Luikov Equations Research Articles

Investigation of Simultaneous Heat and Mass Transfer within the Individual Maize Kernels During Drying

The main aim of this study is to give a mathematical model with numerical solution to follow the heat and moisture distributions inside a cross sectional area of an individual maize kernel as a function of drying time with respect to the effects of the coupled heat and mass transfer processes to be beyond the existing models and solutions published by literature sources. The applied drying models are similar to the modified Luikov's equations, which were applied by Husian firstly. This mathematical model is used to compare fast and slow drying individual maize hybrids. The data (heat physical constants and variables) for the slow and the fast drying individual maize hybrids derive from experiments which have been in progress since 1981. This model can follow the drying process very well. The mathematical model with the boundary and initial conditions can reveal the difference between the fast and slow drying hybrids. The temperature and moisture distributions inside the individual maize kernel produced by the model show more realistic picture than the results published before.

DRYING OF BIOLOGICAL PRODUCTS WITH HIGH WATER CONTENT IN SOLAR REGIME. APPLICATION TO THE POTATO DRYING.

ABSTRACT The experimental results on the drying of biological porous media (potato) are modeled using the Luikov equations, under simulate insolation conditions. The temperature of the environment was regulated, within the typical range corresponding to hot-temperature and rather wet climate (Argentina's Humid Pampa region). The comparison between measurements and calculations gave good agreement. The present study confirms independently the identification of several characteristic parameters of the product obtained under constant conditions in a previous work [1].

Lumped- Differential Formulations for Drying in Capillary Porous Media

ABSTRACT Simultaneous heat and mass transfer, during drying of moist capillary porous media, is modeled through different lumped-differential formulations, obtained from spatial integration of the original set of Luikov's equations for temperature and moisture potential. Besides the classical lumped system analysis, improved formulations are proposed, of same mathematicai simplicity, based on approximate evaluations of both temperature and moisture gradients within the medium. The relative merits of such improved zero-dimensional formulations are established, through critical comparisons against analytical solutions for the full partial diflerential system, over a wide range of the governing parameters.

On the solution of non‐linear drying problems in capillary porous media through integral transformation of Luikov equations

AbstractThe generalized integral transform technique is employed to provide hybrid numerical–analytical solutions to the non‐linear Luikov equations, that govern drying within capillary porous media. The coupled equations for moisture and temperature distributions are integral transformed to eliminate the spatial co‐ordinates, yielding an ordinary differential system for the time variation of the transformed potentials, which is readily solved through scientific subroutine libraries with automatic error control schemes. The analytical inversion formula is then recalled to provide explicit expressions for the original potentials at any desired position. The convergence behaviour of the proposed eigenfunction expansions is illustrated, and a parametric study is performed, for the drying of a slab subjected to non‐linear radiative boundary conditions.

Luikov equations applicable to sublimation-drying

Present paper presents a derivation of Luikov equations applicable to sublimation-drying. The physical situation and transfer mechanism are elucidated clearly. The coefficients appearing in Luikov equations are given in a more explicit way. Some formulation mistakes in recent publications are indicated.

Integral transform solution of Luikov's equations for heat and mass transfer in capillary porous media

The Luikov system of equations for coupled heat and mass transfer within capillary porous bodies is analytically handled through application of the generalized integral transform technique. The problem of temperature and moisture distribution during contact drying of a moist porous sheet is considered to illustrate the development of the present approach. The classical coupled auxiliary problem with the related complex eigenvalues is completely avoided and, instead, two decoupled eigenvalue problems for temperature and moisture are chosen, which are of the conventional Sturm-Liouville type. A set of benchmark results is generated and critically compared with previously reported approximate solutions.

A FULLY NONLINEAR ANALYSIS OF TEMPERATURE, MOISTURE CONTENT, AND PRESSURE IN A CAPILLARY POROUS BODY

Abstract This article demonstrates, for the first time, a fully nonlinear finite-element solution to Luikov's three-degree-of-freedom system of partial differential equations, which predict the variation of temperature, moisture, and pressure within a capillary porous body. Previously, only an analytical solution in one dimension was feasible but as physical geometries and boundary conditions of engineering problems became more complex, an analytical solution became impractical. Here, we resort to a numerical technique, namely, the finite-element method, to solve Luikov's equations in two dimensions. To solve Luikov's equations numerically, a fully nonlinear model was developed, where all material properties are permitted to vary as the transient solution progresses; previously, only a solution using a partially nonlinear model was possible. The numerical solutions obtained from both numerical models are compared for a two-dimensional container example.

Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies

This paper presents an analytical method to solve the Luikov system of linear partial differential equations subject to specified initial and boundary conditions. Luikov equations are the governing equations in analyzing heat and mass diffusion problems for capillary-porous bodies. However, an analytical method to obtain complete and satisfactory solutions of these equations is still lacking in the literature. The method of solution presented in this paper is illustrated by considering the transient distributions of temperature and moisture in a slab of wood during drying. Numerical results are obtained and compared with published finite element solutions and experimental data for spruce specimens. The method should have a general application to problems of heat and mass transfer in capillary-porous bodies.

A fast approximate analytical solution to Luikov's equations with variable thermophysical properties

A study has been carried out to investigate the rehydration of foods during storage, employing the coupled partial differential equations proposed by Luikov. Variations of mass and thermal diffusivities with temperature and moisture content have been included in the model. The Method of Weighted Residuals has been applied to develop approximate analytical expressions from the resulting set of partial differential equations to predict moisture and temperature profiles. The influence of dimensionless variables on the moisture transfer has been examined.