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TECHNICAL PAPERS

Thermal Stresses in a Freezing Sphere and its Application to Cryobiology

[+] Author and Article Information
Y. Rabin

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890; Department of Human Oncology, Allegheny University of the Health Sciences, 320 East North Avenue, Pittsburgh, PA 15212-4772

P. S. Steif

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890

J. Appl. Mech 65(2), 328-333 (Jun 01, 1998) (6 pages) doi:10.1115/1.2789058 History: Received February 17, 1997; Revised August 11, 1997; Online October 25, 2007

Abstract

Thermal stresses in an inwardly solidifying sphere are studied analytically. A closed-form solution is given which accounts for thermal expansion associated with temperature gradients and volume changes associated with phase transition. Consistent with the target application of cryopreservation of biological solutions and tissues, the material is modeled as elastic-perfectly plastic. Parametric studies using appropriate material properties and typical cryopreservation protocols suggest that strains associated with phase transition lead to far higher stresses than those associated with thermal expansion, with important implications for cryopreservation procedures.

Copyright © 1998 by The American Society of Mechanical Engineers
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