CROSS-EFFECT OF HEAT AND MASS TRANSFER OF LU1KOV EQUATION: MEASUREMENT AND ANALYSIS

Abstract

This paper mainly focuses on cross-effect of heat and mass transfer of capillary porous media which A.B.Luikov set up on irreversible thermodynamics principle. On the basis of perfecting the equations of heat and mass transfer, the heat and mass transfer parameters are determined during drying processes, and thermal gradient coefficient δ and moisture gradient coefficient ξ are obtained which show the cross-effect of heat and mass transfer. Thus the fundamentals are provided for quantitative analysis of cross-effect of heat and mass transfer. The convective drying mathematical model under the first unsteady boundary condition is therefore proposed. By the application of Henry transform, the theoretical solution of unsteady drying process is given and its validity is verified     

MEASUREMENT OF COEFFICIENTS FOB SIMULTANEOUS HEAT AND MASS TRANSFER IN FOOD PRODUCTS

Two experimental devices were designed and built to determine four coefficients K_T K_M D_M D (or δ_T = D_T / D_M occurring in simultaneous heat and mass transfer equations, where,K _T and D_M are thermal conductivity and moisture diffcusivity respectively, D_T ( or δ _T is temperature gradient Induced moisture migration coefficient and K_M is moisture gradient Induced heat transfer coefficient. Three food materials, i.e. potato, bread dough and bread, were tested. From this study, it was found that the value of 5 was higher for low density food materials, such as bread, than for high density materials, such as potato. The coefficient & measures moisture migration contribution due to temperature gradient within the material. The average values of δ _T for potato, bread dough and bread were 0.0014, 0.0059 and 0.0127 per °C, respectively. The contribution of temperature gradient to the overall moisture migration is negligible In high density materials. However, this contribution may be important in the moisture migratlon analysls for low density materials. The moisture gradient induced heat transfer coefficient % as found to be negligible for the materials tested in this study     

ESTIMATION OF THE EFFECT OF PRODUCT SHRINKAGE ON THE DRYING TIMES,HEAT INPUT AND CONDENSER LOAD OF THE PRIMARY AND SECONDARY DRYING STAGES OF THE LYOPHILIZATION PROCESS IN VIALS

ABSTRACT

The effects of cake shrinkage on the drying times and energy requirements of the primary and secondary drying stages of the freeze drying process involving the drying of a material in a vial, are estimated through the construction and solution of an extended unsteady state and spatially multidimensional model that accounts for the changes introduced by cake shrinkage on the internal and external mass and heat transfer mechanisms of the freeze drying     

ESTIMATION OF FUNCTIONS IN DRYING EQUATIONS

In drying problem, particularly for drying foodstuff, modelling is very difficult. Many physical effects have to be taken into account for mass transfer ; then mass transfer coefficient varies

In different models unknown functions must be estimated. It is particularly the case in simple models of drying using average values of water content, where the mass transfer varies versus mean water content in falling rate period. On the other hand in the “diffusion model” we have the same problem concerning the diffusion coefficient which must be also estimated

The method we propose in this paper for these two models : simple and “diffusion model” of drying consists from measurements of temperature and water content of the product to search a numerical approach of the unknown function. This method uses optimization techniques on computer and least squares criterion between model values and experimental data

Results are given for the “diffusion model” applied to shelled corn drying to find the diffusion coefficient and for a simple 11107 del applied to plum drying to find the mass transfer coefficient.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

A review of: “Developments in Drying,Vol. 2” Edited by A.S. Mujumdar and S. Suvachittanont Kasetsart University Press,Bangkok, Thailand 2000

Although pulse combustion devices exhibit a high thermal efficiency and low pollutant emission when used in a drying process, a broad application of these dryers has been limited because of a lack of understanding of the fundamental controlling heat and mass transfer. This paper reports the results of an experimental investigation of heat transfer between unsteady airflow and a brass sphere under various oscillating frequencies. In order to generate an unsteady flow, we constructed a gas-fired, water-cooled pulse burner. The burner is of a Helmholtz type and its operating frequency can be adjusted by changing the tailpipe length. The heat transfer coefficient between unsteady air outflow and brass was determined by the lumped capacity method. The effect of airflow oscillating frequency on heat transfer coefficient was investigated and their correlation was established. Refractory clay particles in the oscillating airflow were dried and the effect of the frequency on the drying process was predicted using the heat transfer coefficients obtained.     

干燥过程中脉动气流与物料间的热量传递特性

脉动燃烧装置用于干燥过程时具有热效率高和污染物排放量少等优点，但由于目前对其热质传递的特性缺乏深入的了解，限制了此类干燥器的广泛应用。为了深入了解脉动燃烧干燥过程的传热特性，我们建立了一台Hehnholtz型脉动燃烧器，所用燃料为液化气，采用水冷方式。通过脉动气流与黄铜球之间的对流传热实验，应用集总热容法确定了在不同频率脉动气流中黄铜与气流间的对流传热系数，探究了脉动频率对脉动燃烧干燥过程气流与物料间对流传热系数的影响，并建立了相应的准数关联式。应用建立的关联式，对耐火土颗粒在脉动燃烧气流中的干燥过程进行了预测，并与实验值作了比较，结果表明预测值与实验值吻合较好。     

EXPERIMENTAL INVESTIGATION AND MODELING OF THE INFLUENCE OF INDIRECT HEATING ON FLUIDIZED BED DRYING

Experimental results of fluidized bed drying with additional energy input by indirect heating are presented. A clear influence of moisture on wall-to-bed heat transfer coefficients is observed for particle diameters of 250 μm and 50 μm. Two different reasons for this influence may be distinguished in both, the measurements and theoretical considerations: 1 The change of bed and particle properties and 2 the increase of the local wall-to-particle heat transfer.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

A theoretical and experimental study of simultaneous heat and mass transport resistances in a shallow fluidized bed dryer of mate leaves

A theoretical and a semi-theoretical modeling approach were applied in order to predict drying kinetics of mate leaves in a shallow fluidized bed dryer. The first procedure involves an internal diffusive mechanism of mass transport (Fick's second law), while the second one assumes that the resistance for water transport is represented by an apparent convective term analogous to the Newton's law of cooling (Lewis model). Since heat and mass transfer occurs at the same time, an energy equation assuming negligible internal conduction was written to the solid phase and it was coupled to the mass balance representing the mechanism of mass transfer. Model parameters were simultaneously tuned on experimental transient moisture content and on temperature profiles of mate leaves, which were obtained by varying the equivalent particle diameter approximately from 5.2 × 10⁻³ to 1.1 × 10⁻² m at the drying temperatures of 52 and 101 °C. A regression analysis based on the uncertainties in the calculated parameters as well as on the identification of possible tendencies in residuals corroborates the assumption of negligible internal heat transfer conduction and evidences that the semi-theoretical model of Lewis describes better than the purely diffusive model the transport of water over the whole period of drying. The estimated Biot number (0 < Bi < 100) reveals that both internal and external mass transport resistances play an important role for mate leaves drying and demonstrates that the single parameter of the Lewis model represents an effective coefficient that takes into accounts both diffusion and convection. A significant effect of the equivalent particle diameter and temperature on the drying constant and on the external heat transfer coefficient is also evidenced.     

A NEW CLASS OF SIMILARITY SOLUTIONS OF AN UNSTEADY ELECTRICALLY CONDUCTING FREE-FORCED CONVECTIVE FLOW IN A VERTICAL POROUS SURFACE WITH DUFOUR AND SORET EFFECTS

The 2-D unsteady magnetohydrodynamic free-forced convective boundary layer flow of a viscous incompressible fluid is studied numerically taking into account heat and mass transfer. The fluid is subjected to uniform heat and mass fluxes embedded in a porous medium by the presence of coupled Dufour and Soret effects. A new class of similarity equations has been obtained by introducing a time-dependent length scale and a corresponding similarity variable. The resulting equations are then integrated numerically using the Nachtsheim-Swigert shooting iteration technique along with the sixth-order Runge-Kutta integration scheme. By developing locally similar solutions of the fluid flow, the behavior of the velocity, temperature, and concentration fields as well as the rate of heat transfer, wall temperature gradient, rate of mass transfer, and skin friction coefficient have been investigated. The effects of Grashof number (Gr), modified Grashof number (Gm), combined effects of the porous and magnetic parameter (S), suction/injection parameter Fw, Brinkman number (Br), Soret number (Sr), and Dufour number (D_f) have been observed on the flow field and discussed.     

BOUND MOISTURE REMOVAL: HEAT AND MASS TRANSFER IN CONTACT DRYING

ABSTRACT

Coupled heat and mass transfer in short-term contact of the moist material and the heating surface (the physical model of drying with agitation) is examined. Technological characteristics of the drying process: heating rate and drying rate, heat transfer coefficient, etc. have been determined based on solutions of the diffusion and diffusion-filtration heat and mass transfer. The usage of non-field method of determination of mass and heat fluxes on the phase interface allows calculation of the drying equipment efficiency without preliminary determination of the fields of required quantities. The results may be used for estimation of the influence of drying conditions and material properties on the moisture removal process.     

MODELLING OF HEAT TRANSFER IN HOT PRESSING AND IMPULSE DRYING OF PAPER

A modelling and simulation study regarding the heat transfer in hot pressing as well as in impulse drying of paper has been performed. The study is focused on modelling the heat transfer from a hot surface to a moist paper sheet and the heat transfer inside the paper sheet. The model is based on solving the equation for unsteady heat transfer by conduction. The model was compared with experimental data from a heated laboratory platen press and data from the experimental paper machine EuroFEX at the Swedish Pulp and Paper Research Institute (STFI) in Stockholm. The results in this study showed that a rather simple heat transfer model could be used to simulate the heat transfer in cases in which the temperature was moderate and the applied pressure did not exceed 0.5 MPa. It was also concluded that a paper could be regarded as a semi-infinite body for basis weights above 110 g/m², considering the assumptions used in the model. It was also shown that a laboratory press could simulate heat transfer in hot pressing and impulse drying with a high degree of accuracy.     

COMBINED MICROWAVE AND CONVECTIVE DRYING OF A POROUS MATERIAL

A model is formulated to describe the drying of a slab of porous material in a combined microwave and convective environment. The model describes the evolution of temperature, pressure, moisture and power distributions that occur during the drying process. The microwave internal heat source is calculated from electromagnetic theory with varying dielectric properties. The inclusion of pressure in the model allows the physical phenomena of “water pumping”, often observed in microwave drying systems, to be accounted for. The influence of sample size; on the drying kinetics 1s examined and found to be an important parameter during the drying process. In particular the effect of resonance on the moisture and temperature profiles and the need for careful consideration of surface mass transfer coefficients are investigated. Simulation results are presented for the combined microwave and convective drying of a homogeneous, isotropic porous material.     

BOUND MOISTURE REMOVAL: HEAT AND MASS TRANSFER IN CONTACT DRYING

Coupled heat and mass transfer in short-term contact of the moist material and the heating surface (the physical model of drying with agitation) is examined. Technological characteristics of the drying process: heating rate and drying rate, heat transfer coefficient, etc. have been determined based on solutions of the diffusion and diffusion-filtration heat and mass transfer. The usage of non-field method of determination of mass and heat fluxes on the phase interface allows calculation of the drying equipment efficiency without preliminary determination of the fields of required quantities. The results may be used for estimation of the influence of drying conditions and material properties on the moisture removal process.     

Multiscale and multilayer structural modeling and simulation on drying of grain packing porous media

ABSTRACT

Aiming at the problem of multilayer physical structure for the skeleton of porous media, a multiscale and multilayer structural model of heat and mass transfer processes for drying of grain packing porous media was established by applying the pore network method and multiscale theory. An experimental study on rice drying was conducted in order to validate this model. The simulation and experimental results indicated that the established model could explain the mechanical properties of rice drying well. The rate of heat transfer was faster than the rate of mass transfer and there was a higher moisture gradient inside the rice grain. The diffusion coefficient of rice embryo played an important role in the drying process, and whose effect on drying was larger than the diffusion coefficient of rice hull and chaff. The moisture was imprisoned effectively inside the rice when the diffusion coefficient of rice embryo was very small.     

MODELLING OF HEAT TRANSFER IN HOT PRESSING AND IMPULSE DRYING OF PAPER

A modelling and simulation study regarding the heat transfer in hot pressing as well as in impulse drying of paper has been performed. The study is focused on modelling the heat transfer from a hot surface to a moist paper sheet and the heat transfer inside the paper sheet. The model is based on solving the equation for unsteady heat transfer by conduction. The model was compared with experimental data from a heated laboratory platen press and data from the experimental paper machine EuroFEX at the Swedish Pulp and Paper Research Institute (STFI) in Stockholm. The results in this study showed that a rather simple heat transfer model could be used to simulate the heat transfer in cases in which the temperature was moderate and the applied pressure did not exceed 0.5 MPa. It was also concluded that a paper could be regarded as a semi-infinite body for basis weights above 110 g/m², considering the assumptions used in the model. It was also shown that a laboratory press could simulate heat transfer in hot pressing and impulse drying with a high degree of accuracy.     

EFFECT OF THE VARIABILITY OF HEAT AND MASS TRANSFER COEFFICIENTS ON CONVECTIVE AND CONVECTIVE-RADIATIVE DRYING OF POROUS MEDIA

A numerical investigation was conducted to study two-dimensional heat and mass transfer during convective drying of a clay brick. The established numerical code has allowed us to determine the effect of heat and mass transfer coefficients variability on state variables and on the drying kinetic.     

MODEL SELECTI0N IN AIR DRYING OF FOODS

ABSTRACT

The purpose of this investigation is to compare various drying models with respect to (a) the accuracy in calculating the material moisture content and temperature versus time and (b) the computation time required.

Mechanistic as well as phenomenological heat and mass transfer models are considered. The mechanistic models are formulated by considering different combinations of mechanisms between (1) moisture diffusion in the solid towards its external surface (2) vaporization and convective transfer of the vapor into the air stream (3) convective heat transfer from the air to the solid's surface (4) conductive heat transfer within the solid mass. The phenomenological model incorporates the drying constant while the mechanistic models incorporate the mass diffusivity, the mass transfer coefficient in the air boundary layer, the thermal conductivity, and the heat transfer coefficient in the air boundary layer.

The proposed methodology is applied to experimental data of four vegetables, namely, potato, onion, carrot, and green pepper. The experiments involve three thickness levels, five temperatures, three water activities, and three air velocities. The results obtained concern (a) the standard deviations between experimental and calculated values of material moisture content andtemperature, which, in combination with the computation time, are the necessary information for model selection for a special application, and (b) the model parameter estimates which are necessary to use the selected model.     

DRYING OF CARROTS. I. DRYING MODELS.

Three models of different complexity are proposed to describe the falling rate period of the carrot drying process with shrinkage. A moving or fixed boundary problem as well as a constant or local moisture and temperature dependent effective diffusivity are considered. The moving boundary problem is solved by an explicit finite difference method. Heat transfer coefficient and effective diffusivity identification were carried out. The results of the heat transfer coefficient show a good agreement with other sources. Using experimental data and the models. describing the heat and mass transfer three different expressions for the effective diffusivity are established. Two of them are only temperature dependent considering or not particle shrinkage. The third one takes into account temperature and local moisture as well as shrinkage.

Drying of foods is a complicated process involving simultaneous coupled heat and mass transfer phenomena which occur inside the material being dried (Chiang and Petersen, 1987). Several models are found in the literature, representing mass and energy transfer which take place during food drying (King, 1968; Sokhansanj and Gustafson, 1980). Usually, approximate solutions are obtained with these