Optimizing the exponent in the heat balance and refined integral methods

International Communications in Heat and Mass Transfer

Volumn 36, Issue 2, 2009, Pages 143-147

  Myers, T G ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Heat Balance Integral Method; Heat flow; Polynomial approximation; Refined integral method

Indexed keywords

DIFFERENCE EQUATIONS; FLOW MEASURING INSTRUMENTS; HEAT FLUX; HEAT TRANSFER; REFINING; SPECIFIC HEAT;

EXACT SOLUTIONS; HEAT BALANCE INTEGRAL METHOD; HEAT BALANCES; HEAT EQUATIONS; HEAT FLOW; REFINED INTEGRAL METHOD; SOLUTION PROCESS;

POLYNOMIAL APPROXIMATION;

EID: 59649114537     PISSN: 07351933     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.icheatmasstransfer.2008.10.013     Document Type: Article

References (15)

1. Antic A., and Hill J.M. The double-diffusivity heat transfer model for grain stores incorporating microwave heating. Appl. Math. Model. 27 (2003) 629-647
2. Braga W.F., Mantelli M.B.H., and Azevedo J.L.F. Approximate analytical solution for one-dimensional finite ablation problem with constant time heat flux. AIAA Thermophys. Conference (June 2004)
3. Goodman T.R. The heat-balance integral and its application to problems involving a change of phase. Trans. ASME 80 (1958) 335-342
4. Grange B.W., Viskanta R., and Stevenson W.H. Diffusion of heat and solute during freezing of salt solutions. Int. J. Heat & Mass Trans. 19 4 (1976) 373-384
5. J. Hristov, The heat-balance integral method by a parabolic profile with unspecified exponent: analysis and exercises, to appear in Thermal Sci. 13(2) 2009.
6. Kutluay S., Wood A.S., and Esen A. A heat balance integral solution of the thermistor problem with a modified electrical conductivity. Appl. Math. Model. 30 (2006) 386-394
7. Langford D. The heat balance integral method. Int. J. Heat Mass Trans. 16 (1973) 2424-2428
8. Mitchell S.L., and Myers T.G. Heat balance integral method for one-dimensional finite ablation, AIAA. J. Thermophys. & Heat Trans. 22 3 (2008) 508-514
9. Mitchell S.L., and Myers T.G. Approximate solution methods for one-dimensional solidification from an incoming fluid. App. Math. Comp. 202 1 (2008) 311-326
10. T.G. Myers and S.L. Mitchell, Application of the heat balance and refined integral methods to the Korteweg-de Vries equation, to appear in Thermal Sci. 13(2) 2009.
11. T.G. Myers, S.L. Mitchell, and G. Muchatibaya, Unsteady contact melting of a rectangular cross-section material on a flat plate, Phys. Fluids 20 (2008) 103101. doi:10.1063/1.2990751.
12. Myers T.G., Mitchell S.L., Muchatibaya G., and Myers M.Y. A cubic heat balance integral method for one-dimensional melting of a finite thickness layer. Int. J. Heat Mass Trans. 50 (2007) 5305-5317
13. Sadoun N., Si-Ahmed E.-K., and Colinet P. On the refined integral method for the one-phase Stefan problem with time-dependent boundary conditions. App. Math. Model. 30 (2006) 531-544
14. Spearpoint M.J., and Quintiere J.G. Predicting the piloted ignition of wood in the cone calorimeter using an integral model - effect of species, grain orientation and heat flux. Fire Safety J. 36 4 (2001) 391-415
15. Wood A.S. A new look at the heat balance integral method. App. Math. Model. 25 (2001) 815-824