Time-averaged Heat Transfer Coefficients Research Articles

Theoretical analysis of heat transfer in laminar pulsating flow

Pulsation effect on heat transfer in laminar incompressible flow, which led to contradictory results in previous studies, is theoretically investigated in this work starting from basic principles in an attempt to eliminate existing confusion at various levels. First, the analytical solution of the fully developed thermal and hydraulic profiles under constant wall heat flux is obtained. It eliminates the confusion resulting from a previously published erroneous solution. The physical implications of the solution are discussed. Also, a new time average heat transfer coefficient for pulsating flow is carefully defined such as to produce results that are both useful from the engineering point of view, and compliant with the energy balance. This rationally derived average is compared with intuitive averages used in the literature. New results are numerically obtained for the thermally developing region with a fully developed velocity profile. Different types of thermal boundary conditions are considered, including the effect of wall thermal inertia. The effects of Reynold and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated. The mechanism by which pulsation affects the developing region, by creating damped oscillations along the tube length of the time average Nusselt number, is explained.

Experimental study of the convective heat transfer from in-line and staggered configurations of two wall-mounted cubes

The paper reports on the experimental investigation of the effects of the relative obstacle position on the convective heat transfer from a configuration of two wall-mounted cubes located in a fully developed turbulent channel flow. Both in-line and staggered arrangements were studied for various streamwise ( S x / H) and spanwise ( S z / H) distances. Distributions of the local heat transfer coefficient (h) were obtained from infrared thermography and local convective heat flux analyses. Laser Doppler anemometry measurements and flow visualisations were performed to document the flow and turbulence fields around the cubes. The results showed a large variation in the distribution of the local convective heat transfer for the various in-line and staggered configurations studied. While the in-line arrangements were featured by symmetric flow pattern and heat transfer distributions, the staggered arrangements showed distinct asymmetric pattern for certain combinations of S x / H and S z / H. Flow reattachment caused typically a monotonic decay of the convective heat transfer. On the other hand, flow separation caused distinct heat transfer extrema at the cube faces. In addition, the effect of vortex shedding on the convective heat transfer of the downstream cube was studied with a fast-responding heat flux sensor. Despite distinct variation in the distribution of the time-averaged heat transfer coefficient, the cube-averaged heat transfer coefficients appeared to be independent of the relative placement of the two cubes.

00/02927 Dynamic simulation and experiments of a heat regenerative adsorption heat pump

In part I, a three-zone flow boiling model is formulated to describe evaporation of elongated bubbles in microchannels. The heat transfer model describes the transient variation in local heat transfer coefficient during the sequential and cyclic passage of (i) a liquid slug, (ii) an evaporating elongated bubble and (iii) a vapor slug. In this part, the time-averaged local heat transfer coefficient is compared to experimental data taken from seven independent studies covering the following seven fluids: R-11, R-12, R-113, R-123, R-134a, R-141b and CO2. The 1591 test data cover tube diameters from 0.77 to 3.1 mm, mass velocities from 50 to 564 kg/m2s, pressures from 124 to 5766 kPa, heat fluxes from 5 to 178 kW/m2, and vapor qualities from 0.01 to 0.99. The new model predicts 67% of the database to within ±30%. The new model illustrates the importance of the strong cyclic variation in the heat transfer coefficient and the strong dependency of heat transfer on the bubble frequency, the minimum liquid film thickness at dryout and the liquid film formation thickness.

Calculations of the time-averaged local heat transfer coefficients in circulating fluidized bed

Based on the cluster renewal theory of heat transfer in circulating fluidized beds, a mathematical model for predicting the time-averaged local bed-to-wall heat transfer coefficients is developed. The effects of the axial distribution of the bed density on the time-average local heat transfer coefficients are taken into account via dividing the bed into a series of sections along its height. The assumptions are made about the formation and falling process of clusters on the wall. The model predictions are in an acceptable agreement with the published data.

Heat Transfer Characteristics in a Channel Flow with a Rectangular Cylinder.

An experimental study of heat transfer has been conducted in a channel flow with a rectangular cylinder having various width-to-hight ratios, b / h, of 0.5, 1, 2 and 3. Time-averaged heat transfer coefficients and the fluctuations of wall heat flux have been measured. Heat transfer is augmented extensively at the downstream region of the cylinder. In order to examine the relationship between the heat transfer enhancement and the shedding vortices from the cylinder, flow visualization by a smoke-wire method using a high-speed video recording system has been carried out simultaneously with wall heat flux measurement. It is clarified that the heat transfer is augmented by the wall-ward flow induced by the clockwise and counterclockwise vortices shed alternately from the cylinder.

Heat Transfer and Hydrodynamics in a Three-Phase Slurry Bubble Column

The instantaneous and time-averaged heat transfer coefficients in the regions near the wall and at the center and average gas holdups were measured in a 0.28 m diameter slurry bubble column for the air−water and air−water−glass beads (35 μm) system. The effects of high gas velocities (up to 0.35 m/s) and high solids concentrations (up to 40 vol %) were investigated. Gas holdup decreased with increasing slurry concentrations; the rate of decline was rapid at high gas velocities. The instantaneous local heat transfer measurements were analyzed to study the bubble behavior in the regions near the wall and at the center for different solids concentrations. Larger bubbles were detected in the wall region in slurry systems compared to the solid-free system. The average heat transfer coefficient decreased with increasing slurry concentrations. The heat transfer coefficient was always lower at the wall than at the center.

Experimental analysis of 2D-unsteady temperature field by using Mach-Zehnder interferogram images

A measurement method for an unsteady temperature field by using a Mach-Zehnder interferometer and image processing technique is presented. In this study, the results measured by this method were compared with the calculated results under Reynolds numbers (Re = UL/v) ranging to less than 350 in the steady-state. The unsteady characteristics of the local Nusselt numbers (Nux = αxL/λ) around an elastically vibrating plate were investigated under the conditions that the reduced frequency (N = 1/Ro) ranged from 4.8 to 8.6 and the amplitude of vibration was kept small relative to the plate length. In this study it was clarified that the distributions of the Local Nusselt numbers were observed flutteringly, and that the phase of the time-averaged Nusselt number is delayed compared to the phase of the velocity at the trailing edge. These results indicate that the enhancement of the time-averaged heat transfer coefficient around the vibrating plate depended on the Rossby number. © 1997 Scripta Technica. Inc. Heat Trans Jpn Res. 25 (2): 88–102, 1996

Experimental Analysis of 2D-Unsteady Temperature Field by Using Mach-Zehnder Interferogram Image.

A measurement method of an unsteady temperature field by using a Mach-Zehnder interferometer and an image-processing technique was presented. In this study, the results measured by this method were compared with the calculated results under Reynolds numbers(Re= UL/v) ranging to less than 350 in the steady state. The unsteady characteristics of the local Nusselt numbers (Nuχ=αχL/λ) around an elastically vibrating plate were investigated under the conditions that the reduced frequency (N=1/Ro) ranged from 4.8 to 8.6 and the amplitude of vibration was kept small relative to the plate-length. In this study it was clarified that the distributions of the local Nusselt numbers were observed flutteringly, and that the phase of the time averaged Nusselt number is delayed compared to the phase of the velocity at the trailing edge. These results indicate that the enhancement of the time-averaged heat transfer coefficient around the vibrating plate depended on the Rossby number.

Local instantaneous and time-averaged heat transfer in a pressurized fluidized bed with horizontal tubes: Influence of pressure, fluidization velocity and tube-bank geometry

Measurements of local instantaneous bed-to-tube heat transfer were carried out in a cold pressurized bed with horizontal tubes. The influence of fluidization velocity and pressure was studied at different circumferential positions around a horizontal tube within a tube bank for three different tube-bank geometries. The signal from a heat transfer sensor was compared with capacitance probe signals sampled simultaneously in an adjacent position. The capacitance probe registers the alternating passage of bubbles and dense phase at the probe, and the respective contributions to the local instantaneous heat transfer from the gas and particle convection were thus identified by comparison with the heat transfer signal. The local time-averaged heat transfer coefficients at the different circumferential positions were determined from the instantaneous heat transfer signals, for the different operating conditions, as were the spatial-averaged heat transfer coefficient for the tube. The time-averaged heat transfer results were correlated with the hydrodynamic properties of the bed obtained in a previous investigation under the same operating conditions, and a strong coupling between the local mean bubble frequency and the local time-averaged heat transfer coefficient was obtained. The heat transfer results show a significant increase of the bed-to-tube heat transfer coefficient with increasing pressure, while results from a previous erosion study in the same bed show that, at high pressures, the tube erosion decreases with increasing pressure. Thus, it should be favourable to operate a bed at high pressure levels. The heat flux was measured using flush-mounted sensors on a heated copper cylinder replacing one of the tubes in the horizontal tube banks. The bed has a cross-section of 0.2m × 0.3 m, and was operated at pressures between 0.1 and 1.6 MPa and at excess gas velocities of 0.2 and 0.6 m/s. Of the three tube-bank geometries used, one had a fairly dense pitch and two had more sparse configurations. The bed material was silica sand with a mean particle diameter of 0.7 mm.

Combined Effect of Free-Stream Turbulence and Unsteady Wake on Heat Transfer Coefficients From a Gas Turbine Blade

The combined effect of free-stream turbulence and unsteady wakes on turbine blade surface heat transfer was studied. The experiments used a five-blade linear cascade in a low-speed wind tunnel facility. A turbulence grid and spoked-wheel type wake generator produced the free-stream turbulence and unsteady wakes. The mainstream Reynolds numbers based on the cascade inlet mean velocity and blade chord length were 100,000, 200,000, and 300,000. Results show that the blade time-averaged heat transfer coefficient depends on the mean turbulence intensity, regardless of whether this mean turbulence intensity is from unsteady wake only, turbulence grid only, or a wake and grid combination. The higher mean turbulence promotes earlier boundary layer transition and causes much higher heat transfer coefficients on the suction surface. It also significantly enhances the heat transfer coefficients on the pressure surface. The unsteady wake greatly affects blade heat transfer for low oncoming free-stream turbulence; however, the wake effect diminishes for high oncoming turbulence. The free-stream turbulence also strongly affects blade heat transfer for a low wake passing frequency, but the oncoming turbulence effect diminishes for a high unsteady wake condition.

An investigation on instantaneous local heat transfer coefficients in high-temperature fluidized beds—I. Experimental results

Experimental results are presented and analysed for instantaneous and time-averaged local surface temperatures and heat transfer coefficients around a water-cooled horizontal tube of 40 mm in outer diameter immersed in a 230 × 160 mm cross section high temperature fluidized bed. Such measurements are made using a specially-designed thin-film thermocouple probe. Silica sands with mean diameter of 0.662, 1.103 and 1.815 mm are used as bed materials. Measurements are taken over a wide temperature range from 270 to 1028°C.

Heat transfer in three-phase fluidized beds containing low-density particles

The complex behavior of heat transfer in three-phase fluidized beds has been attributed to the interaction between phases which varies with the particle size, particle density, gas and liquid velocities. Three-phase fluidization with low-density particles is of considerable interest to biochemical applications. However, the understanding of heat transfer behavior in low-density systems is very limited. A special heat transfer probe is immersed in a three-phase fluidized bed and local instantaneous and time-averaged heat transfer coefficients are measured for calcium alginate beads and other low-density particles. In liquid—solid systems with low-density particles, the instantaneous heat transfer due to single-bubble passage exhibits a local maximum in the primary wake region caused by the enhanced surface renewal at the heat transfer surface. Enhancement in heat transfer due to bubble wake increases with bubble size but decreases with increasing particle density. Accordingly, relative enhancement in time-averaged heat transfer in three-phase systems over liquid—solid fluidized beds is higher for low-density particles compared to heavier particles under identical gas and liquid velocities. Local time-averaged heat transfer in low-density beds is found to be relatively independent of liquid velocity for gas velocity higher than 3 cm/s. Distributor effects on the flow regime and thereby the heat transfer are significant for low-density particles. The heat transfer is observed to be higher in the coalesced flow regime compared to that in the dispersed flow regime primarily due to significant bubble-wake effects. Axial variations in heat transfer coefficients are also observed for systems containing intermediate-density particles due to axial nonuniformities in solids holdup.

A THEORETICAL STUDY OF THE LIMITING HEAT TRANSFER COEFFICIENT IN FLUIDIZED BEDS

Abstract A new model is presented to describe the heat transfer process occurring in fluidized beds under the limiting condition of very short contact times between the heat transfer surface and the emulsion phase. Unlike other work in this area the proposed model assumes that the particles are in constant motion close to the surface throughout the heat transfer process. The effect of the non-continuum gas film assumption (the Smoluchowski effect) when particles are very close to the surface is found to be of secondary importance when compared with the movement of particles close to the surface. Expressions for both the instantaneous and time averaged heat transfer coefficients for individual and a spatial distribution of parlicles are presented.

Momentum, heat and mass transfer in turbulent pipe flow: The extended random surface renewal model

A model is presented for a quantitative prediction of the transfer coefficients of momentum, heat and mass, and the radial profiles of the axial velocity, the temperature, and the concentration in the near-wall fluid of a turbulent pipe flow. In this model, the tube wall is assumed to be covered by a mosaic of fluid elements of random age and laminar flow with unsteady profiles of velocity, temperature, or concentration. This model, which is an extension of the RSR model developed by Fortuin and Klijn, is the extended random surface renewal model, and is referred to as the ERSR model. The distribution and the mean value of the ages of the fluid elements at the tube wall govern the local time-averaged transfer coefficients and radial profiles in the wall region. The mean age of the fluid elements is derived from the friction factor and the Reynolds number using the ERSR model. Both the distribution and the mean ages of the fluid elements at the tube wall agree quantitatively with the experimental results obtained from velocity signals measured with a laser-Doppler anemometer in turbulent pipe flow at thirteen Reynolds numbers between 5 × 10 3 and 43 × 10 3. The equations derived from the ERSR model for the local time-averaged heat and mass transfer coefficients in turbulent pipe flow, and the radial profiles of the axial velocity, the temperature and the concentration in the wall region, agree with correlations or experimental data presented in literature. The analogy between momentum, heat and mass transfer in turbulent pipe flow is elucidated by introducing a dimensionless number for momentum transfer. This so-called Fanning number for momentum transfer ( Fa = k m d/v), is comparable with the Nusselt number for heat transfer and the Sherwood number for mass transfer. Furthermore, the ERSR model provides a basis for both explaining the Chilton-Colburn analogy and the relationship between transfer rates and measured mean ages of fluid elements at the wall in turbulent pipe flow.

The measurement of instantaneous heat transfer coefficients around the circumference of a tube immersed in a high temperature fluidized bed

Instantaneous and time-averaged local heat transfer coefficients are obtained for an immersed heat transfer tube in a high temperature (900 K) fluidized bed. Surface temperature measurements are made by very fine ribbon thermocouples circumferentially located 120° around the surface of the immersed tube. Surface temperature measurements are converted to local instantaneous heat transfer coefficients by solving the conduction equation for the tube wall. Results from this work are compared to previous work in fluidized beds.

Natural-Convection Film Boiling Heat Transfer. 5th Report. Model Analysis of Subcooled Film Boiling with Wavy Interface.

Heat transfer in natural-convection film boiling with a wavy interface is investigated analytically. The vapor-film-unit model proposed in the first report for saturated film boiling is extended to subcooled film boiling with a wavy interface. In this extended model, based on the mean vapor velocity and the vapor film thickness under a subcooled condition, the vapor-film-unit length along an inclined flat plate is determined for subcooled film boiling as a function of the inclination angle. Using this result and accounting for movement of the vapor-film units, vapor-film units are arranged along the vertical surface and the periphery of the horizontal cylinder. The time-averaged local heat transfer coefficient is determined by integrating the time-dependent local heat transfer coefficient. The heat transfer coefficient averaged over the surface is determined by integrating the distribution of the time-averaged local values. The predictions of the model agree well with experimental data for film boiling along long vertical surfaces and around horizontal cylinders of large diameter. It is concluded, thus, that the extended vapor-film-unit model can correctly describe the effects of fluid properties, liquid subcooling, surface superheating and surface dimensions on film-boiling heat transfer with a wavy interface.

A numerical study of heat and momentum transfer for flexible tube bundles in cross flow

A numerical scheme is developed in order to calculate the heat transfer and pressure drop coefficients in heat exchangers made of flexible tubes. The vibrating tubes are modeled in a quasistatic way by taking the first tube of the row to be in 15 asymmetric (with finite eccentricity) positions with respect to the rest of the tubes and averaging in time the steady-state solutions corresponding to each one of these geometries.The results show that the eccentricity of the first tube affects the velocity and temperature profiles significantly.The time-averaged heat transfer and pressure drop coefficients are higher than those for the case of rigid, symmetrically placed, tube bundles.Comparison of the present results shows very good agreement with experimental data from flexible tube heat exchangers.

Local evaporative heat transfer coefficient in turbulent free-falling liquid films

Evaporative heating of a free-falling turbulent liquid film has been investigated experimentally and numerically. The film exhibited a long thermal development length persisting up to more than one half of the 781 mm long heated test section. The increased length of the development region is attributed to the formation of a boundary layer at the film interface. This boundary layer was predicted numerically and observed in temperature measurements within the film. The heat transfer coefficients are averaged over the lower section of the tube and correlated as a function of the Reynolds and Prandtl numbers. Numerical predictions are made for the development region and for fully developed heat transfer coefficients using three different eddy diffusivity models. Comparison with experimental data reveals that two of these models are fairly successful in predicting the extent of the thermal development region and the time-averaged evaporative heat transfer coefficient; yet the data indicate the need for development of a new model which accurately accounts for local and spatial wave-induced variations of film thickness.

Local Heat Transfer Coefficients for Horizontal Tube Arrays in High-Temperature Large-Particle Fluidized Beds: An Experimental Study

An experimental study is described in which time-averaged local heat transfer coefficients were obtained for arrays of horizontal tubes immersed in a hot fluidized bed. Bed temperatures up to 1005 K were achieved. Bed particle sizes of 2.14 mm and 3.23 mm nominal diameter were employed. An array of nine tubes arranged in three horizontal rows was used. The 50.8 mm (2 in.) diameter tubes were arranged in an equilateral triangular configuration with 15.24 cm (6 in.) spacing between centers. The center tube in each of the three rows in the array was instrumented providing data for local heat flux and surface temperature at intervals of 30 deg from the bottom to the top—a total of seven sets of values for each of the center tubes. The three sets of data are representative of the heat transfer behavior of tubes at the bottom, top, and in the interior of a typical array. Data were also obtained for a single horizontal tube to compare with the results of tube bundle performance. Superficial velocities of high-temperature air ranged from the packed-bed condition through approximately twice the minimum fluidization level. Comparisons with results for a single tube in a bubbling bed indicate only slight effects on local heat transfer resulting from the presence of adjacent tubes. Tubes in the bottom, top, and interior rows also exhibited different heat transfer performance.

Instrument for the measurement of heat flux from a surface with uniform temperature

An instrument for the measurement of heat flux from a surface with a nearly uniform temperature is described. This instrument contains a thin-film electrical resistance heater embedded in a copper cone which is thermally isolated from the surrounding walls. A differential thermocouple between the copper cone and the wall is nulled such that the electrical power becomes a direct measure of the surface heat flux. The advantage of this design over earlier sensors is its modular characteristic and its ability to be flush mounted in an external surface or mounted in the wall of a duct. It has been used to measure the local time-average heat transfer coefficient inside a circular duct. The time constant in this application was 43 s. For these measurements an uncertainty analysis is presented which shows that this instrument has an uncertainty of ±3.6% for a convective heat flux of 342 W/sq m. The major source of uncertainty was the surface area.