Tables for solution of the heat-conduction equation with a time-dependent heating rate

Tables are presented for the solution of the transient onedimensional heat flow in a solid body of constant material properties with the heating rate at one boundary dependent on time. These tables allow convenient and rapid estimation of the temperature distribution in the many practical cases where the mathematical model applies. Examples illustrating use of the tables are given

Pressure drop with surface boiling in small-diameter tubes

Pressure drop for water flowing in small-diameter tubes under isothermal, nonboiling, and surface-boiling conditions was investigated. Experimental results for local pressure gradient and heattransfer coefficients are presented. Heat-transfer results for nonboiling and surface boiling are in agreement with previous investigations. Isothermal friction factors compare favorably with conventional smooth-tube data. Nonboiling friction factors were well correlated with a wall-to-bulk fluid viscosity ratio. It is concluded that boiling pressure gradients cannot be correlated on the basis of local conditions alone. The axial build up of nonequilibrium vapor in the tube produces an increase in pressure gradient even when all other local parameters are constant. The heat-transfer - pressure-gradient analogy was investigated in the boiling region. For the chosen boiling-to-nonboiling ratios, the analogy was found to be valid only under limited conditions. Over-all pressure-drop data are presented for numerous geometries and a range of flow conditions. Diameters of 0.062 to 0.180 in. and L/D's of 25 to 200 were considered. Exit pressures ranged from 30 to 80 psia and velocities ranged from 5 to 50 ft/sec. The majority of the data was taken for an inlet temperature of 80 OF. Heat fluxes were increased from zero to near the burnout condition unless the saturation condition was reached first. These results were correlated by a relation which is independent of all parameters except geometry. This correlation is presented graphically for all the geometries used. Either this plot or the original data plots can be readily used for design purposesSponsored by the Solid State Sciences Division, Air Force Office of Scientific Research D.S.R

Subcooled flow boiling of fluorocarbons

A study was conducted of heat transfer and hydrodynamic behavior for subcooled flow boiling of Freon-113, one of a group of fluorocarbons suitable for use in cooling of high-power-density electronic components. Problems arising from the excellent wetting characteristics and large solubility constants of fluorocarbons were also examined. The primary configuration was vertical upflow through a 0.500-in. ID stainless steel tube with direct resistance heating of the tube wall. Operating parameter ranges included up to 4.28 ft/sec velocity, 22.3 psia pressure, 61*F subcooling, 0.40 void fraction, 1.08 X 10-3 moles/mole dissolved gas, and 105 Btu/hr ft2 heat flux. Single-phase heat transfer was adequately correlated by standard methods. Boiling curves had a unique form dominated by large, discontinuous jumps in wall temperature at the incipient point on increasing heat flux traverses. Effects of velocity and subcooling on two-phase heat transfer followed conventional trends. Techniques were devised for accurate determination of the temperature dependence of the air-Freon-113 solubility constant and for measurement and control of dissolved gas content in the main loop. Dissolved gas effects were found to increase heat transfer significantly in the partial boiling mode. Data in the fully-developed boiling mode were successfully described by modifications of existing correlations. A conventional correlation provided, at best, an upper bound for the critical heat flux data. Models and analyses were formulated for predicting delayed nucleation and dissolved gas effects on incipience. Delayed nucleation and hysteresis were successfully eliminated by means of a special surface coating. Transition in gassy boiling heat transfer from gas-dominated to vapor-dominated modes was postulated with reference to adjusted saturation temperatures.(cont.) Single-phase pressure drop was adequately correlated by standard methods. Parametric effects on two-phase total pressure drop were investigated and described. Three novel techniques--photographic, trap, and capacitance-- were employed to obtain accurate void fraction measurements. It was found that dissolved gas drastically retarded bubble collapse rates. Parametric effects on void fraction were examined and approximately correlated on quality coordinates. Modification of an existing analysis for predicting the point of net vapor generation gave reasonable agreement with void data. Void information was used to estimate the gravity component of pressure drop. The remaining friction-acceleration component data were plotted on coordinates suggested in an existing correlation. Alteration of the coordinates to account for issolved gas resulted in fair agreement of data with the correlation curv-. A qualitative description of the gas-dominated to vapor-dominated transition in pressure drop performance, analogous to that for heat transfer, was developed.DSR Project

A study of boiling water flow regimes at low pressures

"A comprehensive experimental program to examine flow regimes at pressures below 100 psia for boiling of water in tubes was carried out. An electrical probe, which measures the resistance of the fluid between the centerline of the flow and the tube wall, was used to identify the various flow regimes. This probe proved to be an ideal detection device, because of its simplicity, reproducibility, and accurate representation of the flow pattern within the heated test section. The major flow regimes observed were bubbly, slug and annular flow. Under certain conditions at high flow rates, a wispy-annular flow patern was observed. The effects of mass velocity (0.2 x 10 - 2.4 x 100 lbm/hr-ft2), inlet temperature (100, 150, 2000F), exit pressure (30, 100 psia), quality (x = -10 - +7 percent), purity (9, 40 PPM NaCl; 1-3 megohm-cm), length (L/D-30, 6Q, 90), diameter 0.094, 0.242 in.), and orientation (vertical and horizontal on the flow regimes were studied. Flow regime maps on coordinates of mass velocity and quality are presented for these conditions. Bubbly and slug flow occurred primarily in the subcooled region, while fully developed annular flow was reached at equilibrium qualities between 2 and 4 percent. The transitions between the different flows were shifted to regions of increased subcooling when velocity, pressure, and heat flux increased, and when inlet temperature decreased. Purity and geometry had little affect on the flow regime boundaries.(cont.) The shifting of the transitions is related to the agglomeration point, which is that point at which the bubbles so coalesce that slug flow is first observed. The agglomeration point depends on the point of incipient boiling, the number of bubbles in the flow, and the number of collisions per bubble. These latter quantities in turn depend on velocity, temperature, pressure, and heat flux. The flow regime information obtained in this study s~hould be of value in correlating and interpreting low pressure heattransfer data. The flow regime data were found to be useful in explaining the effect of inlet temperature on burnout heat flux.Sponsored by the Solid State Sciences Division, Air Force Office of Scientific Research D.S.R

Survey and evaluation of techniques to augment convective heat transfer

This report presents a survey and evaluation of the numerous techniques which have been shown to augment convective heat transfer. These techniques are: surface promoters, including roughness and treatment; displaced promoters, such as flow disturbers located away from the heattransfer surface; vortex flows, including twisted-tape swirl generators; vibration of the heated surface or the fluid near the surface; electrostatic fields; and various types of fluid additives. Natural and forced convection situations for nonboiling, boiling, and condensation heat transfer are included. The conditions under which heat transfer is improved are summarized, and the efficiency of each technique is presented in terms of a performance criterion where possible.Sponsored by the Air Force Office of Scientific Research D.S.R

Forced-convection surface-boiling heat transfer and burnout in tubes of small diameters

A basic heat-transfer apparatus was designed and constructed for the study of forced-convection boiling in small channels. The various regions of forced-convection surface boiling were studied experimentally and analytically. In the region of low wall superheat, the heat flux can be predicted by available correlations for forced convection. Data indicate, however, that these correlations do not properly account for the radial variation of properties for water at high temperature difference. The conventional Dittus and Boelter-McAdams relationship is recommended for design purposes on the basis of its simplicity and conservative predictions. An analysis for the prediction of the inception of first significant boiling was developed. Experimental results are in good agreement with analytical predictions. The analysis provides information necessary for the prediction of the complete forced-convection surface-boiling curve. Data for a small-diameter tube indicate that the bubbles formed at incipient boiling can trip the laminar or transition boundary layer to a fully-developed turbulent boundary layer. The region of vigorous boiling coincides approximately with the extrapolation of the pool-boiling curve in one set of experiments. In other experiments, pool-boiling data were strongly influenced by fluid and surface conditions, as well as by bubble-induced convection in the pool. Due to the complexities in these pool-boiling data, it is impossible to make a conclusive comparison with forced-convection-boiling data. The heat flux obtained by a superposition of pool boiling and forced convection is close to the apparent asymptote for fully-developed boiling. For design purposes, it is concluded that fully-developed -forced-convection boiling can be related to pool boiling by either direct extrapolation or superposition of forced convection.(cont.) The burnout heat flux under conditions of forced convection and surface boiling is shown to be a complicated function of subcooling at low values of subcooling. This appears to be due to the velocity increase caused by the relatively large volume fraction of vapor. Burnout flux is shown to increase with decreasing tube diameter. This effect can be attributed to an increase in void fraction with decreasing tube diameter. Entrance effects are significant in forced-convection surface boiling as shown by the decrease of burnout flux with increasing length. Flow oscillations caused by system compressibility can greatly reduce the burnout heat flux in the subcooled region. This instability is particularly difficult to avoid with tubes of very small diameter.Air Force Office of Scientific Research D.S.R. Projec

Heat transfer and pressure drop in tape generated swirl flow

The heat transfer and pressure drop characteristics of water in tape generated swirl flow were investigated. The test sections were electrically heated small diameter nickel tubes with tight fitting full length Inconel tapes of twist ratios from 2. 48 to 9. 2 inside diameters/180 of tape twist. Heat transfer coefficients and friction factors were determined for non-boiling forced convection heating and cooling while overall pressure drop information and curves of heat flux versus wall superheat were determined for surface boiling conditions. Improvements in heat transfer for equal flow rates of up to 851c were observed for the non-boiling swirl flows with heating, but the improvement with cooling was substantially less. Compared on the basis of equal pumping power, improvements in heat transfer of up to 351c were observed for the tighter tape twists. A method for predicting the heat transfer coefficient for non-boiling swirl flows was developed. It was based upon the theory that the improvement was due primarily to: 1) the increased flow path created by the tape, 2) the increased circulation created with heating due to the buoyancy effect set up by the large centrifugal force present, and 3) the fin effect of the tape. The experimental results of this and previous swirl flow investigations were in good agreement with the analytical prediction. The surface boiling characteristics of swirl flow were found to be similar to those observed in straight flow. The boiling curves for various velocities were asymptotic to a fully developed line at high wall superheats, and the visually observed point of incipient boiling and the transition to the fully developed boiling asymptote were predictable by conventional straight flow methods. It was concluded, therefore, that the dominant surface boiling heat transfer mechanism was similar for both swirl and straight flow.(cont.) For non-boiling swirl flows, the decrease in the pressure drop with heating was slightly less than is usual with straight flows, while the increase in the pressure drop with surface boiling was substantially less. A method for predicting the difference in each case is presented.D.S.R. Project Sponsored by the Solid State Sciences Division, Air Force Office of Scientific ResearchAir Forc

Model of critical heat flux in subcooled flow boiling

The physical phenomenon occurring before and at the critical heat flux (CHF) for subcooled flow boiling has been investigated. The first phase of this study established the basic nature of the flow structure at CHF. A photographic study of the flow in a glass annular test section was accomplished by using microflash lighting and a Polaroid camera. The results showed that the flow structure at CHF for high heat flux (1 x 106 - 5 x 106 Btu/hr-ft2), high subcooling (50-110 *F), at low pressures (less than 100 psia) was slug or froth flow depending on the mass velocity. Nucleation was shown to exist in the superheated liquid film. Pin-holes in the burned-out test sections suggested that the CHF condition was extremely localized. Flow regime studies in tubular and annular geometries, using an electrical resistance probe, provided further evidence of the slug or froth nature of the flow, and also showed that dryout of the superheated liquid film was not responsible for CHF. Since this evidence was contradictory to previously formulated models of CHF,a new model was proposed: Near the CHF condition, nucleation is present in the superheated liquid film near the surface. As a large vapor clot passes over the surface, these nucleating bubbles break the film and cause a stable dry spot which results in an increased local temperature. As the vapor finally passes the site, the dry spot is quenched by the liquid slug, and the temperature drops. At CHF, the volumetric heat generation, slug frequency, and void fraction are such that the temperature rise resulting from the dry spot is greater than the temperature drop during quenching. An unstable situation results where the temperature of this point continues to rise when each vapor clot passes the site until the Leidenfrost temperature is reached, at which point quenching is prevented and destruction is inevitable.(cont.) A new method of measuring surface wall temperatures, in conjunction with high speed (Fastax) 16 mm movies, confirmed the microscopic features of the proposed model. At CHF, the wall temperature cyclically increased with the same frequency as the slug-vapor bubble passage. Destruction finally resulted as the temperature increased beyond the Leidenfrost point. An analytical investigation based on an idealized model demonstrated that the cyclical nature of the temperature increase at CHF could be predicted with appropriate flow pattern inputs. A parametric study using the program indicated that heater thickness and heater material should affect the CHF. It was shown that the proposed model appears to be consistent with parametric trends, i.e. mass velocity, pressure, subcooling, diameter, length, and surface tension. The model indicated that the CHF for thicker walled tubes, keeping all other conditions the same, would increase. CHF tests were conducted which confirmed that thicker walled tubes (0.078 vs. 0.012 in. ) had CHF up to 58 percent higher than thin walled tubes.Sponsored by the Solid State Sciences Division, Air Force Office of Scientific Research (OAR) Sponsored by Air Forc

Single-phase laminar flow heat transfer from confined electron beam enhanced surfaces

An experimental investigation of the thermal-hydraulic characteristics for single-phase flow through three electron beam enhanced structures was conducted with water at mass flow rates from 0.005 kg/s to 0.045 kg/s. The structures featured copper heat transfer surfaces, approximately 28 mm wide and 32 mm long in the flow direction, with complex three-dimensional (3D) electron beam manufactured pyramid-like structures. The channel height varied depending on the height of the protrusions and the tip clearance was maintained at 0.1-0.3 mm. The average protrusion densities for the three samples S1, S2, and S3 were 13, 11, and 25 per cm2 with protrusion heights of 2.5, 2.8, and 1.6 mm, respectively. The data gathered were compared to those for a smooth channel surface operating under similar conditions. The results show an increase up to approximately three times for the average Nusselt number compared with the smooth surface. This is attributed to the surface irregularities of the enhanced surfaces, which not only increase the heat transfer area but also improve mixing, disturb the thermal and velocity boundary layers, and reduce thermal resistance. The increase in heat transfer with the enhanced surfaces was accompanied by an increase of pressure drop, which has to be considered in design.The authors would like to acknowledge Dr Anita Buxton and Dr Bruce Dance of TWI for their contribution to this project and also EPSRC and TSB for funding the EngD programme and sponsoring the ASTIA collaborative research project that helped to develop the Electron Beam enhanced surfaces respectively

Cooling of high-power-density computer components

This report summarizes work carried out during the first two years of a research program sponsored by IBM Corporation. This study has elucidated a number of the heat-transfer characteristics of several fluorochemicals which have potential application as coolants for high power density computer components. Single-phase heat-transfer coefficients have been determined for Freon-113 and FC-78 flowing in a rectangular channel with one of the wide sides heated. Heat-transfer coefficients for the short channels are significantly higher than those predicted by conventional correlations due to entrance effects and superimposed free convection. Uncertainties as to the actual values of certain thermophysical properties introduce corresponding uncertainty in correlation. Subcooled flow boiling data were taken with the rectangular channel for a wide variety of fluid-surface combinations, and over a wide range of flow conditions. These data should facilitate a close estimate of surface temperatures in actual systems. Data taken with an annular test section delineated hysteresis effects which were tentatively identified in the rectangular channel tests. Pool boiling tests indicated large temperature overshoots in the boiling curve with Freon-113. It was found that conventional correlations do not adequately describe critical heat flux data for horizontal circular heaters. The critical heat flux increases as diameter decreases, and increases as the wall thickness increases. The observed hysteresis effects in pool and flow boiling were examined in detail. It is suggested that the phenomenon of temperature overshoot hysteresis is due to two causes: a) the existence of metastable bubbles which are triggered only at sufficiently high disturbance level, and b) the deactivation of larger nucleation sites by displacing the vapor by liquid during subcooling.(cont.) Under conditions of low velocity or pool boiling, a) is probably most important, but at high velocity b) should be controlling. Increased heat-transfer coefficients observed prior to nucleation appear to be due to thermocapillary circulation induced by the metastable bubbles. It is demonstrated that a random array of Teflon pits on the surface is effective in augmenting heat transfer for pool boiling or low velocity flow boiling of water; however, there is no improvement in heat transfer with boiling of Freon-113 or FC-78. The mechanism of augmentation is examined from the standpoint of incipient boiling, and a plausible explanation for this behavior is suggested. An investigation of the factors controlling the void fraction for subcooled boiling was carried out with a horizontal visual section using Freon-113 and Freon TA. The observed point of net vapor generation was much farther upstream than that indicated by a recent prediction, due primarily to the dominance of the buoyant force. An examination of the void collapse in the unheated downstream portion of the tube revealed that bubble collapse theory cannot be used to predict the void fraction. The large void fractions produced by boiling fluorochemicals can be minimized by using twisted-tape inserts.Heat Transfer Development Laboratory, Systems Development Division, International Business Machines Corporation Massachusetts Institute of Technology, Division of Sponsored Researc