Simplified 2D Transient Heat Transfer Simulation Using Gauss Error Function and FDM

• Autorzy: du Plessis M.
• Języki publikacji: EN

Abstrakty

EN

This article documents the methodology used to compile a transient heat transfer simulation with the goal of calculating the time to full solidification or any specified temperature of a metal casting, this simulation may serves as a confirmation of Chvorinov's rule, furthermore the simulation will identify the heat transfer topography, allowing the user to identify the location of possible solidification errors, however for the purpose of simplification, only the liquid phase cooling of pure iron will be considered in this report. Euler methods will be discussed with special attention paid to explicit forward approximation and how Gaussian error can be used to simplify the simulation, in an attempt to reduce processing time. A look at the advantages and disadvantages of using this method will be considered and explanations given the decisions taken in the methodology of the simulation, the use of software will be discussed. The article will conclude with a look at the other applications for this simulation as well as the limits of this simulation.

Słowa kluczowe

EN

Euler method; solidification; Chvorinov's rule; Gauss error; simulation

PL

metoda Eulera; krzepnięcie; funkcja błędu Gaussa; symulacja

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2013
• Tom: Vol. 13, iss. 3 spec.
• Strony: 21--24
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr.

Twórcy

autor

du Plessis M.

• AGH University of Science and Technology, Department of Foundry Engineering, 30-059 Krakow, Poland; Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town, 7441, Western Cape, South Africa

Bibliografia

• [1] Boz, Z., Erdogdu, F. i Tutar, M. (2013). Effects of mesh refinement, time step size and numerical scheme on the computational modeling of temperature evolution during natural-convection heating. Journal of Food Engineering, Vol 123, 8-16.
• [2] Cengel, Y. (2002). Heat Transfer A Practical Approach 2nd edition. New York: Mc Graw Hill.
• [3] Davies, T. (2011, February 2). DOI: 10.1615/AtoZ.b.biot_number. http://www.thermopedia.com/content/585/.
• [4] DeGormo, P., Black, T. i Kosher, R. (2012). DeGarmo's Materials and Processes in Manufacturing 11th Edition. NJ: John Wiley & Sons.
• [5] Frey, P. (2010). Finite Differences. Pobrano z lokalizacji UPMC Sorbonne Universities: https://www.ljll.math.upmc.fr/frey/cours/UPMC/finite-differences.pdf.
• [6] Mahamud, R. i Chanwoo, P. (2013). Spatial-resolution, lumped-capacitance thermal model for cylindrical Li-ion batteries under high Biot number conditions. Applied Mathematical Modelling, 2787–2801.
• [7] Mochnacki, B. and Suchy, J. (1995). Numerical methods in computations of foundry processes. Krakow: Polish Foundrymen's Technical Association.
• [8] Trethewey, K. i Chamberlain, J. (1995). Corrosion for Science and Engineering, 2nd edition. Longman.