ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Regular Article
A Probabilistic Approach to Model Interfacial Phenomena during Hot Flat Rolling of Steels
Sumitesh DasIan C. HowardEric J. Palmiere
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2006 Volume 46 Issue 4 Pages 560-566


The conventional method of representing the nature and magnitude of heat transfer at the strip–roll interface during hot rolling is to use a mean or “average” heat transfer coefficient (h). However, an examination of the real strip surface reveals a spatial variation of features, characterised by varying asperities and distributed topography of the oxide scale. The scale distribution can vary both along and across the strip, with details being dependent on the rolling schedule, thereby rendering formulations that use a mean h-value good only to a first approximation.
The paper develops a probabilistic approach, implemented within a conceptually flat and thin imaginary oxide layer, the so-called “phantom layer”, to gain an insight into the probable natural variation of the heat transfer coefficient at the strip–roll interface. Here, the evolving oxide-scale parameters of instantaneous reduction, thickness and temperature are process-driven random variables whose cumulative effect on the instantaneous h is derived using a Probability Distribution Diagram (PDD).
The PDD model proves to be particularly useful in addressing the practical issues of non-uniformity and local scale variations.

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© 2006 by The Iron and Steel Institute of Japan
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