Meshless analysis of casting process considering non-Fourier heat transfer

Document Type : Research Paper

Authors

1 School of Mechanical Engineering, Shiraz University

2 Department of Mechanical Engineering, Shiraz University, Shiraz, Iran

Abstract

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phase-lag during the phenomenon of solidification is investigated. This concept is considered by utilization of the hyperbolic heat conduction equation, known generally as the Maxwell–Cattaneo relation. In this way, the effect of finite heat wave speed on the thermal behavior of a solidifying medium is studied. In this context, some numerical example problems are analyzed with the meshless radial point interpolation method. The effect of the relaxation time on the thermal behavior of the solidifying medium is investigated. Moreover, the results of Fourier and non-Fourier heat conduction equations are compared. It is observed that based on the specific solidification process and the amount of relaxation time, the results of the Fourier and non-Fourier conduction laws can be quite different. The most prominent effect of the relaxation time is to alter the initiation of the solidification at each point.

Keywords

References

 [1] A. Khosravifard and M.R. Hematiyan, Analysis of phase-change heat conduction problems by an improved CTM-based RPIM, Advances in Boundary Element techniques XIII, BETEQ 2012, 3-5 September, Prague, (2012).
[2] R. Vertnik and B. Sarler, Meshless local radial basis function collocation method for convective-diffusive solid– liquid phase change problems, International Journal of Numerical Methods for Heat & Fluid Flow, 16 (2006) 617–640.
[3] G. Kosec and B. Sarler, Solution of phase change problems by collocation with local pressure correction, CMES: computer Modeling in Engineering and Sciences, 47 (2009) 191–216.
 
 [4] R. Vertnik, M. Zaloznik and B. Sarler, Solution of transient direct-chill aluminium billet casting problem with simultaneous material and interphase moving boundaries by a meshless method, Engineering Analysis with Boundary Elements, 30 (2006) 847–855.
[5] L. Zhang, Y.M. Rong, H.F. Shen and T.Y. Huang, Solidification modeling in continuous casting by finite point method, Journal of Materials Processing Technology, 192–193 (2007) 511–517.
[6] L. Zhang L., H.F. Shen, Y.M. Rong and T.Y. Huang, Numerical simulation on solidification and thermal stress of continuous casting billet in mold based on meshless methods, Materials Science and Engineering A, 466 (2007) 71–78.
[7] G. Zhihua, L. Yuanming, Z. Mingyi, Q. Jilin and Z. Shujuan, An element free Galerkin method for nonlinear heat transfer with phase change in Qinghai–Tibet railway embankment, Cold Regions Science and Technology, 48 (2007) 15–23.
[8] H.S. Fang, K. Bao, J.A. Wei, H. Zhang, E.H. Wu and L. Zheng, Simulations of droplet spreading and solidification using an improved SPH model, Numerical Heat Transfer, Part A: Applications, 55 (2009) 124–143.
[9] M. Zhang, H. Zhang and L. Zheng, Application of smoothed particle hydrodynamics method to free surface and solidification problems, Numerical Heat Transfer, Part A, 52 (2007) 299–314.
[10] H. Yang and Y. He, Solving heat transfer problems with phase change via smoothed effective heat capacity and element free Galerkin methods, International Communication in Heat and Mass Transfer, 37 (2010) 385–392.
[11] M. Alizadeh, S.A. Jenabali Jahromi and S.B. Nasihatkon, Applying finite point method in solidification modeling during continuous casting process, ISIJ International, 50 (2010) 411–417.
[12] G. Kosec and B. Sarler, Meshless Approach to Solving Freezing with Natural Convection, Materials Science Forum, 649 (2010) 205–210.
[13] B. Sarler, G. Kosec, A. Lorbicka and R. Vertnik, A meshless approach in solution of multiscale solidification modeling, Materials Science Forum, 649 (2010) 211–216.
[14] H. Thakur, K.M. Singh and P.K. Sahoo, Phase change problems using the MLPG method, Numerical Heat Transfer: Part A, 59 (2011) 438–458.
[15] G. Kosec, M. Zaloznik, B. Sarler and H. Combeau, A meshless approach towards solution of macrosegregation phenomena, Computers, Materials & Continua, 580 (2011) 1–27.
[16] S.Y. Reutskiy, The method of approximate fundamental solutions (MAFS) for Stefan problems, Engineering Analysis with Boundary Elements, 36 (2012) 281–292.
[17] R. Vertnik and B. Sarler, Solution of a continuous casting of steel benchmark test by a meshless method, Engineering Analysis with Boundary Elements, 45 (2014) 45–61.
[18] M. Kumar, S. Roy and S.S. Panda, Numerical simulation of continuous casting of steel alloy for different cooling ambiences and casting speeds using immersed boundary method, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, (2015), doi: 10.1177/0954405415596140.
[19] S.L. Sobolev, The local-nonequilibrium temperature field around the melting and crystallization front induced by picosecond pulsed laser irradiation, International Journal of Thermophysics, 17 (1996) 1089–1097.
[20] A. Vedavarz, K. Mitra and S. Kumar, Hyperbolic temperature profiles for laser surface interactions, Journal of applied physics, 76 (1994) 5014–5018.
[21] D.E. Glass, M.N. Ozisik and S.S. McRae, Formulation and solution of hyperbolic Stefan problem, Journal of applied physics, 70 (1991) 1190–1194.
[22] M.A. Al-Nimr and M.A. Hader, Melting and Solidification under the Effect of the Phase-Lag Concept in the Hyperbolic Conduction Equation, Heat Transfer Engineering, 22 (2001) 40–47.
[23] H. Ahmadikia and A. Moradi, Non-Fourier phase change heat transfer in biological tissues during solidification, Heat and Mass Transfer, 48 (2012) 1559–1568.
 
 [24] A.M. Bakken, Cryopreserving Human Peripheral Blood Progenitor Cells, Current stem cell research & therapy, 1 (2006) 47–54.
[25] C.J. Hunt and P.M. Timmons, Cryopreservation of human embryonic stem cell lines, Methods in Molecular Biology, 368 (2007) 261–270.
[26] N.B. Ishine, C. Rubinsky and Y. Lee, Transplantation of mammalian livers following freezing: vascular damage and functional recovery, Cryobiology, 40 (2000) 84–89.
[27] R.M. Nerem, Tissue engineering: Confronting the transplantation crisis, Proceedings of the Institution of Mechanical Engineers Part H: Journal of Engineering in Medicine, 214 (2000) 95–99.
[28] Siraj-ul-Islam, R. Vertnik and B. Sarler, Local radial basis function collocation method along with explicit time stepping for hyperbolic partial differential equations, Applied Numerical Mathematics, 67 (2013), 136–151.
[29] A. Khosravifard and M.R. Hematiyan, A new method for meshless integration in 2D and 3D Galerkin meshfree methods, Engineering Analysis with Boundary Elements, 34 (2010) 30–40.
[30] A. Khosravifard, M.R. Hematiyan and L. Marin, Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method, Applied Mathematical Modelling, 35 (2011), 4157–4174.
Iranian Journal of Materials Forming
Volume 3, Issue 2
October 2016
Pages 13-25

Files

Share

How to cite

Statistics