Inverse Approach Using Bio-Inspired Algorithm Within Bayesian Framework for the Estimation of Heat Transfer Coefficients During Solidification of Casting

In any parameter estimation problem, it is desirable to obtain more information in one single experiment. However, it is difficult to achieve multiple objectives in one single experiment. The work presented in this paper is the simultaneous estimation of heat transfer coefficient parameters, latent heat, and modeling error during the solidification of Al–4.5 wt %Cu alloy with the aid of Bayesian framework as an objective function that harmoniously matches the mathematical model and measurements. A 1D transient solidification problem is considered to be the mathematical model/forward model and numerically solved to obtain temperature distribution for the known boundary and initial conditions. Genetic algorithm (GA) and particle swarm optimization (PSO) are used as an inverse approach and the estimation of unknown parameters is accomplished for both pure and noisy temperature data. The use of Bayesian framework for the estimation of unknown parameters not only provides the information about the uncertainties associated with the estimates but also there is an inherent regularization term in which the inverse problem boils down to well-posed problem thereby plethora of information is extracted with less number of measurements. Finally, the results of this work open up new prospects for the solidification problem so as to obtain a feasible solution with the present approach.

Theoretical Modeling of Thermal Transients in a PCM Substrate During Drop Impact

The physics of transient behavior of liquid drops impacting hot and cold surfaces is of significance in many different applications such as spray cooling, condensation and aircraft icing, and analogous to the process of bubble formation and departure in boiling. The resulting local thermal transients in these processes are primarily dictated by passive parameters such as substrate and liquid thermal properties and flow conditions. We are exploring the use of a surface-embedded phase change material (PCM) to actively manipulate these thermal transients as a means to enhance overall heat transfer performance. The thermal effect of the embedded PCM can be parametrically studied using controlled drop impact experiments. In this work, we perform an analytical and numerical study to model the effect of a liquid drop impacting a hot PCM-embedded substrate. By solving an analytical heat transfer solidification problem, we study the effect of PCM properties and PCM initial temperature on the thermal transients encountered during drop impact. Further, we validate the numerical analysis by showing agreement with experimental results.

An Optimum Enthalpy Approach for Melting and Solidification with Volume Change

Classical numerical methods for solving solid–liquid phase change assume a constant density upon melting or solidification and are not efficient when applied to phase change with volume expansion or shrinkage. However, solid–liquid phase change is accompanied by a volume change and an appropriate numerical method must take this into account. Therefore, an efficient algorithm for solid–liquid phase change with a density change is presented. Its performance for a one-dimensional solidification problem and for the quasi two-dimensional melting of octadecane in a cubic cavity was tested. The new algorithm requires less than 1/9 of the iterations compared to the source based method in one dimension and less than 1/7 in two dimensions. Moreover, the new method is validated against PIV measurements from the literature. A conjugate heat transfer simulation, which includes parts of the experimental setup, shows that parasitic heat fluxes can significantly alter the shape of the phase front near the bottom wall.

Numerical model of solidification process of Fe-C alloy taking into account the phenomenon of shrinkage cavity formation

Mathematical and numerical models of Fe-C alloy solidification process based on the finite element method (FEM) are presented in the paper. The phenomenon of the defect called "shrinkage cavity" is introduced to the model. It is very important aspect of presented work which makes possible the prediction of the location and shape of mentioned defect depending on the geometry of the casting and cooling condition of the process. An original computer program using Visual C++ environment has been written in order to simulate described process. The results of computer calculations of the three-dimensional solidification problem of the casting with riser are presented and discussed in details.

An application of finite element method for a moving boundary problem

The Stefan problems called as moving boundary problems are defined by the heat equation on the domain 0 < x < s(t). In these problems, the position of moving boundary is determined as part of the solution. As a result, they are non-linear problems and thus have limited analytical solutions. In this study, we are going to consider a Stefan problem described as solidification problem. After using variable space grid method and boundary immobilization method, collocation finite element method is applied to the model problem. The numerical solutions obtained for the position of moving boundary are compared with the exact ones and the other numerical solutions existing in the literature. The newly obtained numerical results are more accurate than the others for the time step ?t = 0.0005, it is also seen from the tables, the numerical solutions converge to exact solutions for the larger element numbers.