Development of an inverse heat conduction model and its application to determination of heat transfer coefficient during casting solidification

The interfacial heat transfer coefficient (IHTC) is required for the accurate simulation of heat transfer in castings especially for near net-shape processes. The large number of factors influencing heat transfer renders quantification by theoretical means a challenge. Likewise experimental methods applied directly to temperature data collected from castings are also a challenge to interpret because of the transient nature of many casting processes. Inverse methods offer a solution and have been applied successfully to predict the IHTC in many cases. However, most inverse approaches thus far focus on use of in-mold temperature data, which may be a challenge to obtain in cases where the molds are water-cooled. Methods based on temperature data from the casting have the potential to be used however; the latent heat released during the solidification of the molten metal complicates the associated IHTC calculations. Furthermore, there are limits on the maximum distance the thermocouples can be placed from the interface under analysis. An inverse conduction based method have been developed, verified and applied successfully to temperature data collected from within an aluminum casting in proximity to the mold. A modified specific heat method was used to account for latent heat evolution in which the rate of change of fraction solid with temperature was held constant. An analysis conducted with the inverse model suggests that the thermocouples must be placed no more than 2 mm from the interface. The IHTC values calculated for an aluminum alloy casting were shown to vary from 1,200 to 6,200 Wm^?2 K^?1. Additionally, the characteristics of the time-varying IHTC have also been discussed.     

Importance of heat transfer phenomena during DSC polymer solidification

In this work, solidification of semi-infinite polymer slabs was modelled accounting for heat transfer and phase change. Transient one-dimensional energy balance was numerically solved, coupled with a suitable crystallization kinetic model, coming from literature [1]. To this purpose a generalized code was adopted, which was proposed in a previous communication, together with its preliminary validation [2]. Solidification runs were simulated both under isothermal conditions and under slow cooling rates, comparable to the ones attainable in standard differential scanning calorimetry (DSC). The output DSC signals were simulated, and it is shown that traditional analysis, usually performed on these signals in the frame of crystallization kinetics studies, can give correct results for isothermal tests, but can give suggestions consistently far from real material behaviour during cooling ramps.     

Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

Numerical simulation of heat transfer in pressurized solidification of Magnesium alloy AM50

Based on finite difference and control-volume scheme, a model was developed to simulate fluid flow in forced convection and heat transfer in pressurized solidification of a cylindrical squeeze casting of magnesium alloy AM50. Pressure-dependent heat transfer coefficients (HTC) and non-equilibrium solidification temperatures were determined by experimental measurements. With the measured HTC and temperatures under the different pressures, the temperature distributions and the cooling behaviors of squeeze cast were simulated.     

Determination of heat transfer coefficients at metal/chill interface in the casting solidification process

The present work focuses on the determination of interfacial heat transfer coefficients (IHTCs) between the casting and metal chill during casting solidification. The proposed method is established based on the least-squares technique and sequential function specification method and can be applied to calculate heat fluxes and IHTCs for other alloys. The accuracy and stability of the method has been investigated by using a typical profile of heat fluxes simulating the practical conditions of casting solidification. In the test process, the effects of various calculation parameters in the inverse algorithm are also analyzed. Moreover, numerically calculated and experimental results are compared by applying the determined IHTCs into the forward heat conduction model with the same boundary conditions. The results show that the numerically calculated temperatures are in good agreement with those measured experimentally. This confirms that the proposed method is a feasible and effective tool for determination of the casting-mold IHTCs.     

Characteristics of heat transfer coefficient during nucleate pool boiling of binary mixtures

Experimental studies were conducted on heat transfer on a horizontal platinum wire during nucleate pool boiling in nonazeotropic binary mixtures of R12+R113, R134a+R113, R22+R113 and R22+R11, at pressures of 0.25 to 0.7 MPa and at heat fluxes up to critical heat flux. The substances employed were chosen such that the components of a given mixture had a large difference in saturation temperatures. The boiling features of the mixtures and the pure substances were observed by photography. The relationship between the boiling features and the reduction in heat transfer coefficient in binary mixtures is discussed in order to propose a correlation useful for predicting the experimental data measured over a wide range of low and high heat fluxes. It is shown that the correlation is applicable also to alcoholic mixtures. The physical role of k, which was introduced to evaluate the effect of heat flux on the reduction in heat transfer coefficient, is clarified based on the measured nucleate pool boiling heat transfer data and the visual observations of the boiling features. Received on 13 May 1997     

Comparison of different kinetic models for the heat transfer problem

The steady-state heat transfer problem between two parallel plates is investigated using kinetic models of the Boltzmann equation: BGK, S-model and ES-model. The discrete velocity method is used to determine the values of physical parameters: density, bulk velocity, temperature and heat flux. The obtained results are compared with the analytical expressions and some experimental data.     

Mass transport effect on the heat transfer coefficient during boiling of multicomponent mixture

In this work a simplified calculation method taking into account the effect of mass transport on the heat transfer coefficient (HTC) during boiling of multicomponent mixture has been elaborated. The calculation results were compared with own experimental data for ternary system methanol–isopropanol–water and Grigoriev data [1] (acetone–methanol–water). The experiments were performed in different hydrodynamic conditions such as: pool boiling and liquid evaporation at the free surface of the falling film. The experimental data covered wide range of heat fluxes from 6 to 30 kW/m² in the case of liquid evaporation from the falling film and from 30 to 240 kW/m² for pool boiling. The analysis of the results indicates that the mass transfer resistance in the liquid phase caused a significant reduction of experimental value HTC in comparison to so-called ideal HTC.     

A numerical study of heat transfer during flow of melt in a cylindrical mould

A numerical analysis of transient heat transfer during the flow of a melt in a cylindrical mould is presented. The analysis includes thermal resistance at the melt-mould interface, and axial conduction inside both melt and mould. Energy equations are formulated in a domain that expands continuously due to the advance of the melt inside the empty mould, and solved by the finite difference method using a time-stepping procedure. Calculations are compared to existing analytic results. It is found that axial conduction in the melt can significantly influence the rate of heat loss from the flowing melt, and that analytic approximations, which neglect axial conduction, may give erroneous predictions for the rate of heat loss.     

Enhancement of nucleate pool boiling heat transfer coefficient by reentrant cavity surfaces

The pool boiling of acetone, isopropanol, ethanol and water at atmospheric pressure has been carried out on a plain tube, and five different reentrant cavity (REC) heating tubes. The heat flux has remained in a range of 11–42 kW/m² for all the heating tubes. The enhancement factor, E, has been found to increase with the rise in heat flux, irrespective of the boiling liquid and the test-section tube combinations. For the pool boiling of acetone and isopropanol, the maximum enhancement factor has been attained for REC-2 tube with mouth size of 0.3 mm and for ethanol and water the mouth size could not be optimized, however, the maximum enhancement factor has been attained for REC-4 tube with mouth size of 0.2 mm. A correlation has also been developed to predict the enhancement factor, E, for the pool boiling of the test-liquids on REC heating tubes. This correlation has predicted the enhancement factor, E, in an error band of +12.5 to –7.5%.     

Effect of magnetic field on 3D flow and heat transfer during solidification from a melt

We present the effect of a magnetic field on three-dimensional fluid flow and heat transfer during solidification from a melt in a cubic enclosure. The walls of the enclosure are considered perfectly electrically conducting and the magnetic field is applied separately in three directions. The finite-volume method with enthalpy formulation is used to solve the mathematical model in the solid and liquid phases. The results obtained by our computer code are compared with the numerical and experimental data found in the literature. For Gr = 5 × 10⁵ and Ha = 0, 25, 50, 75, and 100 (where Gr and Ha are the Grashof and Hartmann numbers, respectively), the effects of magnetic field on flow and thermal fields, and on solid/liquid interface shape are presented and discussed. The interface is localized with and without magnetic field. The results show a strong dependence between the interface shape and the intensity and orientation of magnetic field. When the magnetic field is applied along the X-direction, the magnetic stability diagrams (V_max–Ha) and (Nu_avg–Ha) show the strongest stabilization of the flow field and heat transfer.     

Experimental investigation of the start-up phase during direct chill and low frequency electromagnetic casting of 6063 aluminum alloy processes

On the basis of conventional hot-top casting and Casting, Refining and Electromagnetic process, a lower frequency electromagnetic field was applied during the conventional hot-top casting process. Nine thermocouples (type K) were introduced into the metal to study the temperature profile in the ingot during the start-up phase of casting process. The experimental results show that under the effect of the low frequency electromagnetic filed, the heat transfer is changed greatly and the film boiling disappears, which could restrain the formation of fine subsurface cracks; the sump is shallow, and the macrostructure of the ingot butt is fine during the start-up phase of direct chill casting process.     

Determination of surface heat transfer coefficients from measured temperature data for spherical and cylindrical bodies during cooling

In this paper which is a combination of the methodological and experimental aspects, models were developed for determining surface heat transfer coefficients for spherical and cylindrical bodies from their center temperature measurements during forced-cooling. Experiments involved the cooling of the individual spherical and cylindrical products as test samples in the air flow. The cooling parameters in terms of the cooling coefficients and lag factors were also determined to use in the present models. The results show that the surface heat transfer coefficients of the individual spherical and cylindrical products increased with an increase in the flow velocities from 1 to 2 m/s. It can be concluded that the present models have the capabilities of determining the surface heat transfer coefficients for spherical and cylindrical bodies with a single transient experiment.     

Experimental study of heat transfer due to interaction of two separated flows of different scales

This paper describes an experimental study of heat transfer in a channel behind a backward-facing step in the presence of a disturbance in front of it in the form of a single rib in the range of the Reynolds numbers Re = 5000-15 000. The influence of the rib position and height on heat transfer intensity behind the backward-facing step is investigated. It is shown that reattachment of the flow disturbed by the obstacle intensifies the heat transfer on the surface behind the backward-facing step.     

Enhancement of heat transfer in compact heat exchanger by different type of rib with holographic interferometry

An experimental study was carried out to investigate enhancement of heat transfer in compact heat exchanger by keeping pressure drop constant in a given range. Two different test matrices, cylindrical and triangular, used to find the optimum ribs were compared with a smooth channel. The investigation was performed with both laminar and turbulent forced flow for Reynolds numbers from 250 to 7000. The geometric parameters, in order to satisfied manufacturer demands, were fixed at p/e=6.67 and the wall temperature was held constant at 50°C. The technique of holographic interferometry was used to determine the temperature distribution in the test duct. Velocity distribution was measured using laser doppler anemometer techniques. For comparison the technique of global measurement was also used. The results revealed that cylindrical ribs are optimum heat transfer for conversion of pressure drop. An 8% experimental error was found in global measurement compared to holographic interferometry.     

Investigation on the plastic work-heat conversion coefficient of 7075-T651 aluminum alloy during an impact process based on infrared temperature measurement technology

The plastic work-heat conversion coefficient is one key parameter for studying the work-heat conversion under dynamic deformation of materials. To explore this coefficient of 7075-T651 aluminum alloy under dynamic compression, dynamic compression experiments using the Hopkinson bar under four groups of strain rates were conducted, and the temperature signals were measured by constructing a transient infrared temperature measurement system. According to stress versus strain data as well as the corresponding temperature data obtained through the experiments, the influences of the strain and the strain rate on the coefficient of plastic work converted to heat were analyzed.The experimental results show that the coefficient of plastic work converted to heat of 7075-T651 aluminum alloy is not a constant at the range of 0.85–1 and is closely related to the strain and the strain rate. The change of internal structure of material under high strain rate reduces its energy storage capacity, and makes almost all plastic work convert into heat.