Determination of interface heat transfer coefficient between aluminum casting and graphite mold

To produce castings of titanium, nickel, copper, aluminum, and zinc alloys, graphite molds can be used, which makes it possible to provide a high cooling rate. No die coating and lubricant are required in this case. Computer simulation of casting into graphite molds requires knowledge of the thermal properties of the poured alloy and graphite. In addition, in order to attain adequate simulation results, a series of boundary conditions such as heat transfer coefficients should be determined. The most important ones are the interface heat transfer coefficient between the casting and the mold, the heat transfer coefficient between the mold parts, and the interface heat transfer coefficient into the environment. In this study, the interface heat transfer coefficient h between the cylindrical aluminum (99.99%) casting and the mold made of block graphite of the GMZ (low ash graphite) grade was determined. The mold was produced by milling using a CNC milling machine. The interface heat transfer coefficient was found by minimizing the error function reflecting the difference between the experimental and simulated temperatures in a mold and in a casting during pouring, solidification, and cooling of the casting. The dependences of the interface heat transfer coefficient between aluminum and graphite on the casting surface temperature and time passed from the beginning of pouring are obtained. It is established that, at temperatures of the metal surface contacting with a mold of 1000, 660, 619, and 190°C, the h is 1100, 4700, 700, and 100 W/(m² K), respectively; i.e., when cooling the melt from 1000°C (pouring temperature) to 660°C (aluminum melting point), the h rises from 1100 to 4700 W/(m² K), and after forming the metal solid skin on the mold surface and decreasing its temperature, the h decreases. In our opinion, a decrease in the interface heat transfer coefficient at casting surface temperatures lower than 660°C is associated with the air gap formation between the surfaces of the mold and the casting because of the linear shrinkage of the latter. The heat transfer coefficient between mold parts (graphite–graphite) is constant, being 1000 W/(m² K). The heat transfer coefficient of graphite into air is 12 W/(m² K) at a mold surface temperature up to 600°C.     

Determination of interfacial heat transfer coefficients in casting and quenching using a solution technique for inverse problems based on the boundary element method

Both casting and quenching are processes during which several physical phenomena like heat transfer, fluid flow, phase transformation,etc. interact in a complex manner. To obtain a nu-merical model which is capable of accurately simulating the actual process, one has to be able to quantify all the parameters affecting the process. One parameter which substantially influ-ences heat transfer in these processes is the heat transfer coefficient at the interface between the mold and the metal in casting and that between the metal and the quenchant in quenching. The heat transfer coefficient could vary on the surface of a casting or a quench metal both spatially and with time. Its accurate determination is imperative for a realistic simulation of these processes. In this work, an algorithm based on the boundary element technique is proposed to solve for the interface heat transfer coefficient. The problem is cast as one of inverse heat conduction in two dimensions where some of the boundary conditions, namely, the previously mentioned heat transfer coefficients, are unknowns. Since it is the boundary properties that are being determined, the boundary element method (BEM) is the most suitable technique to use. The algorithm uses experimentally measured temperature data inside the domain to determine the interface heat transfer coefficient. The technique is outlined in detail and some casting and quenching examples are presented to demonstrate its capability.     

Influence of oxide scales on heat transfer in secondary cooling zones in the continuous casting process,part 1: heat transfer through hot-oxidized steel surfaces cooled by spray-water

For the cooling of steels in the continuous casting process it is necessary to know the heat transfer from the solidifying strand to the cooling water to enable calculation of the secondary cooling zone. Previous investigations have only determined this variable for non-oxidizing metallic surfaces. For many steels cast in practice, however, the formation of oxide layers prevents a direct transfer of the previous results. In the present research the influence of the oxide layers on the heat transfer has been investigated for spay-water cooling. Results have shown that heat transfer in the range of stable film boiling is determined for a constant spray-water temperature in the same way as for non-oxidizing metals, i.e. using the water mass flux density ·_s only. The changed surface qualities resulting from the oxide formation cause the Leidenfrost temperature, however, to shift considerably to higher values.     

Estimation of multiple heat-flux components at the metal/mold interface in bar and plate aluminum alloy castings

In the present investigation, a serial solution of the inverse heat-conduction problem (IHCP) is extended for Al-3 pct Cu-4.5 pct Si alloy square bars and rectangular plates cast in metal molds. The metal/mold interface was divided into three segments, viz., the half face, the quarter face, and the corner. The heat-flux transients during casting solidification were then estimated at these segments. Three configurations were considered, viz., (1) one boundary segment for the whole length on the interface, (2) two boundary segments delineating two heat-flux components, and (3) three boundary segments leading to three heat-flux components. In order to identify the most acceptable spatial distribution of interface heat flux, two types of analyses were performed on the results of the IHCP, viz., convergence of absolute error in the computed and the measured temperatures at the sensor locations and total heat energy transferred across the boundary from the casting to the mold. The error convergence at the thermocouple locations was more or less identical for all the three cases in both bars and plates. However, the total heat absorbed by the mold, in the case of the one-segment model in bars and the three-segment model in plates, was found to be a minimum. This indicated that the interface heat flux did not show any spatial distribution in the case of bars, while a distinct spatial distribution could be identified in the case of plates. The individual heat fluxes at the different interface segments for the plate casting showed a peak within 3 to 3.5 seconds of pouring, after which it reduced and reached stable values in about 200 seconds. The maximum heat flux occurred at the corner segment. The analysis of heat-flux gradients showed that the air gap initiated at the corner and spread toward the center.     

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m² to peak values of 0.95 to 2.0 MW/m². A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m² °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (μm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.     

Numerical Accuracy Test on Heat Transfer in a Single‐belt Strip Casting Simulator

The heat removal rate from the solidifying molten metal is one of the most important issues in casting processes. The analysis of the inverse heat conduction problem (IHCP) with an assumption of one‐dimensional heat flow is a typical approach to clarify the heat transfer characteristics between the solidifying metal and the mould, and the authors have also developed a single‐belt strip casting simulator applying this technique. In this study the effects of the mould geometry and the temperature measurement on the estimation accuracy of surface temperature and interfacial heat flux in this method were examined through numerical experiments. The mould profile of the simulator where a side dam is integrated generates a multi‐dimensional heat flow and causes a non‐uniform heat flux along the metal‐mould interface. The heat flow in the central part, however, is unidirectional in the initial period and the thermal status at the interface can well be reproduced by the IHCP analysis. Furthermore, the disturbances in the temperature measurement, for example the interfacial thermal resistance between the inserted thermocouples and the casting mould, directly cause estimation errors and should be removed. These results indicate that the single‐belt strip casting simulator developed by the authors is capable to measure the interfacial heat flux and the surface temperature in the casting process although the measuring period and the location are limited. They also suggest the methods how to imporve the measurement accuracy for the various casting simulation techniques.     

Heat flow parameters affecting the unidirectional solidification of pure metals

Unidirectional solidification of pure metals has been studied as a function of liquid superheat, heat transfer coefficient of the metal/mold interface(h _i ), and mold material. Experimental results show that the position of the solid/liquid interface (X) varies with time (l) following the relationshipX(t) = A . t ^1/2 -B, where, for a fixed metal,B is a constant only dependent on the superheat through a parabolic law andA is another constant that is independent of the superheat but dependent on the mold heat sink capacity,i.e., mold material and coefficienth _i At the same time, it has been calculated that the constantA varies withh _i through an error-function type law tending asymptotically to Lyubov’s exact analytic solution.     

Numerical determination of heat transfer coefficient for boiling phenomenon at runout table of hot strip mill

Abstract

The heat transfer coefficient during film boiling at the runout table of the hot strip mill is usually determined by experimental methods. Described in the present paper is a finite difference based model for analysis of the thermal behaviour of the strip during cooling at the runout table of the hot strip mill at Tata Steel, India. The model, developed for the prediction of strip temperature, is used to determine the heat transfer coefficient at the water/strip interface while water cooling occurs. A simple form of polynomial as a function of the strip surface temperature is proposed to describe the heat transfer coefficient at the water/strip interface. Good correlation has been found between model predicted temperatures considering the polynomial type heat transfer coefficient and the actual coiling temperature.     

Selection of Initial Mold–Metal Interface Heat Transfer Coefficient Values in Casting Simulations—a Sensitivity Analysis

Mold–metal interface heat transfer coefficient values need to be determined precisely to accurately predict thermal histories at different locations in automotive castings. Thermomechanical simulations were carried out for Al-Si alloy casting processes using a commercial code. The cooling curve results were validated with experimental data from the literature for a cylindrical-shaped casting. Our analysis indicates that the interface heat transfer coefficient (IHTC) initial value choice between chill–metal and the sand mold–metal interfaces has a marked effect on the cooling curves. In addition, after choosing an IHTC initial value, the solidification rates of the alloy near the chill–metal interfaces varied during subsequent cooling when the gap began to form. However, the gap formation, which results in an IHTC change from the initial value, does not affect the cooling curves within the vicinity of the sand–metal interface. Optimized initial IHTC values of 3000 and 7000 W m⁻²-K⁻¹ were determined for a sand–metal interface and a chill (steel or copper)–metal interfaces, respectively. The initial IHTC had a significant effect on the prediction of secondary dendrite arm spacing (SDAS) (varying between approximately 15 microns and 70 microns) and ultimate tensile strength (UTS) (varying between approximately 250 MPa and 370 MPa) for initial IHTC values that were less than the optimized value of 7000 W m⁻² K⁻¹ for the chill–metal interfaces.     

Influence of heat transfer on the development of residual stresses in quenched steel cylinders

In this paper results of systematic FE-calculations about the influence of characteristic points of the temperature dependent heat transfer coefficient, especially the Leidenfrost point and the point of maximum heat transfer coefficient on the development of residual stresses are discussed. The numerical investigations were carried out for SAE 1045 and 4140 steel cylinders with 10 and 20 mm 0 quenched in water and oil, respectively. In this work experimentally determined h, T-curves are linearly approximated in the successive stages of heat transfer. Changes of the Leidenfrost-temperature do not influence the middle plane residual stresses of the cylinders investigated. Increasing maximum heat transfer coefficients and low temperatures of maximum heat transfer coefficient, respectively, cause higher magnitudes of residual stress. The development of residual stresses is determined by the temperature dependent gradient of the heat flux density δq/δT in the temperature range of martensitic transformation. Increasing Leidenfrost-temperatures cause more homogeneous stress and residual stress states at the surface of quenched cylinders due to the symmetrical cooling of the sample in axial as well as in radial direction. In particular, it was shown that during immersion cooling of cylindrical parts the heat transfer is locally dependent. Simulating immersion cooling this dependence has to be considered using effective local heat transfer coefficients.     

Interfacial heat transfer and nucleation of steel on metallic substrates

A modified levitated drop technique and an immersion technique were used to study the wetting and nucleation behavior of steel melts on a metallic substrate. Thermal histories of the solidifying shell and the substrate were recorded and used to elucidate the mechanisms of interfacial heat transfer and nucleation. The melt/substrate wetting behavior was shown to be controlled by the melt surface tension. The interfacial heat transfer resistance was controlled by the degree of melt/substrate wetting consequently affecting the heat flux across the interface. According to the classical heterogeneous nucleation theory, improved wetting is expected to reduce the energy barrier for nucleation while increasing the cooling rate of the liquid. Because the overall nucleation rate is controlled by both the rate of cluster formation and the rate of atom transfer to the nucleus, increasing the cooling rate above a critical level is expected to reduce the nucleation rate. The measured experimental data allowed the melt undercooling and the time for nucleation of the first solid phase to be determined and compared to the theoretical predictions. The implications of the mechanisms of nucleation on early shell growth are also considered. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.     

Effects of substrate surface conditions on heat transfer and shell morphology in the solidification of a copper alloy

The effect of substrate surface conditions on the heat transfer and morphology of solidifying shells of a copper alloy has been characterized by a series of dip tests. Results showed that in the early stages of solidification, rough and grooved surface conditions provide a greater heat transfer than polished ones. The shells solidified on rough and grooved surfaces had significant localized variations in thickness, indicating that heat transfer at the substrate-metal interface was not uniform. The implication of these results on strip casting is discussed.     

High-speed temperature measurements during rapid solidification of iron-silicon ribbons,produced by planar flow casting

In order to investigate the melt undercooling and the non-equilibrium solidification of crystalline Fe 5 wt.% Si melt spun ribbons, produced by planar flow casting (PFC), high speed temperature measurements and appropriate process simulations have been performed. Using a rotating fibre optical system with a fast response double pyrometer, the temperature radiation of the solidifying ribbon during the casting process has been recorded with a measuring frequency of 50 kHz. The obtained cooling curves have been interpreted by computer simulations. It is shown that with increasing wheel temperature the overall cooling becomes more efficient. This is caused by an improved wetting behaviour of the melt-wheel system and an increase in the heat transfer coefficient at the interface of the solidifying ribbon and the wheel from 6 · 10⁴ to about 2 · 10⁵ W/(m²K). The solidification of 100 to 200 μm thick ribbons takes place in a time interval of 2 to 5 ms. The average growth rate varies between 10 and 60 mm/s. The high cooling rate results in a fine dendritic solidification morphology with diminishing microsegregations.     

An Epitaxial Model for Heterogeneous Nucleation on Potent Substrates

In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ΔT _c). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h _c), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h _c and ΔT _c; h _c decreases; and ΔT _c increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.     

Modelling of crystal growth during the ribbon formation in planar flow casting

The crystalline solidification during rapid substrate quenching in planar-flow casting was simulated by using a numerical model based on a rapid solidification algorithm and the infinite viscosity approximation. The calculation shows that the existence of a real melt puddle shape suppresses undercooling and recalescence on the melt surface as well as on the solidifying ribbon. The melt puddle length is mainly determined by the heat-transfer coefficient. With increasing heat transfer across the melt – substrate interface the melt puddle length decreases. If the formation rate of critical nuclei on the substrate surface is low compared to the present cooling rate a large undercooling may occur. The performed calculations reveal that an undercooling of up to 600 K does neither affect the temperature distribution on the surface of the melt nor the melt puddle length, perceptibly. Therefore, investigations on microstructural features of rapidly quenched metals might give detailed information on the amount of undercooling present at the beginning of solidification.     

Estimating the Effective Metal-Mould Interfacial Heat Transfer Coefficient via Experimental-Simulated Cooling Curve Convergence

The design of improved casting systems requires accurate modeling of metal cooling processes. This can only be accomplished after determining the interfacial heat transfer coefficient (IHTC) between a solidifying casting and its mould. In the current work, a simple and robust inverse heat conduction technique was applied for the estimation of the effective IHTC between an aluminum alloy casting and a steel permanent mould during solidification. The solidification of the alloy at varying mould preheating temperatures was monitored using a thermocouple, and the experimental cooling curves were compared with curves simulated by casting solidification modeling software. The IHTC value applied to the software was varied until its output converged with the experimental data, leading to an estimation of 6000 W/m²K for this system. This technique is useful as a preliminary tool in materials modeling, and it will promote the development of improved casting processes without the need for excessive experimentation.     

The use of water cooling during the continuous casting of steel and aluminum alloys

In both continuous casting of steel slabs and direct chill (DC) casting of aluminum alloy ingots, water is used to cool the mold in the initial stages of solidification, and then below the mold, where it is in direct contact with the newly solidified surface of the metal. Water cooling affects the product quality by (1) controlling the heat removal rate that creates and cools the solid shell and (2) generating thermal stresses and strains inside the solidified metal. This work reviews the current state-of-the-art in water cooling for both processes, and draws insights by comparing and contrasting the different practices used in each process. The heat extraction coefficient during secondary cooling depends greatly on the surface temperature of the ingot, as represented by boiling water-cooling curves. Thus, the heat extraction rate varies dramatically with time, as the slab/ingot surface temperature changes. Sudden fluctuations in the temperature gradients within the solidifying metal cause thermal stresses, which often lead to cracks, especially near the solidification front, where even small tensile stresses can form hot tears. Hence, a tight control of spray cooling for steel, and practices such as CO₂ injection/pulse water cooling for aluminum, are now used to avoid sudden changes in the strand surface temperature. The goal in each process is to match the rate of heat removal at the surface with the internal supply of latent and sensible heat, in order to lower the metal surface temperature monotonically, until cooling is complete.     

Effect of Bath Temperature on Cooling Performance of Molten Eutectic NaNO3-KNO3 Quench Medium for Martempering of Steels

Martempering is an industrial heat treatment process that requires a quench bath that can operate without undergoing degradation in the temperature range of 423 K to 873 K (150 °C to 600 °C). The quench bath is expected to cool the steel part from the austenizing temperature to quench bath temperature rapidly and uniformly. Molten eutectic NaNO₃-KNO₃ mixture has been widely used in industry to martemper steel parts. In the present work, the effect of quench bath temperature on the cooling performance of a molten eutectic NaNO₃-KNO₃ mixture has been studied. An Inconel ASTM D-6200 probe was heated to 1133 K (860 °C) and subsequently quenched in the quench bath maintained at different temperatures. Spatially dependent transient heat flux at the metal–quenchant interface for each bath temperature was calculated using inverse heat conduction technique. Heat transfer occurred only in two stages, namely, nucleate boiling and convective cooling. The mean peak heat flux (q _max) decreased with increase in quench bath temperature, whereas the mean surface temperature corresponding to q _max and mean surface temperature at the start of convective cooling stage increased with increase in quench bath temperature. The variation in normalized cooling parameter t ₈₅ along the length of the probe increased with increase in quench bath temperature.

     

Heat flow model for surface melting and solidification of an alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The eq11Ations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer eq11Ation is written in terM_s of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region,a, and time. General trends established show that for a given product ofqa all isotherM_s are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

Dynamics of the hot metal dephosphorization with Na2O slags

Dephosphorization reaction of hot metal by Na₂CO₃ has been studied experimentally to determine the reaction mechanism and thermodynamics. Most of the experiments were carried out at 1300 °C using Fe-C_sat.-Si-P-S alloys. The results indicate that the CO₂ gas released from Na₂CO₃ is important in the dephosphorization reaction as an oxidizer and increasing mass transfer by stirring the slag and metal. As the initial Si content in hot metal is increased, the degree of dephosphorization decreases significantly and the rephosphorization takes place earlier. The primary reason for the rephosphorization is that the activity of PO_2.5 increases in the slag because of the evaporation of Na₂O from the slag. The loss of Na₂O increases the activity coefficient of PO_2.5 and decreases the slag volume. At the later stage of Na₂CO₃ treatment, the reactions reach equilibrium with respect to phosphorus and sulfur, and the oxygen potential,P _o2, at the slag-metal interface is determined by the C-CO equilibrium (a _c=1 and 1 atm CO). The presence of sulfur in the metal increases the rate of the dephosphorization because of the electrochemical nature of the reaction; sulfur transfer to the slag accepts the electrons from phosphorus transfer.