Heat transfer to superheated steam flowing in tubes and annular channels

Heat transfer measurements with superheated steam have been performed in the pressure range of 10.5–33.3 bar, steam temperatures: 229–470 °C and heat fluxes: 2.6·10⁴–5.7·10⁵ W/m². The measured data with steam flowing in an electrically heated tube of 10 mm inner diameter and 1 m length could be correlated with two different expressions, the mean steam temperature resp. the film temperature being used as reference for physical properties. The results of measurements in annular channels, with a heated rod of 14 mm outer diameter and channel diameters of 21 and 28 mm, were 10–15% lower than the proposed tube correlations. This could be explained by the differences in velocity and temperature distributions between tubes and annular channels. A satisfactory agreement was achieved between the tube correlations and transformed annular channel results.

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Zusammenfassung Wärmeübergangsmessungen an überhitztem Wasserdampf wurden im folgenden Bereich durchgeführt: Druck: 10,5–33,3 bar, Dampftemperatur: 229–470 °C, Wärmestromdichte: 2,6 · 10⁴-5,7 · 10⁵ W/m². Die Eesultate der in einem elektrisch beheizten Rohr von 10 mm Innendurchdurchmesser und 1 m Länge durchgeführten Meß-Serie konnten durch zwei verschiedene Beziehungen je nach Bezugstemperatur der thermodynamischen Stoffwerte des Kühlmittels beschtieben werden. Als Bezugsgröße wurde die mittlere Dampf — temperatur bzw. die Filmtemperatur verwendet. Messungen, die in einem Ringspalt mit einem beheizten Stab von 14 mm Außendurchmesser und mit einem Kanaldurchmesser von 21 bzw. 28 mm durchgeführt wurden, ergaben 10–15% niedrigere Wärmeübergangszahlen, als die vorgeschlagenen Gleichungen für Rohrgeometrie. Dies kann durch den Unterschied der Geschwindigkeitsverteilungen in Rohren und Ringspalten erklärt werden. Die auf Rohrgeometrie umgerechneten Resultate der Ringspaltmessungen zeigten gute Übereinstimmung mit den vorgeschlagenen Gleichungen.

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Nomenclature

Symbol Dimension A m² surface area - C constant - c _p J/kg °C heat capacity - D m channel outer wall diameter - d m channel inner wall diameter - F m² flow area - f friction coefficient - h W/°C m² heat transfer coefficient - k W/°C m thermal conductivity - L, l m lenght - m kg/s mass flow - m exponent ofRe-number - n exponent of Pr-number - p N/m², bar pressure - Q W power - q W/m² heat flux - r m radius - t °C temperature - w m/s velocity - dimensionless factor for reference temperature - y exponent of the temperature ratio - z exponent of the temperature ratiot _w/t _s - Nusselt-Number - Prandtl-Number - Reynolds-Number - Stanton-Number - _B m boundary layer thickness - kg/ms dynamic viscosity - W/°C m heat conductivity including the influence of turbulence - =t _w–t _s°C temperature difference - m²/s kinematic viscosity - kg/m³ density - N/m² shear stress Indices B boundary layer - F film - S steam - SS stainless steel - T turbulent core - W wall - a outside - h hydraulic - i inside - x based on reference temperaturet _x - 0 based on zero shear surface - 1 based on inner subchannel of an annulus - 2 based on outer subchannel of an annulus - - (over a symbol): average - * (over a symbol): transformed     

Heat transfer enhancement in grooved channels due to flow bifurcations

The flow bifurcation scenario and heat transfer characteristics in grooved channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element methods for increasing Reynolds numbers in the laminar and transitional regimes. The Eulerian flow characteristics show a transition scenario of two Hopf bifurcations when the flow evolves from a laminar to a time-dependent periodic and then to a quasi-periodic flow. The first Hopf bifurcation occurs to a critical Reynolds number Rec₁ that is significantly lower than the critical Reynolds number for a plane-channel flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω₁ and m· ω₁+n·ω₂, respectively, with m and n integers. Friction factor and pumping power evaluations demonstrate that these parameters are much higher than the plane channel values. The time-average mean Nusselt number remains mostly constant in the laminar regime and continuously increases in the transitional regime. The rate of increase of this Nusselt number is higher for a quasi-periodic than for a periodic flow regime. This higher rate originates because better flow mixing develops in quasi-periodic flow regimes. The flow bifurcation scenario occurring in grooved channels is similar to the Ruelle-Takens-Newhouse transition scenario of Eulerian chaos, observed in symmetric and asymmetric wavy channels.     

Augmented heat transfer and pressure drop of strip-type inserts in the small tubes

An experiment is carried out to investigate the characteristics of the augmentation of heat transfer and pressure drop by different strip-type inserts in small tube having an inside diameter of 2.0 mm. The effects of the imposed wall heat flux, mass flux, strip inserts with various configurations (heights, widths, pitches) on the measured augmentative heat transfer and pressure drop are examined in detail. In order to obtain insight into the fluid flow phenomena, flow visualization was also made to observe the detailed fluid flow characteristics of the present tubes inserted with strip-type inserts. In addition, comparisons are made with a plain tube having the same length, heat transfer area and experimental conditions. The measured heat transfer coefficients and pressure drops for this small pipe are also emphasized to compare with those for larger pipes. Furthermore, in order to compare results from the different configurations of strip-type inserts, several enhancement factors and performance ratios are defined to account for the effects of augmentation. Moreover, correlation equations for the heat transfer coefficient and pressure drop of the present study are proposed.The financial support extended by the National Science Council of the Republic of China through grant No. NSC-89-2212-E-230-004.