Papers by Keyword: Inverse Heat Conduction

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Authors: Josée Colbert, Dominique Bouchard
Abstract: A heat transfer model was built to predict the temperature evolution of semi-solid aluminum billets produced with the SEED process. An inverse technique was used to characterize the heat transfer coefficient at the interface between the crucible and the semi-solid billet. The effect of several process parameters on the heat transfer coefficient was investigated with a design of experiments and the coefficient was inserted in a computer model. Numerical simulations were carried out and validated with experimental results.
Authors: Etienne J.F.R. Caron, Mary A. Wells
Abstract: Accurate knowledge of the boundary conditions is essential when modeling the Direct-Chill (DC) casting process. Determining the surface heat flux in the secondary cooling zone, where the greater part of the heat removal takes place, is therefore of critical importance. Boiling water heat transfer phenomena are quantified with boiling curves which express the heat flux density as a function of the surface temperature. Compilations of boiling curves for the DC casting of aluminum alloys present a good agreement at low surface temperatures but a very poor agreement at higher surface temperatures, in the transition boiling and film boiling modes. Secondary cooling was simulated by spraying instrumented samples with jets of cooling water. Quenching tests were conducted first with a stationary sample, and then with a sample moving at a constant “casting speed” in order to better simulate the DC casting process. The ejection of the water film in quenching tests with a stationary sample and the relative motion between the sample and the water jets both lead to an Advanced Cooling Front (ACF) effect, in which cooling occurs through axial conduction within the sample rather than through boiling water heat transfer at the surface. The heat flux density and surface temperature were evaluated using the measured thermal history data in conjunction with a two-dimensional inverse heat conduction (IHC) model. The IHC model developed at the University of British Columbia was able to take into account the advanced cooling front effect. The effect of various parameters (initial sample temperature, casting speed, water flow rate) on the rate of heat removal in the film boiling and transition boiling regimes was investigated.
Authors: S. Sanman, K.V. Sreenivas Rao, K.C. Anil
Abstract: Experiments were conducted to study the effect of mold material on boundary heat flux variation during gravity die-casting. Inverse method was used for determining heat flux on the inside and outside surface of the mold during casting of pure Aluminum and Al-B4C composites. Different chill materials were used as mold material on one side of the rectangular mold cavity. K- type thermocouples were used for measurement of mold temperature during casting solidification. The mold temperatures at various locations were recorded using a data logger. These measured temperatures were used as input by the inverse algorithm for the assessment of the surface heat flux as a function of time. It was observed that the temperature difference between the inner and outer surface of the copper is very less in comparison to the cast iron mold and stainless steel mold. The cooling curve of the insulation mold indicates that there is no heat transfer through the insulation mold. The boundary heat flux is much higher in the case of copper mold than in the cases of cast iron mold and stainless steel mold.
Authors: K. Babu
Abstract: In this paper, the effect of quench probe diameter on the heat transfer rate during immersion quenching of stainless steel (SS) probes in still water has bee studied. Quench probes of different diameters with an aspect ratio of 2.5 were prepared from SS. These probes were heated to 850 °C and then quenched in water. Time-temperature data were recorded during quenching. The surface heat flux and temperature were estimated based on the inverse heat conduction (IHC) method. The results of the computation showed that the different cooling regimes during quenching in water were significantly affected by the diameter of the quench probes. The peak heat flux was higher for the probe having larger diameter followed by the next larger diameter probes.
Authors: Sung Deok Hong, Mi Gyung Cho, Chan Soo Kim, Cheol Ho Bai, Sung Yull Hong, Jae Sool Shim
Abstract: The Levenberg-Marguardt algorithm is used to study effects on convergence for inverse heat conduction in the unsteady state. In this model, the finite volume method is usedto obtain anestimated temperature, which is necessary for minimizing inverse error. To validate the model, constant thermal conductivity (k) and heat capacity (ρCpC) are identified from a semi-infinite slab subjected to constant heat flux. These properties are inserted into the theoretical equation for a semi-infinite slab, and an analytical solution is obtained by solving the theoretical equation including the two identified properties. The analytical solution and the identified resultare in very good agreement. Three simulations were performed to investigate the sensitivity of computation time and conversion to initial thermo-physical values by changing three different damping ratios of the Levenberg-Marquardt algorithm. Our results show that agood initial guessallowsgood convergence, but convergence time decreases as the value of damping ratio decreases.A poor initial guess results in more convergence time, and causes divergence when a small damping ratio is used. Once the simulation converges, our model shows that results areobtained within an error of 0.01%.
Authors: K.V. Sreenivas Rao, P. Usha, S. Sanman, R. Anilchoudary
Abstract: One of the key controllable and influential factors to obtain a casting simulation, representative of reality, is the choice of boundary condition. The thermal boundary condition to be specified at the metal-mold interface must account for complex heat transfer phenomena associated with solidifying casting. The present study aims at estimating the heat flux at the interface of the mold and the solidifying metal by Inverse Heat Conduction Problem (IHCP) approach. Solidification studies were conducted on casting of aluminum reinforced with boron carbide composite. Copper, cast iron and stainless steel were used as mold materials. The temperature data of the mold was recorded from the beginning to end of solidification using k-type thermocouples connected to temperature data logger. This time-temperature history was used as input to the IHCP algorithm to simulate the interface heat flux and thermal field of the mold. The results indicate that the interface heat flux is highly transient and varies with the variation in the thermo-physical properties of the mold materials. The study also demonstrates that heat conduction is one dimensional in copper mold and two dimensional in cast iron and stainless steel mold during phase change.
Authors: Zi Ran Liu, Cai Xia Ren, Xian Guo Yan
Abstract: In the process of the finite element analogy of the Cryogenic Treatment of the high speed steel cutter with respect to the material of W9Mo3Cr4V, the surface heat transfer coefficient is a crucial parameter. In order to get this parameter, this paper employed the method of inverse heat conduction to process the temperature curve generated through the cryogenic treatment of the tested work piece with the material of W9Mo0Cr4V, thereby obtaining the surface heat transfer coefficient of the tested work piece. This coefficient can be considered the surface heat transfer coefficient of cryogenic treatment of the cutter with the same material. The principle of the inverse heat conduction is as follows: firstly, according to the boundary condition and the initial value in the tri-dimensional space, the equation of the sensitivity coefficient and the temperature field can be deduced. Second, the coupling of two equations is carried out, and the heat flux density is calculated based on above result. The heat flux density will be revise to get the reasonable value . Lastly, the surface heat transfer coefficient can be obtained by the heat flux density. In this paper, all the work is automatically accomplished with the aid of FEPG soft ware and Visual C++ programmable language.
Authors: Chin Ru Su, Cha'o Kuang Chen
Abstract: The contour of a two dimensional plate with a rectangular cavity was predicted by the linear least-squares error method. In the analysis process the heat conduction equation and the boundary conditions were discretized to form a linear matrix equation. On the basis of the concept of a virtual area, the unknown contour of the two dimensional plate was converted into virtual boundary temperatures that can be definitely expressed. Under the condition that the solution form and the initial values didn’t need to be preset, the contour of the two dimensional plate was predicted from temperatures of some points in the plate by only two inverse processes. The results show that even though the positions of the measured points are different the temperature field of the whole virtual system doesn’t change. When the number of the measured points is decreased or the measurement error is increased, the error of the prediction will increase. With reasonable measurement error, the geometry of the plate can be successfully predicted from a few measured points by the method proposed in this work.
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