Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins

Experiments were performed to determine the heat transfer and pressure drop characteristics in the entrance and fully developed regions of tubes with internal wave-like longitudinal fins. The test tube has a double-pipe structure, with the inner tube as an insertion. The wave-like fins are in the annulus and span its full width. Experiments were conducted for two cases: one with the inner tube blocked (no air flowing through it) and the other with the inner tube unblocked. The outer tube was electrically heated. Local and average heat transfer coefficients and friction factors were measured. The friction factor and Nusselt number correlations in the fully developed region were obtained in the Reynolds number range of 9×10² to 3.5×10³. It has been found that the wave-like fins enhance heat transfer significantly with the blocked case being superior. In addition, the in-tube heat transfer process is characterized by an earlier transition from laminar to turbulent flow and Reynolds number-dependent thermal entrance length. Received on 12 May 1998     

Correlation equations for friction factors and convective coefficients in tubes containing bundles of internal, longitudinal fins

Finned tubes are commonly employed in tubular heat exchangers to augment the heat transfer rates between two dissimilar fluid streams. The goal of this study is two-fold: a) to determine the laminar, fully developed velocity and temperature fields for long, internal, longitudinal finned tubes; and b) to construct empirical correlation equations applicable for the asymptotic friction factor and the asymptotic Nusselt numbers as a function of the number of fins and the relative fin height in the bundle. Neither the fluid dynamics nor the heat transfer literature provides information for the second goal, which can be extremely useful to thermal engineers for the implementation of Computer-Aided Design (CAD) of internal, longitudinal finned tubes in heat exchange devices. Moreover, for the validity of the correlation equations, a seldom adopted criterion for the critical Reynolds number has also been introduced as an indispensable guideline to warrant laminar regimes. Received on 24 January 1997     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under turbulent flow in a helically dimpled tube

An experimental investigation on the convective heat transfer and friction factor characteristics in the plain and helically dimpled tube under turbulent flow with constant heat flux is presented in this work using CuO/water nanofluid as working fluid. The effects of the dimples and nanofluid on the Nusselt number and the friction factor are determined in a circular tube with a fully developed turbulent flow for the Reynolds number in the range between 2500 and 6000. The height of the dimple/protrusion was 0.6 mm. The effect of the inclusion of nanoparticles on heat transfer enhancement, thermal conductivity, viscosity, and pressure loss in the turbulent flow region were investigated. The experiments were performed using helically dimpled tube with CuO/water nanofluid having 0.1%, 0.2% and 0.3% volume concentrations of nanoparticles as working fluid. The experimental results reveal that the use of nanofluids in a helically dimpled tube increases the heat transfer rate with negligible increase in friction factor compared to plain tube. The experimental results showed that the Nusselt number with dimpled tube and nanofluids under turbulent flow is about 19%, 27% and 39% (for 0.1%, 0.2% and 0.3% volume concentrations respectively) higher than the Nusselt number obtained with plain tube and water. The experimental results of isothermal pressure drop for turbulent flow showed that the dimpled tube friction factors were about 2-10% higher than the plain tube. The empirical correlations developed for Nusselt number and friction factor in terms of Reynolds number, pitch ratio and volume concentration fits with the experimental data within ±15%.     

Visualization of flow pattern and thermal image analysis of enhanced heat transfer surface

Experimental studies on flow visualization and heat transfer measurements of finned surface in a narrow duct were carried out to understand the flow behavior and its effect on heat transfer. In this experiment, short rectangular fins were attached to a surface (endwall) with having inclination angle of 20° and exposed to air flow. Several flow visualization results reveal that horse shoe vortex was formed just at the front of the fin whereas the main longitudinal vortex was formed by the side top edge of the fin. Some important features of the vortex structure, size and flow reattachment positions were noticed from the smoke flow visualization. Detailed heat transfer distributions were discussed from the thermal image. Nusselt number shows that the finned surface achieved average heat transfer enhancement at a factor of four times than that of without fins.     

Analysis of heat transfer in a partially wet radial fin assembly during dehumidification

This paper presents the analysis of heat transfer in a partially wet annular fin assembly during the process of dehumidification. In past studies, both fully dry and fully wet fins have been analyzed. New analytical formulation leading to a closed-form solution has been developed for a partially wet fin, which is most common in dehumidifier coil operation during air conditioning. The parameters that influenced the heat transfer rate in the finned tube structure are ratio of fin and wall thermal conductivities, ratio of fin thickness to fin pitch, ratio of wall thickness to fin pitch, ratio of fin length to fin pitch, cold fluid Biot number, ambient Biot number, the relative humidity and dry bulb temperature of the incoming air, and the cold fluid temperature inside the coil. Calculations were carried out to study the performance of the heat exchanger. The computed results included the temperature distribution in the wall and the fin and the fin efficiency.     

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.     

Fins and turbulence promoters for heat transfer enhancement in latent heat storage systems

One of the serious problems associated with the operation of PCM storage system is the heat transfer in and out of the element containing the PCM. This paper presents the results of an experimental investigation of the effects of radial fins and turbulence promoters on the enhancement of phase change heat transfer external to a horizontal tube submersed in the PCM with the working fluid flowing through it. The experimental measurements were realized on a bare cupper tube and an identical cupper tube fitted with radial fins. The fins investigated are 40, 60, 120 and 180 mm diameters. A turbulence promoter made of stainless steel wire of 1.0 mm diameter coiled in a helical form with a pitch of 25.0 mm was inserted into the cupper tubes. The tests were realized on bare tubes, finned tubes and finned tubes with the turbulence promoter inserted into the finned tubes. The measurements were realized for the working fluid temperatures in the range of −10 °C, to −25 °C and six values of the mass flow rate ranging from 0.013 to 0.031 kg/s. The position of the phase interface was photographed by a high resolution digital camera and scanned to determine the real interface position by comparison with a precision measuring scale. The results of the phase interface position, velocity of the interface, solidified mass fraction and the time for complete solidification are presented in function of the working fluid temperature, the working fluid mass and the tube arrangements. The results are presented and discussed.     

Heat transfer from a vertical tube bundle under natural circulation conditions

A rectangular loop (thermosyphon) was used to measure the average heat transfer coefficients for water at atmospheric pressure under natural circulation conditions. A twenty-one tube bundle with tubes 1.65 m long and 9.55 mm in diameter, and a pitch-to-diameter ratio of 1.33, was used as a test heat exchanger in one of the vertical legs of the loop. A natural circulation flow in the loop developed due to buoyancy differences of the fluid in its two vertical legs. Flow visualization experiments were performed to determine the flow regimes associated with natural circulation flow longitudinal to a tube bundle. Empirical correlations for the average Nusselt number have been developed and are reported. Grid spacers arranged on tube bundles were shown to enhance heat transfer, especially for laminar flow, without any noticeable increase in pressure drop.     

Laboratory investigation and commercial test for rotors-assembled strand applied in smooth tube

In the commercial test for smooth tube inserted with rotors-assembled strand comparing with non-inserted ones on condensers in electric power plant, using water as working fluid, the single-phase pressure drop and heat transfer were measured. It was found difficult to receive reliable and accurate enough data through commercial test. Meanwhile, the single-phase pressure drop and heat transfer in a rotors-assembled strand inserted tube were measured in laboratory, with the tube side Prandtl numbers varying from 5.67 to 5.80 and the tube side Reynolds numbers varying from 21,300 to 72,200. Before that, a validation experiment based on the same smooth tube was carried out to testify the experimental system and the data reduction method, in which fixed mounts were employed to eliminate entrance effects. The Prandtl numbers varied from 5.64 to 5.76 and the Reynolds numbers varied from 19,000 to 56,000 in the tube. The annular side Reynolds numbers remained nearly constant at the value of around 50,000 for all experiments, with the annular side Prandtl numbers varying from 8.02 to 8.22. The experimental results of smooth tube show that employment of fixed mounts leads to a visible bias of friction factor at relative low Reynolds numbers while it hardly affects the Nusselt numbers. On the other hand, experiment for the tube inserted with rotors-assembled strand show remarkable improvement for heat transfer with the Nusselt number increased by 9.764–11.87% and the overall heat transfer coefficient increased by 7.08–7.49% within the range of Reynolds number from about 21,300 to 55,500. Meanwhile, friction factor increases inevitably by 278.1–353.9% within the same range of Reynolds number. Based on through multivariant linear normal regression method, the Reynolds number and Prandtl number dependencies of the Nusselt number and friction factor were determined to be Nu = 0.0031Re^0.9Pr^1.0849 and f = 0.993Re^−0.22.     

Numerical investigation of heat transfer and fluid flow characteristics inside a wavy channel

The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on SIMPLER algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop. An erratum to this article can be found at     

Effect of corner angle on convection enhancement in wavy ducts with trapezoidal cross‐sections

The effect of corner angle variations on pressure drop and heat transfer characteristics is investigated in the fully developed region of wavy ducts with trapezoidal cross‐sections. The resulting enhancement of convection, with respect to corresponding straight ducts, can be attributed to the formation of longitudinal vortices close to the two parallel surfaces. Numerical simulations show that Nusselt numbers and friction factors increase with the decrease of corner angle from 90 to 60^°, before levelling out around 60^°. Nusselt numbers and friction factors also increase with the Reynolds number, and the slopes of their representative curves increase above a critical value of the Reynolds number because of the onset of time‐periodic flow oscillations. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelluntersuchungen des Wärmeaustausches und Strömungswiderstandes an den Heizflächen mit Diagonalflossen

This paper presents the results of an experimental study on the heat transfer and pressure drop in diagonally finned tube banks. The investigations have been carried out using the napthalene analogy. The performance of a heat exchanger with fins arranged a certain angle to the flow direction with the plain tube heat exchanger have been compared.     

Automatic generation of unstructured grids with Delaunay triangulation and its application

This paper is consisted of two parts. In the first part, a method is described which generates two-dimensional triangle mesh using the Delaunay triangulation criterion. An automatic algorithm was proposed which combines several advantages of the existing methods. Local mesh refinement can also be easily performed with this method. Examples of generated grids were presented for several convex, non-convex and multi-connected domains to demonstrate the effectiveness and feasibility of the proposed method. In the second part, the turbulent heat transfer in an annular space finned by wave-like longitudinal fins was numerical simulated. The proposed technique was adopted to generate the grid in the cross-section. The standard K-ɛ model in conjuction with wall function method was used to simulate the fluid flow and heat transfer in the complex geometry. The discretization of the governing equations was described. The computational results were compared with the authors' test data and the agreement was reasonably good. Received on 9 July 1998     

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.     

Thermally developing flow in curved square ducts with internal fins

The laminar incompressible hydrodynamically fully developed and thermally developing flow is studied in a curved square duct with four longitudinal fins. The duct is successively subjected to constant wall temperature, to circumferentially uniform temperature and axially linearly or exponentially varying temperature. The local and fully developed Nusselt numbers are examined for various values of the Dean number and it is found that the heat transfer rate increases for high fins. The parameters that affect the entry length are studied and the fluctuations of the local Nu that appear in the entrance region are investigated. Temperature contour plots are presented for the visualization of the temperature field and functional relations for the Nusselt number are proposed in terms of the Dean and Prandtl numbers.     

Momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls

An analysis and measurement were made of momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls. The eddy diffusivities of momentum and heat obtained in the turbulent flow in a circular tube were applied to the annular flow in the analysis. The result indicates that the calculated friction factor and average Nusselt numbers on the inner and outer tube walls are in fairly good agreement with the measurements.     

Convective heat transfer in the thermal entrance region of finned double-pipe

Numerical simulation of the steady and laminar convection in the thermal entry region of the finned annulus is carried out for the case of hydrodynamically fully developed flow when subjected to uniform heat flux thermal boundary condition. Finite difference based marching procedure is used to compute the numerical solution of the energy equation. The results to be presented include Nusselt number, as a function of dimensionless axial length and thermal entrance length for various configurations of the finned double-pipe. The numerical results show that Nusselt number has complex dependence on the geometric variables like ratio of radii, fin height, and number of fins. A comparison of the computed results for certain limiting cases with the results available in the literature validates the numerical procedure used in this work.