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The double-diffusivity heat transfer model for grain stores incorporating microwave heating. (English) Zbl 1043.80001
Summary: Australia’s reputation is well established in the international marketplace as a producer of high-quality grain. One of the largest problems faced by the Australian grain industry is protecting grain, while in storage, from infestation by insect pests. The standard practice employed is to fumigate with chemicals such as phosphine. Currently, there is an ongoing reduction in the number of chemicals permitted for pest control, as insects have developed resistance to some chemicals and others are currently being phased out due to safety and environmental reasons. As a result, the grain storage industry is moving towards physical methods as opposed to chemical methods, as a safer and potentially better alternative. One well studied area is known as thermal disinfestation, with one of the potentially best forms being heat disinfestation via microwave radiation. The mathematical modelling of microwave heating processes in general requires the solution of a complex system of equations, which can be very difficult to obtain. In this work we illustrate the possibility of reducing the problem to one which involves extending the double-diffusivity heat transfer model, as previously developed by the authors [Aust. NZ Ind. Appl. Math. J. 42 (E), C117--C133 (2000)], to include a nonlinear body heating source term to account for the heating due to microwave radiation. This model is known as the double-diffusivity heat transfer model incorporating microwave heating. Such a dual-region model is well suited to the analysis of grain bulks as air and grain are two different mediums with different heat conduction properties. A semi-analytical solution is obtained via the heat-balance integral method and is compared with an explicit finite difference numerical solution. Very good agreement is found between both forms of the solutions. We also compare these results to the case of no microwave heating, that is, the double-diffusivity heat transfer model [loc. cit.].

80A20Heat and mass transfer, heat flow
Full Text: DOI
[1] Antic, A.; Hill, J. M.: A mathematical model for heat transfer in grain store microclimates. Aust. NZ ind. Appl. math. J. 42 (E), C117-C133 (2000) · Zbl 0989.80008
[2] H.J. Banks, Prospects for heat disinfestation, Aust. Postharvest Tech. Conf. Canberra, 26--29 May 1998, pp. 227--232
[3] Barenblatt, G. I.; Zheltov, Iu.P.; Kochina, I. N.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. appl. Math. mech. 24, 1286-1303 (1960) · Zbl 0104.21702
[4] Coleman, C. J.: The microwave heating of frozen substances. J. appl. Math. modell. 14, 439-443 (1990) · Zbl 0716.65111
[5] Coleman, C. J.: On the microwave hotspot problem. J. aust. Math. soc. (Ser. B) 33, 1-8 (1991) · Zbl 0738.73003
[6] Fohr, J. -P.; Moussa, H. B.: Heat conduction mass transfer in a cylindrical grain silo submitted to a periodical wall heat flux. Int. J. Heat mass transfer 37, 1699-1712 (1994)
[7] J.M. Hill, J.N. Dewynne, Heat conduction, Department of Mathematics, University of Wollongong, 1986
[8] Hill, J. M.; Jennings, M. J.: Formulation of model equations for heating by microwave radiation. J. appl. Math. modell. 17, 369-379 (1993) · Zbl 0784.35114
[9] Hill, J. M.; Pincombe, A. H.: Some similarity temperature profiles for the microwave heating of a half-space. J. aust. Math. soc. (Ser. B) 33, 290-320 (1992) · Zbl 0757.35081
[10] Hill, J. M.; Smyth, N. F.: On the mathematical analysis of hot-spots arising from microwave heating. Math. eng. Ind. 2, 267-278 (1990)
[11] Von Hippel, A. R.: Dielectrical materials and applications. (1954)
[12] Jia, C.; Sun, D. -W.; Cao, C.: Finite element prediction of transient temperature distribution in a grain storage bin. J. agric. Eng. res. 76, 323-330 (2000)
[13] Jia, C.; Sun, D. -W.; Cao, C.: Mathematical simulation of temperature and moisture fields within a grain kernel during drying. Drying technol. 18, 1305-1325 (2000)
[14] Jolly, P.; Turner, I.: Nonlinear field solutions of one-dimensional microwave heating. J. microwave power 25, 3-15 (1990)
[15] Kreigsmann, G. A.; Brodwin, M. E.; Walters, D. G.: Microwave heating of a ceramic halfspace. Soc. ind. Appl. math. J. appl. Math. 50, 1088-1098 (1990) · Zbl 0719.34099
[16] Metaxas, A. C.; Meredith, R. J.: Ind. micr. Heating. (1988)
[17] Nelson, S. O.: Review and assessment of radio-frequency and microwave energy for stored-grain insect control. Trans. am. Soc. agric. Eng. 39, 1475-1484 (1996)
[18] Nelson, S. O.; Bartley, P. G.; Lawrence, K. C.: RF and microwave dielectric properties of stored-grain insects and their applications for potential insect control. Trans. am. Soc. agric. Eng. 41, 685-692 (1998)
[19] J.L. Parry, Mathematical Modelling and Computer Simulation of Heat and Mass Transfer in Agricultural Grain Drying: A Review, 1964
[20] Portis, A. M.: Electromagnetic fields: sources and media. (1978)
[21] Rubinstein, L. I.: Process of conduction of heat in heterogeneous media. Izv. akad. Nauk. SSSR, geogr. 12, 12-45 (1948)
[22] Smyth, N. F.: Microwave heating of bodies with temperature dependent properties. Wave motion 12, 171-186 (1990) · Zbl 0706.73007
[23] Sutherland, J. W.; Banks, P. J.; Griffiths, H. J.: Equilibrium heat and moisture transfer in air flow through grain. J. agric. Eng. res. 16, 368-386 (1971)
[24] Thorpe, G. R.; Whitaker, S.: Local mass and thermal equilibria in ventilated grain bulks. Part I: The development of heat and mass conservation equations. J. stored prod. Res. 28, 15-27 (1992)
[25] Thorpe, G. R.; Whitaker, S.: Local mass and thermal equilibria in ventilated grain bulks. Part II: The development of constraints. J. stored prod. Res. 28, 29-54 (1992)
[26] Trabelsi, S.; Kraszewski, A. W.; Nelson, S. O.: Microwave dielectric properties of shelled, yellow-dent field corn. J. microwave power electromagn. Energy 32, 188-194 (1997)