Simple Numerical Procedure for the Digital Computer Solution of Non-Linear Transient Heat Conduction with Changes of Phase

Abstract

A practical numerical method is described for the solution of transient heat conduction where the thermal properties are temperature dependent and changes of phase occur. The procedure involves the use of the explicit finite difference technique, for which a stability criterion is given, in conjunction with two integral transformations.

Get full access to this article

View all access options for this article.

References

Carslaw

H. S.

Jaeger

J. C.

Conduction of heat in solids 1959, 2nd edition (Clarendon Press, Oxford).

Eyres

N. R.

Hartree

D. R.

Ingham

Jackson

Sargant

R. J.

Wagstaff

J. B.

‘The calculation of variable heat flow in solids’, Phil. Trans. roy. Soc. 1946–8, 240 (Series A), 1.

Price

P. H.

Slack

M. R.

‘The effect of latent heat on the numerical solution of the heat flow equation’, Brit. J. appl. Phys. 1954, 5 (No. 8), 285.

Richtmeyer

R. D.

Difference methods for initial value problems 1957, chapters 1 and 6 (Interscience Publishers Inc.).

Crank

Nicolson

‘A practical method for numerical integration of solutions of partial differential equations of heat conduction type’, Proc. Camb. Phil. Soc. 1947 43, 50.

Dusinberre

G. M.

‘A note on the implicit method for finite difference heat transfer calculations’, J. Heat Trans. 1961 83C (No. 1), 92.

Crandall

S. R.

Engineering analysis 1956, 380 (McGraw-Hill).

Ryan

J. U.

‘Study of gypsum plastic exposed to fire’, J. Research Nat. Bur. Stds, 1962, 66C, 373.

Perry

J. H.

Chemical Engng Handbook 1963, 4th edition (McGraw-Hill).

10.

Kelly

K. K.

‘Contributions to the data on theoretical metallurgy, XIII. High temperature heat content, heat capacity and entropy data for the elements and inorganic compounds’, Bur. Min. Bull. 1960, 584.

11.

Ryder

J. T.

Building Research Station, Ministry of Technology, private communication.