On the convergence of the heat balance integral method

Applied Mathematical Modelling

Volumn 29, Issue 10, 2005, Pages 903-912

  Mosally, F ^a   Wood, A S ^b   Al Fhaid, A ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b UNIVERSITY OF BRADFORD   (United Kingdom)

Author keywords

Convergence; Heat balance integral; Phase change

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; HEAT FLUX; HEAT TRANSFER; MATHEMATICAL MODELS; PHASE TRANSITIONS; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING;

CONVERGENCE PROPERTIES; HEAT BALANCE INTEGRAL METHOD; PIECEWISE LINEAR INTEGRAL SOLUTION; STEFAN NUMBERS;

INTEGRAL EQUATIONS;

HEAT CAPACITY;

EID: 24144494590     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2004.12.001     Document Type: Article

References (13)

1. T.R. Goodman Heat balance integral and its application to problems involving a change of phase Trans. ASME J. Heat Transfer 80 1958 335-342
2. T.R. Goodman Application of integral methods in transient non-linear heat transfer In T.F. Irvine J.P. Hartnett eds. Advances in heat transfer vol. 1 1964 Academic Press New York pp. 51-122
3. A.S. Wood A new look at the heat balance integral method Appl. Math. Mod. 25 2001 815-824
4. B. Noble Heat balance methods in melting problems In J.R. Ockendon W.R. Hodgkins eds. Moving boundary problems in heat flow and diffusion 1974 Clarendon Press Oxford pp. 208-209
5. G.E. Bell A refinement of the heat balance integral method applied to a melting problem Int. J. Heat Mass Transfer 21 1978 1357-1362
6. G.E. Bell Solidification of a liquid about a cylindrical pipe Int. J. Heat Mass Transfer 22 1979 1681-1686
7. G.E. Bell Accurate solution of one-dimensional melting problems by the heat balance integral method In R.W. Lewis K. Morgan eds. Numerical methods in thermal problems 1979 Pineridge Press Swansea pp. 196-203
8. G.E. Bell The prediction of frost penetration Int. J. Numer. Anal. Meths. Geomechanics 6 1982 287-290
9. G.E. Bell S.K. Abbas Convergence properties of the heat balance integral method Numer. Heat Transfer 8 1985 373-382
10. J. Crank R.D. Phahle Melting ice by the isotherm migration method Bull. IMA 9 1973 12-14
11. J. Stefan Über einige Probleme der Theorie der Wärmleitung Sber. Akad. Wiss. Wien 98 1889 473-484 (in German)
12. M. Abramowitz I.A. Stegun Handbook of mathematical functions 1965 Dover Press New York
13. K. Pearson Tables of the Incomplete Gamma Function 1934 Cambridge University Press Cambridge