Coupled Integral Equations Approach in the Solution of Luikov Equations with Microwave Effect

Document Type : Full Lenght Research Article


1 School of Chemical Engineering, Federal University of Para, Belem, PA, Brazil

2 Federal University of Para

3 Universidade do Estado do Para


The objective of this study is to present a mathematical modeling and solution approach for the drying process of spheroidal solids with the application of microwave in capillary porous media based on the Luikov equations, composed of a system of linear and coupled partial differential equations arising from the energy, mass and pressure balances inside the solid matrix. Additionally, the power generation term from the application of microwaves is added to this differential system. The solution to this problem is achieved through a Coupled Integral Equations Approach (CIEA), whose objective is the transformation of the initial PDE system into an ODEs one. A computer code was developed in FORTRAN 90/95 programming language, which uses the subroutine IVPAG from the IMSL library to solve the system of ODEs from the application of the CIEA. The results obtained were compared with other previously reported in the literature to verify the methodology and showed satisfactory agreement.


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