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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.244 SNIP: 0.434 CiteScore™: 0.7

ISSN Print: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2018019984
pages 493-519

FINITE ELEMENT LEGENDRE WAVELET GALERKIN APPROACH IN INVESTIGATION OF NON-FOURIER'S AND NON-FICK'S EFFECTS ON HEAT AND MASS TRANSFER DURING DRYING OF FOODS

Subrahmanayam Upadhyay
DST-CIMS, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
Kabindra Nath Rai
Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi- 22005, Uttar Pradesh, India; DST-CIMS, Banaras Hindu University,Varanasi-22005, Uttar Pradesh, India

ABSTRACT

In this article, we developed a single phase lag model (SPL) on heat mass transfer within foods of different geometrical configurations such as slab, cylinder, or sphere, under the most generalized boundary conditions in application of drying of foods. The present model is a generalization of diffusion model, Luikov's model, and Chang and Weng's, and Win-Jin et al.'s model. The finite element Legendre wavelet Galerkin method (FELWGM) is used in the solution. The discretization in space and then application of Legendre wavelet Galerkin method converts the problem into a coupled system of Sylvester equations. The use of the Kronecker product of matrices and then application of the Gauss elimination method provides a solution. Stability analysis of the present method is provided. In the absence of relaxation time, the present model is Chang and Weng's and Win-Jin et al.'s model. In this case, the solution obtained by the present method is approximately the same as that obtained by Win-Jin et al. Again, in a particular case, the solution obtained by the present method is compared with an exact analytical solution obtained using Laplace transform technique and are exactly the same. The whole analysis is done in nondimensional form. The effect of shape (slab, cylinder, or sphere) in the process of heat and mass transfer is discussed in detail. The slab shape of foods takes higher time than the spherical shape of foods and less time than the cylindrical shape of food in drying. Furthermore, the effects of relaxation time parameter (η0, η1), Luikov number (Lu), Kirpichev number (Kiq, Kim), Biot number (Biq, Bim), Kossovich number (Ko), Predvoditelev number (Pd1, Pd2), and Possnov number (Pn) on heat and mass transfer are discussed in detail for the slab shape of foods.


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