Microwave heating of two-dimensional slabs with small Arrhenius absorptivity

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 62, Issue 2, 1999, Pages 137-166

  Liu, B ^a   Marchant, T R ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION; BOUNDARY CONDITIONS; ELECTRIC CONDUCTIVITY; GALERKIN METHODS; HEAT LOSSES; MAGNETIC PERMEABILITY; MAXWELL EQUATIONS; MICROWAVE HEATING; PERMITTIVITY; THERMAL EFFECTS;

APPROXIMATE ANALYTICAL SOLUTIONS; ARRHENIUS LAW; CONTROL PROCESS; FORCED HEAT EQUATION; THERMAL ABSORPTIVITY; THERMAL RUNAWAY; TWO DIMENSIONAL SLABS;

WAVEGUIDES;

EID: 0032690028     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/62.2.137     Document Type: Article

References (20)

1. AYAPPA, K. G., DAVIS, H. T., DAVIS, E. A., & GORDON, J. 1992 Two-dimensional finite element analysis of microwave heating. AIChE J. 38, 1577-1592.
2. CHAPMAN, A. J. 1974 Heat Transfer. New York: Macmillan.
3. GEANKOPLIS, C. J. 1983 Transport Processes: Momentum, Heat and Mass. Boston: Allyn & Bacon.
4. HILL, J. M. & JENNINGS, M. J. 1993 Formulation of model equations for heating by microwave radiation. Appl. Math. Modelling 17, 369-379.
5. HILL, J. M. & MARCHANT, T. R. 1996 Modelling microwave heating. Appl. Math. Modelling 20, 3-15.
6. HILL, J. M. & SMYTH, N. F. 1990 On the mathematical analysis of hotspots arising from microwave heating. Math. Eng. in Industry 2, 267-278.
7. KRIEGSMANN, G. A. 1991 Microwave heating of ceramics. In Ordinary and Partial Differential Equations Vol. 3 ed. B. Sleeman and R. Jarvis. London: Longman, 45-56.
8. KRIEGSMANN, G. A. 1992a Thermal runaway and its control in microwave heated ceramics. Mat. Res. Soc. Symp. Proc. 269, 257-264.
9. KRIEGSMANN, G. A. 1992b Thermal runaway in microwave heated ceramics: a one-dimensional model. J. Appl. Phys. 71, 1960-1966.
10. KRIEGSMANN, G. A. 1997 Cavity effects in microwave heating of ceramics. SIAM J. Appl. Math. 57, 382-400.
11. KRIEGSMANN, G. A., BRODWIN, M. E., & WATTERS, D. G. 1990 Microwave heating of a ceramic halfspace. SIAM J. Appl. Math. 50, 1088-1098.
12. MARCHANT, T. R. 1994 Microwave heating of materials with impurities. J. Engng Math. 28, 379-400.
13. MARCHANT, T. R. & KRIEGSMANN, G. A. 1996 Thermal runaway of microwave heated materials with small losses. Research report 96/11, Department of Mathematics, University of Wollongong, Wollongong, Australia.
14. MARCHANT, T. R. & LIU, B. 1998 The steady-state microwave heating of slabs with small arrhenius absorptivity. J. Engng Math 33, 219-236.
15. MARCHANT, T. R. & PINCOMBE, A. H. 1994 Microwave heating of materials with temperature dependent wavespeed. Wave Motion 19, 67-81.
16. PINCOMBE, A. H. & SMYTH, N. F. 1991 Microwave heating of materials with low conductivity. Proc. R. Soc. A 433, 479-498.
17. PORTIS, A. M. 1978 Electromagnetic Fields: Sources and Media. New York: Wiley.
18. ROUSSY, G., BENNANI, A., & THIEBAUT, J. 1987 Temperature runaway of microwave irradiated materials. J. Appl. Phys. 62, 1167-1170.
19. SMYTH, N. F. 1990 Microwave heating of bodies with temperature dependent properties. Wave Motion 12, 171-186.
20. ZHU, S. P., ZHANG, Y. L., & MARCHANT, T. R. 1995 A DRBEM model for microwave heating. Appl. Math. Modelling 19, 287-297.