Experimental investigation of heat transfer and pressure drop characteristics of flow through spirally fluted tubes

Spirally fluted tubes are used extensively in the design of tubular heat exchangers. In previous investigations, results for tubes with flute depths e/D_vi < 0.2 were reported, with most correlations applicable for Re ≥ 5000. This paper presents the results of an experimental investigation of the heat transfer and pressure drop characteristics of spirally fluted tubes with the following tube and flow parameter ranges: flute depth e/D_vi = 0.1−0.4, flute pitch p/D_vi = 0.4−7.3, helix angle θ/90° = 0.3−0.65, Re = 500−80,000, and Pr = 2−7. The heat transfer coefficients inside the fluted tube were obtained from measured values of the overall heat transfer coefficient using a nonlinear regression scheme. The friction factor data obtained consisted of 507 data points. The proposed correlation for the friction factor predicts 96% of the database within ±20%. The heat transfer correlation for the range 500 ≤ Re ≤ 5000 predicts 76% of the database (178 data points) within ±20%, and the correlation for the higher Re range predicts 97% of the 342 data points within ±20%. Comparison of heat transfer and friction data show that these tubes are most effective in the laminar and transition flow regimes. The present results show that the increase of flute depth in the range considered does not improve heat transfer.     

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 transfer correlation for boiling flows in small rectangular horizontal channels with low aspect ratios

In the present experimental study, a correlation is proposed to represent the heat transfer coefficients of the boiling flows through horizontal rectangular channels with low aspect ratios. The gap between the upper and the lower plates of each channel ranges from 0.4 to 2 mm while the channel width being fixed to 20 mm. Refrigerant 113 was used as the test fluid. The mass flux ranges from 50 to 200 kg/m² s and the channel walls were uniformly heated up to 15 kW/m². The quality range covers from 0.15 to 0.75 and the flow pattern appeared to be annular. The modified Lockhart–Martinelli correlation for the frictional pressure drop was confirmed to be within an accuracy of ±20%. The heat transfer coefficients increase with the mass flux and the local quality; however the effect of the heat flux appears to be minor. At the low mass flux condition, which is more likely to be with the smaller gap size, the heat transfer rate is primarily controlled by the liquid film thickness. A modified form of the enhancement factor F for the heat transfer coefficient in the range of Re_LF200 well correlates the experimental data within the deviation of ±20%. The Kandlikar's flow boiling correlation covers the higher mass flux range (Re_LF>200) with 10.7% mean deviation.     

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.     

Two-phase frictional pressure drop multipliers for SUVA R-134a flowing in a rectangular duct

The adiabatic two-phase frictional multipliers for SUVA, R-134a flowing in a rectangular duct (with D_H = 4.8 mm) have been measured for three nominal system pressures (0.9 MPa, T_sat = 35.5 °C; 1.38 MPa, T_sat = 51.8 °C; and 2.41 MPa, T_sat = 75.9 °C) and three nominal mass fluxes (510, 1020 and 2040 kg/m²/s). The data is compared with several classical correlations to assess their predictive capabilities. The Lockhart–Martinelli model gives reasonable results at the lowest pressure and mass flux, near the operating range of most refrigeration systems, but gives increasingly poor comparisons as the pressure and mass flux are increased. The Chisholm B-coefficient model is found to best predict the data over the entire range of test conditions; however, there is significant disagreement at the highest pressure tested (with the model over predicting the data upwards of 100% for some cases). The data shows an increased tendency toward homogeneous flow as the pressure and flow rate are increased, and in fact the homogeneous model best predicts the bulk of the data at the highest pressure tested.     

Experimental study of in-tube cooling heat transfer and pressure drop characteristics of R134a at supercritical pressures

The in-tube cooling flow and heat transfer characteristics of R134a at supercritical pressures are measured experimentally for various pressures and mass fluxes in a horizontal tube. The tube is made of stainless steel with an inner diameter of 4.01 mm. Experiments are conducted for mass fluxes from 70 kg/m² s to 405 kg/m² s and pressures from 4.5 MPa to 5.5 MPa. The inlet refrigerant temperature is from 80 °C to 140 °C. The results show that the refrigerant temperature, the mass flux and the pressure all significantly affect the flow and heat transfer characteristics of R134a at supercritical pressures. The experimentally measured frictional pressure drop and heat transfer coefficient are compared with predicted results from several existing correlations. The comparisons show that the predicted frictional pressure drop using Petrov and Popov’s correlation accounting for the density and viscosity variations agree well with the measured data. Gnielinski’s correlation for the heat transfer coefficient agrees best with the measured data with deviations not exceeding 25%, while correlations based on supercritical CO₂ heat transfer data overcorrect for the influence of the thermophysical property variations resulting in larger deviations. A new empirical correlation is developed based on the measured results by modifying Gnielinski’s equation with thermophysical property terms including both the property variations from the inlet to the outlet of the entire test section and from the bulk to the wall. Most of the experimental data is predicted by the new correlation within a range of 15%.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

Heat transfer by conduction,natural convection and radiation across a rectangular cellular structure

This paper describes results on the effects of wall conduction and radiation heat exchange among surfaces on laminar natural convection heat transfer in a two-dimensional rectangular cavity modelling a cellular structure. Parametric heat transfer calculations have been performed, and numerical results are presented in graphical and tabular form. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The findings suggest that the local or the average Nusselt number is one of many parameters that control conjugate heat transfer problems. The results indicate that natural convection heat transfer in the cavity is reduced by heat conduction in the walls and radiation exchange among surfaces. The results obtaibed for the total heat transfer rate through the system using the two-dimensional model are compared with those based on a one-dimensional model.     

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.     

Two-phase pressure drop in multiple thick- and thin-orifice plates

Two-phase flow pressure changes through singularities such as sudden expansion and sudden contraction of thick- and thin-orifice plates were modeled. The modeling was based on the reversible and irreversible losses through contractions and expansions. The volume-averaged momentum equation and the reversible mechanical energy equation were used to evaluate the irreversibilities. Local slip ratios, which were necessary for the prediction of pressure drop through these singularities, were correlated from a large number of experimental data. To check the validity of the analytical predictions, an experimental test section was designed, and experiments were performed to produce benchmark pressure-drop data for thin- and thick-plate orifices. The working fluid used for these experiments was R-113. The predictive methods developed agree well with the experiments by the authors and with a wide range of two-phase flow test results obtained by others for steam-water systems. A parametric study shows the relative importance of geometry and of the flow variables such as quality, liquid-to-vapor density, and viscosity ratios on the pressure drop multipliers conventionally used in two-phase flows.     

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.     

Aerodynamics and heat transfer in cyclones with particle-laden gas flow

Experiments were performed on a 204 mm diameter water-cooled cyclone to measure the pressure drop and heat transfer in different sections of the cyclone. Hot gas at 250°C entered the cyclone with and without suspended particles. Heat transfer and pressure drop in solids-free gas flow were compared with those measured for particle-laden gas flow of different solids.     

Flow pattern based correlations of two-phase pressure drop in rectangular microchannels

Numerous pressure drop correlations for microchannels have been proposed; most of them can be classified as either a homogeneous flow model (HFM) or a separated flow model (SFM). However, the predictions of these correlations have not been compared directly because they were developed in experiments conducted under a range of conditions, including channel shape, the number of channels, channel material and the working fluid. In this study, single rectangular microchannels with different aspect ratios and hydraulic diameters were fabricated in a photosensitive glass. Adiabatic water-liquid and Nitrogen-gas two-phase flow experiments were conducted using liquid superficial velocities of 0.06–1.0 m/s, gas superficial velocities of 0.06–72 m/s and hydraulic diameters of 141, 143, 304, 322 and 490 μm. A pressure drop in microchannels was directly measured through embedded ports. The flow pattern was visualized using a high-speed camera and a long-distance microscope. A two-phase pressure drop in the microchannel was highly related to the flow pattern. Data were used to assess seven different HFM viscosity models and ten SFM correlations, and new correlations based on flow patterns were proposed for both HFMs and SFMs.     

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     

Heat transfer enhancement in a channel with a built-in rectangular cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in rectangular cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two rectangular cylinder aspect ratios. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study show that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.

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Erhöhung des Wärmeübergangs in einem Spaltkanal mit quer eingebautem Rechteckprisma

Zusammenfassung Es wird eine zweidimensionale numerische Untersuchung des instationären Wärmeübergangs und Druckverlustes im laminar durchströmten Spaltkanal mit quer eingebautem Rechteckprisma dargelegt und zwar für verschiedene Reynoldszahlen und zwei Prismenabmessungen. Als Lösung der Navier-Stokes- und der Energiegleichung resultieren selbsterregt oszillieren de Strömungs- und Temperaturfelder, verbunden mit starker Erhöhung des Wärmeübergangs und des Druckverlustes.

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List of symbols C _f skin friction coefficient, Eq. (11) - C _D drag coefficient, Eq. (11) - D drag [N/m] - f _app apparent friction factor, Eq. (10) - h cylinder height [m] - H channel height [m] - k thermal conductivity of cylinder [W/mK] - k ₀ thermal conductivity of air [W/mK] - l cylinder length [m] - L channel length [m] - Nu Nusselt number, Eq. (7) - P dimensionless pressure - Pr Prandtl number of air - Re Reynolds number, Eq. (6) - t time [s] - T temperature [K] - T _b bulk temperature [K], Eq. (8) - U, V dimensionless velocity components - X, Y dimensionless coordinates Greek symbols thermal diffusivity [m²/s] - velocity factor, Eq. (11) - dimensionless temperature, Eq. (5) - fluid density [kg/m³] - kinematic viscosity [m²/s] - dimensionless time, Eq. (5) - difference     

Local mass/heat transfer from a wall-mounted block in rectangular channel flow

This investigation explores the mass/heat transfer from a wall-mounted block in a rectangular fully developed channel flow. The naphthalene sublimation scheme was used to measure the level of local mass transfer from the block’s surfaces. The heat transfer coefficient can be obtained by analogy between heat and mass transfer. The effects of the Reynolds number on the local mass transfer from the block’s surfaces have been widely discussed. Results showed that, owing to the flow complexity induced by vortices around the block, the block’s surfaces appeared four different spatial Sherwood number distributions, termed “Wave type”, “U type”, “Slant type”, and “Pit type”. A change in the Reynolds number significantly altered the spatial Sherwood number distributions on the block’s surfaces. Besides, four correlations between the Reynolds number and the surface-averaged Sherwood number were presented for the front, top, side, and rear surfaces of the block at a given block’s height, for the purpose of practical applications.     

Flow boiling heat transfer and pressure drop of R-134a in a mini tube: an experimental investigation

This paper presents the results of an experimental study carried out with R-134a during flow boiling in a horizontal tube of 2.6 mm ID. The experimental tests included (i) heat fluxes in the range from 10 to 100 kW/m², (ii) the refrigerant mass velocities set to the discrete values in the range of 240-930 kg/(m² s) and (iii) saturation temperature of 12 and 22 °C. The study analyzed the heat transfer, through the local heat transfer coefficient along of flow, and pressure drop, under the variation of these different parameters. It was possible to observe the significant influence of heat flux in the heat transfer coefficient and mass velocity in the pressure drop, besides the effects of saturation temperature. In the low quality region, it was possible to observe a significant influence of heat flux on the heat transfer coefficient. In the high vapor quality region, for high mass velocities, this influence tended to vanish, and the coefficient decreased. The influence of mass velocity in the heat transfer coefficient was detected in most tests for a threshold value of vapor quality, which was higher as the heat flux increased. For higher heat flux the heat transfer coefficient was nearly independent of mass velocity. The frictional pressure drop increased with the increase in vapor quality and mass velocity. Predictive models for heat transfer coefficient in mini channels were evaluated and the calculated coefficient agreed well with measured data within a range 35% for saturation temperature of 22 °C. These results extend the ranges of heat fluxes and mass velocities beyond values available in literature, and add a substantial contribution to the comprehension of boiling heat transfer phenomena inside mini channels.     

Forced convection from an isolated heat source in a channel with porous medium

A numerical study is made of flow and heat transfer characteristics of forced convection in a channel that is partially filled with a porous medium. The flow geometry models convective cooling process in a printed circuit board system with a porous insert.The channel walls are assumed to be adiabatic. Comprehensive numerical solutions are acquired to the governing Navier-Stokes equations, using the Brinkman-Forchheimer-extended Darcy model for the regions of porous media. Details of flow and thermal fields are examined over ranges of the principal parameters; i.e., the Reynolds number Re, the Darcy number Da (≡K/H²), the thickness of the porous substrate S, and the ratio of thermal conductivities R_k (≡k_eff/k). Two types of the location of the porous block are considered. The maximum temperature at the heat source and the associated pressure drop are presented for varying Re, Da, S, and R_k. The results illustrate that as S increases or Da decreases, the fluid flow rate increases. Also, as R_k increases for fixed Da, heat transfer rates are augmented. Explicit influences of Re on the flow and heat transport characteristics are also scrutinized. Assessment is made of the utility of using a porous insert by cross comparing the gain in heat transport against the increase in pressure drop.     

Heat transfer and pressure drop in dimpled fin channels

Heat transfer characteristics are examined comparatively for four sets of dimpled fin channels with Reynolds number (Re) ranging from 1500 to 11,000 in order to determine the effects of dimple arrangement, fin length (L) to channel hydraulic diameter (d) ratio and Re on heat transfer over the dimpled fin channel. These dimpled fin channels share the identical rectangular section of a channel aspect ratio (AR) of 6 with three different L/d of 8.9, 6.2 and 3.5. The two opposite dimpled fins with four different concave and convex arrangements affect the secondary flows and vortex structures tripped by dimples that signify various heat transfer performances over each dimpled fin. Heat transfer correlations for spatially averaged Nusselt number ($\overline{\mathit{Nu}}$) over each dimpled fin are generated using Re and L/d as the controlling parameters. A set of design criteria for determining the optimal L/d that offers the maximum cooling power available from the dimpled fin for each specified dimple arrangement on two opposite fin walls is derived to assist the design activities using the dimpled fin array.