Luikov Model Research Articles

Numerical analysis of vacuum drying of a porous body in the integrated domain

AbstractIn the present study, the vacuum drying process of an apple slice is numerically modeled based on a control volume method. Transient two‐dimensional Navier–Stokes, energy, moisture, and Luikov equations are solved by numerical coding (Fortran) to simulate the simultaneous heat and mass transfer in the ambient and apple slice, respectively. The privilege of using Luikov's model is that the capillary forces are considered, and a differentiation between air, vapor, liquid, and solid is made. Luikov described the two phenomena associated with the transport of air, vapor, and liquids through the porous media as molecular transport and molar transport. The ambient pressure linearly reduced within a minute until it reached a constant value. One of the intellectually demanding preoccupations among researchers is how to simulate the sample and its surroundings with high accuracy of boundary conditions, which enables to avoid the use of empirical transfer coefficients. This study can be scrutinized from various dimensions, among which nonuse of boundary condition between a porous sample and its surroundings is the most conspicuous novelty. Results showed that although at 50 s, isothermal and iso‐moisture lines inside the sample are symmetric, they are not symmetric at 100, 200, and 400 s. In addition, at first minute, pump operation leads to vary the density of the isothermal and iso‐moisture lines around the sample, but at 100, 200, and 400 s, higher temperature and moisture gradients have been achieved at the right and top of the sample surface.Practical ApplicationsDrying is the main technique of food preservation, so that it reduces the humidity of crops and is the most crucial procedure for safeguarding agricultural crops because it has a considerable impact on the condition of parched goods. In this study, some assumptions of drying including using empirical transfer coefficients between sample and its surrounding and vacuum drying under constant pressure have been eliminated. To achieve this goal, computational fluid dynamics (CFD), plays a crucial role to simulate the parameters inside the sample and its ambient without using boundary condition.

Correlation of the cell disintegration index with Luikov's heat and mass transfer parameters for drying of pulsed electric field (PEF) pretreated plant materials

Currently, the modelling of drying processes of plant tissues pre-treated by pulsed electric field (PEF) is following experimentally identified curves or separate heat and mass transfer and diffusion models with different levels of accuracy. This research had two major objectives: mathematical modeling and control of drying process of different vegetables pretreated by PEF during convective drying. The mathematical modeling was based on Luikov's heat and mass transfer model along with properties of different vegetables. Computer modelling was done using the difference method for predicting moisture and the temperature potentials of untreated and PEF-treated vegetables. The formulation and the solution procedures were applied to simulate the simultaneous heat and mass transfer in selected vegetables subjected to the convective drying. Suggested model had a good correlation with experimental results. Moreover, cell disintegration index can be used as a controllable parameter in heat and mass transfer models to predict drying behavior of potato, onion, and carrot tissues. Obtained drying models can be used as a mathematical tool to predict drying behavior for various types of agricultural products pre-treated by pulsed electric field. • Pulsed electric field (PEF) pre-treatment reduced the drying time. • Obtained methodology is a good tool for the analysis and modelling of PEF assisted drying. • Cell disintegration index is in relationship with the kinetics coefficients of Luikov's model. • Cell disintegration index can be used to predict drying behavior of plant tissues.

Analytical solution of coupled heat and mass transfer equations during convective drying of biomass: experimental validation

In this work, analytical solutions of the thin-layer and the Luikov models were proposed. For the thin-layer model, the moisture content and temperature distribution inside a biomass, assimilated to a parallelepiped material, are uniform whereas the Luikov model considers the sample as a porous medium. Analytical solutions of the Luikov model equations were obtained using Hermite’s zero-order approximation. These analytical solutions and those of the thin-layer model equations were applied to forced convection drying of two types of biomass: raw olive pomace (ROP) and deoiled olive pomace (DOP). It has been shown that the Luikov model is in good agreement with the experimental results except for the case where the sample has a thickness of 0.5 cm. In addition, thermal properties of ROP and DOP have been determined experimentally. On the other hand, a brief parametric study has been conducted and simultaneous effects of the dimensionless numbers: Luikov (Lu < <1), Kossovitch (Ko) and Posnov (Pn), on the drying process are highlighted. Thus, the increase of Luikov number accelerates the drying process and for specific couples (Lu and Ko) or (Lu and Pn), a remarkable change of dimensionless average water content with respect to dimensionless average temperature is observed, at the beginning of the drying process.

Hygrothermal Behavior of Earth-Based Materials: Experimental and Numerical Analysis

Bio-based building materials such as earth bricks are attracting renewed interest throughout the world due to their thermal and environmental properties. In this work, a numerical study of the hygrothermal behavior of building walls consist of compressed earth bricks (CEB) and stabilized earth bricks (SEB) was performed. A two-dimensional Luikov model for evaluating the temperature and the moisture migration in porous building materials was proposed. The coupled heat and moisture transfer problem was modeled. The governing equations of a mathematical model were solved numerically with the finite difference method. Input parameters in the model and their dependency on stabilizers content were determined by laboratory experiments. In order to specify the effect of chemical stabilization on the heat and mass transfer within studied materials, average moisture content and temperature were presented as a function of time. Results show that the addition of chemical stabilizers enhances the heat transfer through the earthen materials and reduces their water vapor permeability.

A new iterative least square Chebyshev wavelet Galerkin FEM applied to dual phase lag model on microwave drying of foods

In this paper, we developed a dual-phase-lag (DPL) model of heat and mass transfer in presence of a source term for microwave drying foods of different geometrical configuration like slab, cylinder or sphere under the most generalized boundary conditions. The particular cases of present model are the diffusion model, Luikov model, Weng-Chang model and Andarwa-Tabrizi model. The proposed model is the most generalized boundary value problem of a coupled system of two hyperbolic second order partial differential equations. Stability analysis of present model is provided. A new iterative least square Chebyshev wavelet Galerkin finite element method provided for solution. The discretization in space and then application of Chebyshev wavelet Galerkin method converts our problem into a coupled system of two most generalized Sylvester equations. The iterative least square method provide solution of coupled system of Sylvester equations. Convergence and stability analysis of present method is discussed in detail. In a particular case of DPL model, the solution obtained by present method is compared with exact solution (Laplace transform technique) and are approximately same. Effect of relaxation time, Fourier number, phase change coefficient, thermo-gradient coefficient, heat generation, radius of the food and diffusion coefficient on heat and mass transfer are discussed in detail. This generalized model and its solution play important role in the study of microwave food drying.

Modeling the Drying of Wheat Seeds in a Fluidized Bed Using a Spatially Resolved Model

Abstract. A mathematical model for simulating heat and mass transfer during fluidized-bed drying of wheat grains has been developed, combining two transfer steps; a movement of moisture inside the grain and outside the grain. Empirical equations have been used for material properties as well as for transfer processes. The developed model is composed of two models coupled to each other; the distributed parameter model (DPM or Luikov model) and the convective model. The coupled mathematical model was solved numerically by a finite difference method after discretization of equilibrium equations distributed in space. The DPM model made it possible to predict the quantity of water extracted from the grain under the effect of known drying conditions. Results showed that the drying rate of wheat increased when air temperature was increased; and that the rates were higher in the first few minutes of drying, achieving 2.6 × 10-5and 1.7 × 10-5 kg water kg-1[d.b.]·s-1 for temperatures of 66.7°C and 58.6°C, respectively. A comparison of experimental and predicted results gave good agreement, and the use of the distributed model improved the predictive capabilities of wheat grain drying in fluidized beds. Keywords: Canada Western Red Spring, Distributed parameter model, Fluidized-bed dryer, Mathematical modeling, Wheat seeds.

Modeling of Coupled Heat and Mass Transfers in a Stabilized Earthen Building Envelope with Thatched Fibers

In order to reduce the heat and mass transfers in buildings, which increase energy bills, the development of composites materials such as earth bricks stabilized with thatch fibers is important for their construction. This paper aims to study a one-dimensional model of heat and moisture transfer through porous building materials. The coupled phenomena of heat and mass transfer are described by the Luikov model. Equations and boundary conditions are discretized using the finite difference method. The results obtained illustrate the temporal evolutions of the temperature and the moisture content, as well as the distributions of the temperature and moisture content inside the wall. The profile of the temperature and water content that are obtained are compared with the other numerical solutions that are available in the literature.

Evaluación de los factores de influencia en el modelo de Luikov durante el secado de ladrillo

The heat and moisture transfer in the drying of porous solid materials is important, since excessive moisture has adverse effects on these materials; then, it exist a wide interest on the reduction of moisture in them. Nowadays, the research of the drying process is carried out both theoretical, as experimentally, because does not exist a universal model which satisfactorily describe the drying process of all kind of solid materials. The developed models apply to restricted groups of materials. To describe the moisture transfer in capillary porous materials, one of the more accepted theoretical models is the Luikov model, which is derived from the principles of thermodynamics of irreversible processes. This model has been applied to many materials; however, to describe the moisture transfer in capillary porous materials, it is needed a comprehensive analysis to identify the thermophysical properties which have major influence in the drying profiles. Also, it is needed to validate the model for those materials in which the model is applied. In this work, the solution of Luikov model (as obtained by Liu et al., 1991) was used to obtain moisture profiles during the drying of brick at different temperatures. Also, an evaluation of the influence factors which affects to the obtained moisture profiles was carried out. It was found that one of the most important mechanisms which control the drying process is the diffusion of moisture. Also, the experimental validation using brick was performed at temperatures of 60 and 80°C; the theoretical and experimental results agree in the falling rate period, which is useful in the moisture content determination.

Numerical Analysis of Simultaneous Heat and Mass Transfer in Cork Lightweight Concretes Used in Building Envelopes

A numerical study was carried out in order to investigate the behaviour of building envelopes made of lightweight concretes. In this work, we are particularly interested to the building envelopes which are consist of cement paste with incorporation of cork aggregates in order to obtain small thermal conductivity and low-density materials. The mathematical formulation of coupled heat and mass transfer in wet porous materials has been made using Luikov's model, the system describing temperature and moisture transfer processes within building walls is solved numerically with the finite elements method. The obtained results illustrate the temporal evolutions of the temperature and the moisture content, and the distributions of the temperature and moisture content inside the wall for several periods of time. They allow us to specify the effect of the nature and dosage of fibre on the heat and mass transfer.

Finite-volume modelling of heat and mass transfer during convective drying of porous bodies – Non-conjugate and conjugate formulations involving the aerodynamic effects

In this study, a numerical procedure is outlined and representative results for heat and mass transfer during convective drying of porous bodies are presented. The Luikov model was implemented and applied both on individual samples of construction materials and agricultural products, as well as on a drying-chamber scale, with parallel flow of a hot air stream over rectangular slabs which represent the product to be dried. In the latter case the configuration is an experimental dryer in which the heat source is a solar air collector with evacuated tubes. A general approach was developed that allows a selection between modelling of phenomena either in the drying solid only, or considering an extended simulation domain encompassing, apart from the solid body, the flow of air as well. In the second case, the solution of the flow field is pursued along with a conjugate heat/mass transfer problem coupling the solid and fluid phenomena and in both cases phase change (evaporation) was taken into account. For the numerical simulation, the finite-volume method was used. The validation of the model was based on experimental and numerical results from the literature and results from simulations that were conducted in the pursuit of the energetic optimization of an experimental solar dryer of NCSR “Demokritos” are presented. In the latter case, the effect of the particular flow field features developing for a single and a double-plate configuration on the heat/mass transport and drying rates is demonstrated. Such a methodology could be used to analyze the transport phenomena in any type of convective dryer, including those utilizing solar energy as the heat source.

Experimental and theoretical investigation of non-isothermal transfer in hygroscopic building materials

In this paper a modified two-dimensional Luikov model for evaluating the non-isothermal moisture migration in porous building materials was proposed. The coupled heat and moisture transfer problem was modeled. Vapor content and temperature were chosen as the principal driving potentials. The coupled equations were solved by a numerical method, which consists of a finite difference technique with a fully implicit scheme in time. Two validation experiments were developed in this study. The evolution of transient moisture distributions in both one-dimensional and two-dimensional cases was measured. A comparison between experimental results and those obtained by the numerical model proves that they are fully consistent with each other. The modified model can be integrated into a whole building heat, air and moisture transfer model.

Thermal modeling of activated carbon based adsorptive natural gas storage system

A homogeneous, isotropic porous matrix of activated carbon inside a portable steel cylinder is considered as the adsorption bed for natural gas (NG) which is idealized as pure methane for the purpose of simulation. The heat and fluid flow inside the porous adsorption bed are modeled using a volume averaging technique and Darcy–Brinkman formulation. The effective thermal conductivity of the activated carbon–methane system is calculated as a function of uptake according to the Luikov model. Heat generation due to the exothermic process of adsorption is considered. The governing equations are solved using an implicit finite volume method for the given boundary conditions. Three different models of adsorption are considered, namely (i) a no-flow model, (ii) flow model with uniform adsorption and (iii) a flow model with local adsorption. For each of these models, transient temperature profiles in the adsorption bed during the charging process are obtained, and the corresponding mass adsorption potentials are calculated. Parametric studies are performed to investigate the effects of gas inlet temperature and rate of charging on the maximum bed temperature and the time required to fill the cylinder.

A study of the evaporation of water on a wet mobile plane surface in a hot draft

The authors study the case of the evaporation of water from a wet plane surface moving with a constant velocity in the same direction as a laminar hot draft. They numerically solve the unsteady transfer equations formulated with vorticity, stream function and constant physical properties, using a finite-difference scheme with an implicit alternating directions method. They determine the space–time distributions of temperatures, humidities and velocity components as well as the local values of their gradients according to the system parameters. In this study, the main results can be summarized as follows: The emission of vapor does not significantly disturb air flow. The velocity of the wall does not affect the hydrodynamic entrance length, that is correctly given by the Schlichting formula, but it increases the mean temperature in a section of the tunnel and the temperature and humidity wall gradients in proportion to the Lewis number. A privileged point exists in a section of the tunnel, at which the longitudinal velocity component is independent of the mobile plane velocity. Finally, the authors study the influence of inner drying with the help of the Luikov model.

Heat and Moisture Transfer and Hygrophysical Changes in Elastoplastic Hollow Cylinder-food During Drying

There are many dried foods of hollow cylinder-shapes in the market. Hygrostress cracks form in these foods during drying without a careful process control. The objective of the present work was to develop a simulation method for heat and moisture transfer in hollow cylinder-food coupled with hygrophysical changes. A modified Luikov's model was used for the development together with a virtual work minimization principle, critical tensile stress criterion for crack formation, and critical crack-tip-opening angle criterion for crack propagation. The developed, computerized simulation model was validated through drying experiments of samples made from a starch hydrate.

Hygrostress-multicrack formation and propagation in cylindrical viscoelastic food undergoing heat and moisture transfer processes

Several foods stress-crack during heat and moisture transfer processes without careful process control. Since published simulation studies on stress-cracking were scarce, the present study aimed to develop and validate a model for simulating heat and moisture transfer, hygrostress crack formation and propagation in cylindrical, viscoelastic food. For this, an improved Luikov's model for heat and moisture transfer was used together with the virtual work principle of a viscoelastically deforming body, a critical tensile stress criterion for stress crack formation and a crack-tip-opening-angle criterion for stress crack propagation.

Drying in capillary‐porous cylindrical media

AbstractAnalytical solutions are presented for temperature and moisture distributions in a cylindrical capillary‐porous body using Luikov's model and employing a solution technique based on the decoupling of the simultaneous heat and mass diffusion problems. The relative importance of the dimensionless parameters governing drying is presented and a comparison of temperature and moisture profiles for the cylinder and the slab is given.

AN ANALYSIS OF DRYING IN CAPILLARY-POROUS PLANAR MEDIA

ABSTRACT Analytical solutions are developed for temperature and moisture distributions in a capillary-porous medium by using Luikov's model and applying a solution methodology based on the decoupling of simultaneous heat and mass diffusion problems. A parametric survey is made to illustrate the relative importance of various dimensionless parameters affecting drying.

Experimental and Theoretical Study of Simultaneous Heat and Moisture Transfer in a Fibrous Insulant

The outcome of the work presented here consists in predicting the moisture and heat transfer phenomena likely to occur in glass fiber insulants subjected to varying environmental conditions. This prediction is obtained by a numerical resolution of the equations govern ing the phenomena (Luikov's model) and an experimental determination of the mass transfer coefficients appearing in these equations. Comparisons between experimental and theoretical results are presented for a particular configuration (closed system with stationary boundary conditions). These comparisons show a good reproduction of the measured moisture distributions but an over estimation of the heat transfer, for reasons developed in the text. Despite its present imperfections, the procedure presented here remains good and has been used for different configurations. Further developments require additional measurement of heat and mass transfer coefficients.