Journal of Engineering Mathematics

, Volume 44, Issue 2, pp 155–171 | Cite as

Microwave heating in multiphase systems: evaluation of series solutions

  • K.G. Ayappa
  • Tirthankar SenGupta


The 1D electric field and heat-conduction equations are solved for a slab where the dielectric properties vary spatially in the sample. Series solutions to the electric field are obtained for systems where the spatial variation in the dielectric properties can be expressed as polynomials. The series solution is used to obtain electric-field distributions for a binary oil-water system where the dielectric properties are assumed to vary linearly within the sample. Using the finite-element method temperature distributions are computed in a three-phase oil, water and rock system where the dielectric properties vary due to the changing oil saturation in the rock. Temperature distributions predicted using a linear variation in the dielectric properties are compared with those obtained using the exact nonlinear variation.

microwaves oil recovery porous media series solutions 


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  1. 1.
    F. E. Vermeulen and B. McGee, In situ electromagnetic heating for hydrocarbonrecovery and environmental remediation. J. Canad. Petr. Technol. 39 (2000) 24–28.Google Scholar
  2. 2.
    M.Y. Soliman, Approximate solutions for flow of oil heated using microwaves. J. Petr. Sci. Eng. 18 (1997) 93–100.Google Scholar
  3. 3.
    R. E. Collins, Flow of Fluids through Porous Materials. New York: ReinholdPubl. Corp. (1961) 270 pp.Google Scholar
  4. 4.
    K. G. Ayappa, H. T. Davis, E. A. Davis and J. Gordon, Analysis ofmicrowave heating of materials with temperature dependent properties. AIChE J. 37 (1991) 313–1667.Google Scholar
  5. 5.
    H. Fricke, The complex conductivity of a suspension of stratified particles of spherical or cylindricalform. J. Phys. Chem. 56 (1955) 168–174.Google Scholar
  6. 6.
    X. Zeng and A. Faghri, Experimental andnumerical study of microwave thawing heat transfer of food materials. ASME Trans. J. Heat Transfer 116 (1994) 446–455.Google Scholar
  7. 7.
    K. G. Ayappa, H. T. Davis, G. Crapiste, E. A. Davis and J. Gordon,Microwave heating: An evaluation of power formulations. Chem. Eng. Sci. 46 (1991) 1005–1016.Google Scholar
  8. 8.
    E. D. Rainville, Elementary Differential Equations. New York: Macmillan (1965) 521 pp.Google Scholar
  9. 9.
    T. Basak and K. G. Ayappa, Analysis of microwave thawing of slabs with effective heat capacity method. AIChE J. 43 (1997) 1662–1667.Google Scholar
  10. 10.
    S. A. Barringer, K. G. Ayappa, J. Gordon, E. A. Davisand H. T. Davis, Power absorption during microwave heating of emulsions and layered systems. J. Food Sci. 60 (1995) 1132–1136.Google Scholar
  11. 11.
    C. M. Bender and S. A. Orszag, Advanced Mathematical Methods forScientists and Engineers. New York: Mc-Graw Hill (1984) 593 pp.Google Scholar
  12. 12.
    C. A. Balanis, AdvancedEngineering Electromagnetics. New York: John Wiley & Sons (1989) 981 pp.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • K.G. Ayappa
    • 1
  • Tirthankar SenGupta
    • 1
  1. 1.Department of Chemical Engineering Indian Institute of ScienceBangaloreINDIA

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