Abstract
The capacity of a metallic mould to absorb heat from the solidifying casting plays a key role in controlling the metallurgical, technological and mechanical properties of the casting. Therefore, the main objective of the present paper is to reveal the nature of the mould cooling capacity-time history and to establish a map for the fundamental patterns of this relationship. The extent of the mutual interactions among the principal variables is also examined.
The analysis of the present work is confined to a spherical mould of uniform wall thickness to simulate a unidirectional heat flow. The solution of the problem is obtained through finite element approximation. An approximate analytical solution, based on the heat balance integral method, is developed to extend the fundamental solution obtained in this study to the case of transient boundary condition. Application of this analytical development is demonstrated using experimental data.
Analysis of the results indicated that the time variation of the mould cooling capacity follows one of two distinctive patterns depending on the combination of govering variables. An unexpected behaviour has been observed; the negative effect of Biot modulus under conditions of no preheat. The effects of various governing variables on the mould cooling capacity have been discussed and summarised.
Similar content being viewed by others
References
R. D. Doherty, P. D. Cooper, M. H. Bradbury, and F. J. Honey, ‘On the Columnar to Equiaxed Transition in Small Ingots’,Metallurgical Transactions A,8A, pp. 397–402, (1977).
M. H. Attia, and M. O. M. Osman, ‘On the Nature of the Thermal Response Behaviour of Metallic Moulds—Characterisation of the Transient Temperature Field’,The International Journal of Advanced Manufacturing Technology, (1), pp. 39–58, (1987).
J. A. Dantzig, and S. C. Lu, ‘Modelling of Heat Flow in Sand Castings: Part I. The Boundary Curvature Method’,Metallurgical Transactions B,16B, pp. 195–202, (1985).
J. A. Dantzig, and J. W. Wiese, ‘Modelling of Heat Flow in Sand Castings: Part II. Applications of the Boundary Curvature Method’,Metallurgical Transactions B,16B, pp. 203–209 (1985).
K. Ho, and R. D. Pehlke, ‘Metal-Mould Interfacial Heat Transfer’,Metallurgical Transactions B,16B, pp. 585–594, (1985).
K. Ho and R. D. Pehlke, ‘Transient Methods for Determination of Metal-Mould Interfacial Heat Transfer’,Trans. American Foundrymen's Society,91, pp. 689–698, (1983).
L. J. D. Sully, ‘The Thermal Interface Between Castings and Chill Moulds’,Trans. American Foundrymen's Society,84, pp, 735–744, (1976).
R. D. Pehlke, P. K. Trojan, R. A. Flinn, B. P. Winter and M. C. Sutton, ‘Thermal Gradient, Volumetric Shrinkage and Mould Wall Movement in Pure Aluminium and 356 Alloy’,48th International Foundry Congress, Chicago, (1982).
J. Majumdar, S. Dasgupta and B. C. Raychaudhuri, ‘An Experimental Method for Measuring Mould/Metal Gap Variation with Time in a Metal Casting Process’,J. Physics D: Appl. Physics,10, pp. 1175–1179, (1977).
J. Majumdar, S. Dasgupta and B. C. Raychaudhuri, ‘An Experimental Method for Measuring Mould/Metal Gap in an Ingot Casting System’,Int. J. Heat Mass Transfer,24 (7), pp. 1089–1095, (1981).
K. Ho and R. D. Pehlke, ‘Mechanisms of Heat Transfer at a Metal-Mould Interface’,Trans. American Foundrymen's Society,92, pp. 587–598, (1984).
P. V. Desai, J. T. Berry and C. Kim, ‘Computer Simulation of Forced and Natural Convection During Filing of a Casting’,Trans. American Foundrymen's Society,92, pp. 519–528, (1984).
X. C. Zeng and R. D. Pehlke, ‘Numerical Simulation of Solidification for a Copper-Base Alloy Casting’,Trans. American Foundrymen's Society,92, pp. 479–488, (1984).
H. S. Carslaw and J. C. Jaeger,Conduction of Heat in Solids, 2nd Edition, Oxford University Press, N.J., (1959).
A. V. Luikov,Analytical Heat Diffusion Theory, Academic Press, N.Y., (1968).
M. Dixmier, ‘Linearization of Sparrow and Koopman's Method for Heat Transfer with Variable Conductivity’,Nucl. Sci. Engng.,48, pp. 121–122, (1972).
W. Koope, ‘Die Erstarrungsgleichung von Sandguss’,Die Giesserei Techn.-Wissensch. Beihefte, Heft28, S. 1535, (1960).
H. Schenk, ‘Theories of Engineering Experimentation’, McGraw-Hill Book Co., N.Y., (1961).
T. R. Goodman, ‘Applications of Integral Methods to Transient Nonlinear Heat Transfer’,Advances in Heat Transfer,1, pp. 51–122, (1964).
T. R. Goodman, ‘Heat-Balance Integral and Its Application to Problems Involving a Change of Phase’,Transactions of ASME,80, pp. 335–342, (1958).
J. Crank, ‘The Mathematics of Diffusion’, 2nd edition, Clarendon Press, Oxford, (1975).
D. Langford, ‘The Heat Balance Integral’,Int. J. Heat Mass Transfer,16, p. 2424, (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Osman, M.O.M., Attia, M.H. A parametric study of the heat absorption capacity of metallic moulds-fundamental patterns of its time variation. Int J Adv Manuf Technol 3, 113–133 (1988). https://doi.org/10.1007/BF02601505
Issue Date:
DOI: https://doi.org/10.1007/BF02601505