Heat and Mass Transfer

, Volume 44, Issue 4, pp 481–493 | Cite as

Investigation of a particulate flow containing spherical particles subjected to microwave heating

  • J. Zhu
  • A. V. KuznetsovEmail author
  • K. P. Sandeep


Microwave heating of a liquid and large spherical particles that it carries while continuously flowing in a circular applicator pipe is investigated. A three-dimensional model that includes coupled Maxwell, continuity, Navier–Stokes, and energy equations is developed to describe transient temperature, electromagnetic, and fluid velocity fields. The hydrodynamic interaction between the solid particles and the carrier liquid is simulated by the force-coupling method (FCM). Computational results are presented for the microwave power absorption, temperature distribution inside the liquid and the particles, as well as the velocity distribution in the applicator pipe and trajectories of particles. The effect of the time interval between consecutive injections of two groups of particles on power absorption in particles is studied. The influence of the position of the applicator pipe in the microwave cavity on the power absorption and temperature distribution inside the liquid and the particles is investigated as well.


Microwave Heating Residence Time Distribution Power Absorption Microwave Cavity Power Density Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ayappa KG, Davis HT, Davis EA, Gordon J (1992) Two-dimensional finite element analysis of microwave heating. AIChE J 38:1577–1592CrossRefGoogle Scholar
  2. 2.
    Ayappa KG, Sengupta T (2002) Microwave heating in multiphase systems: evaluation of series solutions. J Eng Math 44:155–171CrossRefMathSciNetGoogle Scholar
  3. 3.
    Kriegsmann GA (1997) Cavity effects in microwave heating of ceramics. J Appl Math 57:382–400zbMATHMathSciNetGoogle Scholar
  4. 4.
    Araneta JC, Brodwin ME, Kriegsmann GA (1984) High-temperature microwave characterization of dielectric rods. IEEE Trans Microw Theory Tech 32:1328–1335CrossRefGoogle Scholar
  5. 5.
    Basak T, Ayappa KG (1997) Analysis of microwave thawing of slabs with effective heat capacity method. AIChE J 43:1662–1667CrossRefGoogle Scholar
  6. 6.
    O’Brien KT, Mekkaoui AM (1993) Numerical simulation of the thermal fields occurring in the treatment of malignant rumors by local hyperthermia. J Biomech Eng 115:247–253Google Scholar
  7. 7.
    Ayappa KG, Brandon S, Derby JJ, Davis HT, Davis EA (1994) Microwave driven convection in a square cavity. AIChE J 40:1268–1272CrossRefGoogle Scholar
  8. 8.
    Franca AS, Haghighi K (1996) Adaptive finite element analysis of microwave driven convection. Int Commun Heat Mass Transf 23:177–186CrossRefGoogle Scholar
  9. 9.
    Saltiel C, Datta A (1997) Heat and mass transfer in microwave processing. Adv Heat Transfer 30:1–94Google Scholar
  10. 10.
    Ayappa KG, Davis HT, Davis EA, Gordon J (1991) Analysis of microwave heating of materials with temperature dependent properties. AIChE J 37:313–322CrossRefGoogle Scholar
  11. 11.
    Ratanadecho P, Aoki K, Akahori M (2002) Influence of irradiation time, particle sizes, and initial moisture content during microwave drying of multi-layered capillary porous materials. J Heat Transfer 124:151–161CrossRefGoogle Scholar
  12. 12.
    Clemens J, Saltiel C (1995) Numerical modeling of materials processing microwave furnaces. Int J Heat Mass Transfer 39:1665–1675CrossRefGoogle Scholar
  13. 13.
    Basak T, Ayappa KG (2002) Role of length scales on microwave thawing dynamics in 2D cylinders. Int J Heat Mass Transfer 45:4543–4559zbMATHCrossRefGoogle Scholar
  14. 14.
    Barringer SA, Davis EA, et al (1995) Microwave heating temperature profiles for thin slabs compared to Maxwell and Lambert law predictions. J Food Sci 60:1137–1142CrossRefGoogle Scholar
  15. 15.
    Aoki K, Ratanadecho P, Akahori M (2000) Characteristics of microwave heating for multi-layered materials using a rectangular wave guide. In: Proceeding of the fourth JSME-KSME thermal engineering conference 2:191–196Google Scholar
  16. 16.
    Zhang Q, Jackson TH, Ungan A (2000) Numerical modeling of microwave induced natural convection. Int J Heat Mass Transfer 43:2141–2154zbMATHCrossRefGoogle Scholar
  17. 17.
    Ratanadecho P, Aoki K, Akahori M (2002) A numerical and experimental investigation of the modeling of microwave heating for liquid layers using a rectangular wave guide (effects of natural convection and dielectric properties). Appl Math Model 26:449–472zbMATHCrossRefGoogle Scholar
  18. 18.
    Zhu J, Kuznetsov AV, Sandeep KP (2007) Numerical simulation of forced convection in a duct subjected to microwave heating, Heat and Mass Transfer, 43:255–264CrossRefGoogle Scholar
  19. 19.
    Zhu J, Kuznetsov AV, Sandeep KP (2007) Mathematical modeling of continuous flow microwave heating of liquids (effects of dielectric properties and design parameters). Int J Thermal Sci 46:328–341CrossRefGoogle Scholar
  20. 20.
    Zhu J, Kuznetsov AV, Sandeep KP (2006) Numerical modeling of a moving particle in a continuous flow subjected to microwave heating, Numerical Heat Transfer, Part A. (in press)Google Scholar
  21. 21.
    Cheng DK (1992) Field and wave electromagnetics. Addison-Wesley, New YorkGoogle Scholar
  22. 22.
    Mur G (1981) Absorbing boundary conditions for the finite difference approximation of the time domain electromagnetic field equations. IEEE Trans Electromag Compat EMC-23, No. 4, pp 377–382Google Scholar
  23. 23.
    Maxey MR, Patel BK (2001) Localized force representations for particles sedimenting in Stokes flow. Int J Multiph Flow 27:1603–1626CrossRefGoogle Scholar
  24. 24.
    Lomholt S, Stenum B, Maxey MR (2002) Experimental verification of the force coupling method for particulate flows. Int J Multiph Flow 28:225–246CrossRefGoogle Scholar
  25. 25.
    Dance SL, Maxey MR (2003) Force-coupling method for particulate two-phase flow: Stokes flow. J Comput Phys 184:381–405CrossRefMathSciNetGoogle Scholar
  26. 26.
    Dance SL, Maxey MR (2003) Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow. J Comput Phys 189:212–238zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Glowinski R, Pan TW, Hesla TI, Joseph DD (1999) A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int J Multiph Flow 25:755–794CrossRefGoogle Scholar
  28. 28.
    Kunz KS, Luebbers R (1993) The finite difference time domain method for electromagnetics. CRC, Boca RatonGoogle Scholar
  29. 29.
    Patankar SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. J Heat Mass Transfer 15:1787–1806zbMATHCrossRefGoogle Scholar
  30. 30.
    Clift R, Grace JR, Weber ME (1978) Bubbles, drops, and particles. Academic, San DiegoGoogle Scholar
  31. 31.
    Segre G, Silberberg A (1962) Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J Fluid Mech 14:115–135CrossRefGoogle Scholar
  32. 32.
    Segre G, Silberberg A (1962) Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J Fluid Mech 14:136–157CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringNorth Carolina State UniversityRaleighUSA
  2. 2.Department of Food ScienceNorth Carolina State UniversityRaleighUSA

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