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

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

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

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

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

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

Forced-convection, dispersed-flow film boiling

This report presents the latest results of an investigation of the characteristics of dispersed flow film boiling. Heat transfer data are presented for vertical upflow of nitrogen in an electrically heated tube, 0.4 in. I.D. and 8 ft long. Heat fluxes up to 18,000 Btu/ft 2-hr and mass fluxes up to 200,000 lbm/ft 2-hr were investigated. By variation of the startup procedure, it was possible to operate in two distinct regimes of film boiling. By preheating the tube before introducing the flow, film boiling was observed throughout the test tube. If the flow was established before applying power, film boiling was initiated downstream of the inlet. For similar conditions, the local heat transfer coefficients were different in the two cases due to the different degrees of thermal nonequilibrium. The data for both regimes were satisfactorily predicted by a modified version of the nonequilibrium model presented in earlier reports. The model was also applied to available data for methane, propane, and water. By modification of the empirical constant governing the direct wall-to-droplet heat transfer, these data were generally predicted to within 10 percent. The tests were repeated with tight-fitting, full-length twisted tapes installed in the test tube. Considerable augmentation of the heat transfer was achieved, with the heat transfer coefficient being increased by as much as a factor of 3 with the tightest tape twist. For the higher mass fluxes, it was observed that the tape promoted droplet deposition to such an extent that a continuous liquid film could be reestablished on the wall near the test section exit. The tape-generated swirl flow did not improve the "burnout" condition, primarily due to the fact that a liquid streamer forms on the twisted tape. The semiempirical model gave a reasonable prediction of the heat transfer coefficient when the effects of the swirl flow were included.Sponsored by the National Science Foundation D. S. R

Investigation of heat transfer augmentation through use of internally finned and roughened tubes : final summary report

This report summarizes a three-year program concerned with obtaining basic design information for tubes having a random roughness on the inside wall (RID) and tubing having continuous internal fins (Forge Fin). Test apparatus and procedures were developed to obtain accurate heat-transfer and friction data for a wide variety of tube geometries using water as the test fluid. For the random roughness the heat-transfer coefficient was above the smooth tube value, for comparable flow conditions, by over 60 percent at a Reynolds number of 30,000. Larger percentage improvements can be expected for higher Reynolds numbers and for fluids having higher Prandtl numbers. Improvements in performance, based on equal pumping power for augmented and smooth tubes, of about 50 percent were observed. The heat-transfer characteristics for tape-generated swirl flow through rough tubes were investigated in order to determine the interaction of swirl flow and roughness effects. For the particular range of parameters covered, for equal flow rates, the maximum improvement in heat transfer with swirl flow in smooth tubes was 70 percent, whereas with swirl flow in rough tubes, the improvement was as much as 100 percent. The heat-transfer coefficient for rough tube swirl flow was accurately correlated by a modification of an additive expression previously suggested for prediction of smooth tube swirl flow data.(cont.) The test program for internally finned tubes established that short spiralled fins produce the greatest improvement in heat transfer. On the basis of equal flow conditions, the heat transfer was improved by over 200 percent; while at equal pumping power, the performance was as high as 170 percent. These improvements, which are attributed to increased area and turbulence promotion, appear to equal the improvements displayed by any of the schemes used to augment heat transfer inside tubes. In order to bring the augmentation problem into perspective, a discussion of data for other types of roughness and finning is included.DS

Boiling and condensation in a liquid-filled enclosure

A combined experimental and analytical investigation of boiling and condensation in a liquid-filled enclosure, with water and Freon- 113 as the working fluids, is described. The operating characteristics of a boiling system, utilizing a condenser submerged in the fluid, are presented and related to specific operational modes and thermal transport mechanisms. A lower bound of operation, corresponding to natural convection heat transfer at both the heated and condenser surfaces, is identified. Similarly, for the commonly encountered range of system operation, a condensive upper bound is identified and shown to correspond to vapor space condensation. A nondimensional vapor bubble collapse length, L c/W, is found to govern the rate and mechanism of heat transfer at the submerged condenser surface. LValues of wC > 1 condensation is found to dominate thermal transport at the condenser surface. 4 possible technique for augmenting condensation heat transfer on horizontal surfaces is examined in an attempt to raise the condensive upper bound of submerged condenser operation. A doubly-rippled surface with small, constant radius of curvature undulations is shown to yield a factor of two increases in the rate of vapor space condensation based on the projected area of the condenser surface.(cont.) A systematic design procedure for submerged condenser systems utilizing the proposed models and correlations is described and related to typical design considerations