Abstract




 
   

Vol. 9, No. 2 (May 1996) 29-35   

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  FREEZING IN A FINITE SLAB USING EXTENSIVE PERTURBATION EXPANSIONS METHOD
 
 
A. Baradaran Rahimi
 
(Sabbatical from Ferdowsi Univ. of Mashhad, Iran)
#5 King's College Road, Dept. of Mech. Engr., Univ. of Toronto
Toronto,Ontario, Canada M5S 1A4
 
 
 
 

Abstract    In this paper Mathematica is used to solve the moving boundary problem of freezing in a finite slab for higher order perturbations. Mathematica is a new system which makes it possible to do algebra with computer. More specifically, it enables researchers to find the location of the ice at any time for as high order of perturbation as one whishes. Using of Mathematica and outer solution and an inner solution for the quantities involved are developed and then these solutions are matched together using the method of matched asymptotic expansions. At the end the composite solutions are compared to the available low-order solutions.

 

Keywords    Moving Boundary, Transient Conduction, Freezing Problem, Perturbation, Finite Slab

 

References   

1. Weinbaum, A. S. and Jiji, L. M., "Conduction in Irregular Domains"; Journal of International Heat and Mass Transfer, Vol. 20, (1977).

2. Aziz, A. and Na, T. Y., "Perturbation Methods in Heat Transfer", Hermisphere Publishing Corporation, U. S. A., (1984).

3. Wolfram, S., "Mathematica a System for Doing Mathematics by Computers", Addison-Wesley Company, Inc. U.S.A., (1991).

4. Arpaci, V. S., "Conduction Heat Transfer", Addision-Wesley Publishing Company, Reading, Massachusetts, (1984).

5. Nayfeh, A. H., "Perturbation Methods", John Wiley and Sons, New York, U.S.A., (1992).

6. Bender, C. M. and Orszag, S. A., "Advanced Mathematical Methods for Scientists and Engineers", McGraw-Hill Book Company, U.S.A., (1980).





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