Heat Flux Curves Research Articles

Roll-strip Interfacial Heat Fluxes in Twin-roll Casting of Low-carbon Steels and Their Effects on Strip Microstructure.

In twin-roll casting, interfacial heat transfer between the rolls and the solidifying metal can affect strip quality and limit productivity. In the present work, interfacial heat fluxes between the roll and the solidifying metal were evaluated in a pilot twin-roll caster used in the production of strips of low-carbon steel. This evaluation was based on an inverse heat transfer analysis and on readings of thermocouples inserted at different positions of the roll sleeve of the IMI pilot scale TRC caster in Boucherville, Quebec. Variations in transient roll-melt interfacial heat fluxes during contact of the freezing shells with the roll surfaces exhibited two patterns, one characterized by a simple peak, the other by a double peak in the heat flux versus time curves, depending on the casting conditions. Mechanisms explaining the two types of curve are advanced. Solidification and as-cast structures of strips produced in the pilot caster were also studied, and their characteristics analyzed in terms of fluid flow and heat transfer within the caster's sump.

A flame-wall interaction model for combustion and heat transfer in S.I. engines

A new premixed charge turbulent combustion model has been developed to take flame-wall interaction into account. The flame-wall interaction model is based on the combined turbulent-dissipation/laminar-mixing flamelets based on fractal theory. The model features a variable fractal dimension formulated as a function of the turbulence Reynolds number. The computed heat release rate and pressure are shown to be in good agreement with measurements. The results exhibit realistic outward-curved flame shapes. The fractal dimension is shown to vary from 2.7 in the core regions to around 1.9 in the near wall regions. A fractal dimension less than 2 is consistent with the framework of the present model. Computed local wall heat fluxes are also presented and indicate reasonable time histories. It is shown that the constant fractal-dimension model gives incorrect flame shapes, being inward-curved, and unreasonable local heat flux curves. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(3): 205–215, 1998

Study on Mist Cooling of a Superheated Surface. Heat Transfer Characteristics in Range of Small Degree of Superheating.

In order to determine the heat transfer characteristics of mist cooling in the range of small degree of superheating, detailed experiments have been conducted on mist cooling heat transfer from a circular superheated surface. The experimental results indicate that the heat flux curve obtained is a function of parameters such as sprayed mass flow rate and degree of superheating, in relation to the boiling and evaporation behavior of the liquid film formed on the heated surface. The effects of size, velocity and temperature of spray droplets on heat flux are also clarified. The mechanism of mist cooling heat transfer is discussed and theoretical and experimental results are compared.

A theoretical investigation of the preconditions for obtaining the true thermodynamic transition temperature from only one DSC measurement

The true thermodynamic transition temperature can be obtained from one DSC measurement alone. It can be determined by drawing the tangent to the left side of the transition peak in the heat flux versus temperature curve. The intercept of this tangent with the abscissa shows the true thermodynamic transition temperature. This intercept temperature is independent of heat transfer coefficients, heat capacities and the heating rate, provided that (1) the heat capacity of the sample is five or more times higher than that of the sample pan; (2) the heat transfer coefficient between the sample and pan is not smaller than 2 × 10 −2 W cm −2 K −1

Nucleate pool boiling data for five refrigerants on plain, integral-fin and enhanced tube geometries

Data are presented for nucleate pool boiling on five different horizontal tube geometries using five refrigerants at two saturation temperatures. The refrigerants tested are R-11, R-12, R-22, R-123 and R-134a at saturation temperatures of 4.44°C (40°F) and 26.7°C (80°F). The tube geometries tested are a plain tube, a 1024 fins/m integral-fin tube, and three commercially used enhanced tube geometries (GEWA TX19, GEWA SE, and Turbo-B). The wide range of data reported here is new to the literature. The ability of the Cooper and the Stephan-Abdelsalam correlations to predict the plain tube data is evaluated. The slopes of the boiling coefficient vs heat flux curve are found to be heat flux dependent. Of particular importance are the data on R-123 and R-134a, which are intended to replace R-11 and R-12, respectively. Except for the Turbo-B with R-11, it appears that the boiling coefficients for R-123 and R-134a are within 10% of the values for R-11 and R-12, respectively.

Heat flux transients at the casting/chill interface during solidification of aluminum base alloys

Heat flow at the metal/chill interface of bar-type castings of aluminum base alloys was modeled as a function of thermophysical properties of the chill material and its thickness. Experimental setup for casting square bars of Al-13.2 pct Si eutectic and Al-3 pet Cu-4.5 pct Si long freezing range alloys with chill at one end exposed to ambient conditions was fabricated. Experiments were carried out for different metal/chill combinations with and without coatings. The thermal history at nodal locations in the chill obtained during the experiments was used to estimate the interface heat flux by solving a one-dimensional Fourier heat conduction equation inversely. Using the data on transient heat flux q, the heat flow at the casting/chill interface was modeled in two steps: (1) The peak in the heat flux curve qmax was modeled as a power function of the ratio of the chill thickness d to its thermal diffusivity a, and (2) the factor (q/qmax) X α0.05 was also modeled as a power function of the time after the solidification set in. The model was validated for Cu-10 pct Sn -2 pct Zn alloy chill and Al-13.2 pct Si and Al-3 pct Cu-4.5 pct Si as the casting alloys. The heat flux values estimated using the model were used as one of the boundary conditions for solidification simulation of the test casting. The experimental and simulated temperature distributions inside the casting were found to be in good agreement.

Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm × 12 cm × 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60% and 90% glycerin-water solutions, and 100% glycerin. The depth ratio ď, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger ď in order to keep the temperature difference across the tank within reasonable limits. The top and bottom walls were kept at different constant temperatures. Onset of convection was detected by a change of slope in the heat flux curve. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed (i) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (ii) an eightfold decrease in the critical wavelength between ď = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen & Chen 1988).

Reconstruction of the original heatflux curve for a calorimetric measuring device

The paper presents an improved method of de-smearing of calorimetric measuring curves. The advantages of this method, which is derived from an electrical analogy, will be discussed in comparison with the corresponding simplified de-smearing method of first approximation. The method to be discussed is of special interest for calorimetric investigations of relatively light specimens. In this case two different relaxation times exist. The signal reconstruction is based on a second order differential equation.

Double-diffusive convection in a porous medium

An experimental study has been carried out to examine double-diffusive convection in a porous medium. The experiments were performed in a horizontal layer of porous medium consisting of 3 mm diameter glass beads contained in a box 24 cm × 12 cm × 4 cm high. The top and bottom walls were made of brass and were kept at different constant temperatures by separate baths, with the bottom temperature higher than that of the top. The onset of convection was detected by a heat flux sensor and by the temperature distribution in the porous medium. When the porous medium was saturated with distilled water, the onset of convection was marked by a change in slope of the heat flux curve. The temperature distribution in the longitudinal direction in the middle of the layer indicated a convection pattern consisting of two-dimensional rolls with axes parallel to the short side. This pattern was confirmed by flow visualization. When the porous medium was saturated with salinity gradients of 0.15% cm−1 and 0.225% cm−1, the onset of convection was marked by a dramatic increase in heat flux at the critical ΔT, and the convection pattern was three-dimensional. When the temperature difference was reduced from supercritical to subcritical values, the heat flux curve established a hysteresis loop. Results from linear stability theory, taking into account effects of temperature-dependent viscosity, volumetric expansion coefficients, and a nonlinear basic state salinity profile, are discussed.

Further Aspects of Transitions in Two-Dimensional Thermal Convection

Abstract In this paper we present the results of numerical investigation of a two-dimensional nonlinear set of Boussinesq equations governing Benard–Rayleigh convection using spectral representation in the horizontal direction and finite-difference formulation in the vertical direction. Integrations were characterized by high resolution (up to 171 horizontal modes on 32 levels in the vertical direction) and large domain size (ten linear cells were represented). The results presented were obtained for moderate values of Rayleigh number (1150 < Ra < 33 000) that was varied in a near continuous fashion. It is found that two-dimensional heat flux transitions lead to simulations of various temporal states when sufficient resolution and high aspect-ratio domain of integration are used. The change of slope of the time-averaged logarithmic heat flux curve (log Nu) is simulated in a gradual manner by means of a series of bifurcated solutions. This study demonstrates that transition from steady to time-dependent co...

Some further studies on the transition to turbulent convection

In a horizontal convecting layer of fluid, several distinct transitions occur at certain distinct Rayleigh numbersR, for a given Prandtl numberPr.The regime diagram has been extended to include the Prandtl-number range2·5 × 10−2[les ]Pr[les ] 0·85 × 104.In particular it is found that distinct changes in the slope of the heat-flux curve occur even forPr= 2·5 × 10−2. The flow is steady up toR=Rt= 2·4 × 103. ForR&gt;Rt, the period of oscillation is compared with the theoretical values of Busse. ForPr= 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.ForRjust greater thanRc, the preferred orientation of rolls in various side-wall geometries is investigated. For high Prandtl number, the effect of curvature of the roll axis, forced by curved side walls, upon the second transition atRIIis investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering ofRII. These results, along with the observed hysteresis, support the view that there are metastable states attainable by finite amplitude instability. Finally the nature of the time-dependent flow at largeRand high Prandtl number is investigated in a Hele-Shaw cell. It is shown unequivocally that the observed periodicity at a fixed point is due to hot or cold plumes moving past the point.

On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow

In a horizontal convecting layer several distinct transitions occur before the flow becomes turbulent. These are studied experimentally for several Prandtl numbers from 1 to 104. Cell size plan form, transitions in plan form, transition to time-dependence, as well as the heat flux, are measured for Rayleigh numbers from 103to 105. The second transition, occurring at around 12 times the critical Rayleigh number, is one from steady two-dimensional rolls to a steady regular cellular pattern. There is associated with this a discrete change of slope of the heat flux curve, coinciding with the second transition observed by Malkus. Transitions to time-dependence will be discussed in part 2.

On the transition to turbulent convection. Part 2. The transition to time-dependent flow

The Rayleigh number at which steady convective flow changes to time-dependent flow is determined experimentally for several fluids with Prandtl numbers from 1 to 104. The time dependence is of two forms: (i) a slow tilting of the cell boundary, with time scale of the vertical thermal diffusion time, (ii) an oscillation with a faster time scale determined by the orbit time of the fluid around the cell. The nature of this oscillation is one of hot (or cold) spots advected with the original cellular motion. At a fixed point in the fluid this produces a time periodic oscillation of the temperature. A discrete change of slope of the heat flux curve accompanies this transition. As the Rayleigh number is increased, transition to disorder is seen to result from an increase in the frequency and number of these oscillations.

Heat Transfer by Free Convection From a Horizontal Wire to Carbon Dioxide in the Critical Region

The free-convection heat transfer from a 0.015-in-dia horizontal platinum wire to carbon dioxide in its critical region is experimentally investigated. The bulk fluid temperature and pressure are varied from 48 deg F to 136 deg F and 1000 psia to 1300 psia, respectively. Wire temperatures up to 1600 deg F are used. The results do not show the sharp rise in the heat flux curves that has been reported in a recent investigation. From the present measurements it appears that the usual free-convection correlation can be used even near the critical state, providing the properties are suitably evaluated.

Heat losses through rarefied fluids

Heat transfors from an electrically heated tungsten filament have been investigated for a range of temperature differences, transfer fluids and test geometries at pressures ranging from 4 × 10 −3 to 770 torr. For the horizontal filament surrounded by an open-ended, coaxial cylinder Nu (±5 per cent) = 2·35 (Ra) 0·12 in the range 10 −4 < Ra < 1. The limit of free molecular conduction is discussed and the onset of convection determined in terms of Gr for large ratios of cylinder to filament diameters. If the axis of the cylinder is skew to the filament a minimum in the heat flux vs. pressure curve occurs in what would otherwise be the constant heat leak region. An analogy between the tested coaxial arrangement and an evacuated envelope container for liquid refrigerants is suggested.

Generalized displacement of the nucleate boiling heat-flux curve, with pressure change

A rational generalized correlation for the displacement of the nucleate boiling heat-flux curve with pressure, as a function of reduced pressure, is formulated. Comparison of the correlation with experimental data shows that it is successful. A hypothesis that the wall superheat at any pressure is proportional to maximum theoretical superheat at that pressure is advanced. The hypothesis appears valid insofar as it can be checked experimentally.

Observations on Boiling Carbon Tetrachloride from Surfaces.

Experimental heat transfer measurements were made on the boiling of CCl/ sub 4/ with the effects of adsorbed or dissolved gases eliminated by fractionation of CCl/sub 4/. The surface roughness was held constant in an effort to study the effects of the chemical nature of the surface. The heat- transfer surfaces were 18-gage solid Cu, 20-gage solid Cu. Ag, and Au wires, and 18-gage Cu wires vapcr-coated with Au, Ag. or Cu; and they were also used as resistance thermometers. The pressures for boiling CCl/sub 4/ were 0.5. 1, and 1.5 atm. Nonboiling natural convection heat transfer data were collected first, and then nucleate pool-boiling heat-transfer data were collected at F Screening tes 50% burnout. In the latter experiment, the boiling heat flux curves shifted with boiling time toward higher temperature excesses together with a slight tarnishing of the surfaces. For Au there was no shift and for Ag only a slight shift: but there was a very definite shift for Cu. The wire diameter appears to have no effect on nucleate boiling flux. Superheat data indicated that extraneous sources of nuclei (gases and dust particles) were removed successfully. Nuclei count data are presented as a function of pressure excess;more » the nucleate contribution is independent of pressure excess for a given pure-metal surface. (D.L.C.)« less

Heat transfer to boiling skimmilk.

This paper was read at "an informal meeting on physics in agriculture", held at Wageningen, Netherlands in September 1955. The author deals with the highly complex phenomena associated with the boiling of liquids in relation to the transfer of heat from a hot wire to the bulk of the liquid. As temperature is raised, the heat-flux curve consists of three regions: (i) convection, when there are no bubbles, (ii) "nucleate boiling", when bubbles are formed at specific points on the surface and (Hi) "film boiling" in which the whole surface gradually becomes covered by a layer of vapour. Skim-milk and even water containing small amounts of skim-milk show characteristically high maxima for region (ii) at a pressure of 10 cm. Hg. Skim-milk is characterized by the formation of rather stable foams and by the rapid coagulation of proteins, but the author is cautious in his attempts to explain the shape of his curves. G.W.S.B. (Abstract retrieved from CAB Abstracts by CABI’s permission)