MODELLING THE INFRARED RADIATIVE HEATING OF AGRICULTURAL CROPS

ABSTRACT

Simultaneous heat and mass transfer equations were developed to simulate the infrared radiative heating of agricultural crops. The equations assume that moisture diffuses to the outer boundaries of the material in liquid form and evaporation occurs at the surface of the kernel. Energy for moisture evaporation is supplied by the infrared radiant energy. The equations were validated with experimental data on surface temperature and average moisture content of barley kernels. Average deviations of predicted surface kernel temperature and average kernel moisture from experimental data were 3.9°C and 0.6%(w.b.), respectively. These comparisons were performed using kernels having initial moisture contents of 12.2%, 17.C% and 23.17%.

Sensitivity analysis of process parameters showed that infrared burner temperature, distance of infrared burner from the grain bed, grain initial moisture content and grain heating time significantly affected kernel temperature. Burner temperature and burner height had no significant effect on grain final moisture content.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

Moisture Adsorption Isotherms of Watermelon Seed and Kernels

The moisture adsorption isotherms of watermelon seeds and kernels from Citrullus lanatus Cv Mateera and Citrullus vulgaris Cv Sugar baby were obtained using standard static method with saturated salt solutions over a range of water activities from 0.113 to 0.92 at 20-60°C. The adsorption capacity of seeds decreased with the increase in temperature at constant water activity. Sorption models were used to explain the adsorption behavior involving water activity and moisture content (Type I) and also temperature (Type II). Oswin's models gave best fit among Type I with coefficient of determination of 0.953-0.995, standard error of 0.031-0.0571, mean relative error of 0.071-0.152, and scattered residual plots. Modified Oswin was the best fit model among Type II for the seeds and kernels of both the cultivars with coefficient of determination of 0.997-0.999, standard error of 0.151-0.255, mean relative error of 0.018-0.244, and scattered residual plots. The net isoelectric heat of adsorption, estimated from Clausius-Clapeyron decreased from about 27.0 to 0.5 kJ/mol in kernels and 18.0 to 0.5 kJ/mol in seeds of both the cultivars as the moisture content increased from 5 to 25% (dry basis).     

Moisture Adsorption Isotherms of Watermelon Seed and Kernels

The moisture adsorption isotherms of watermelon seeds and kernels from Citrullus lanatus Cv Mateera and Citrullus vulgaris Cv Sugar baby were obtained using standard static method with saturated salt solutions over a range of water activities from 0.113 to 0.92 at 20–60°C. The adsorption capacity of seeds decreased with the increase in temperature at constant water activity. Sorption models were used to explain the adsorption behavior involving water activity and moisture content (Type I) and also temperature (Type II). Oswin's models gave best fit among Type I with coefficient of determination of 0.953–0.995, standard error of 0.031–0.0571, mean relative error of 0.071–0.152, and scattered residual plots. Modified Oswin was the best fit model among Type II for the seeds and kernels of both the cultivars with coefficient of determination of 0.997–0.999, standard error of 0.151–0.255, mean relative error of 0.018–0.244, and scattered residual plots. The net isoelectric heat of adsorption, estimated from Clausius-Clapeyron decreased from about 27.0 to 0.5 kJ/mol in kernels and 18.0 to 0.5 kJ/mol in seeds of both the cultivars as the moisture content increased from 5 to 25% (dry basis).     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

ABSTRACT

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

MODELLING THE INFRARED RADIATIVE HEATING OF AGRICULTURAL CROPS

Simultaneous heat and mass transfer equations were developed to simulate the infrared radiative heating of agricultural crops. The equations assume that moisture diffuses to the outer boundaries of the material in liquid form and evaporation occurs at the surface of the kernel. Energy for moisture evaporation is supplied by the infrared radiant energy. The equations were validated with experimental data on surface temperature and average moisture content of barley kernels. Average deviations of predicted surface kernel temperature and average kernel moisture from experimental data were 3.9°C and 0.6%(w.b.), respectively. These comparisons were performed using kernels having initial moisture contents of 12.2%, 17.C% and 23.17%.

Sensitivity analysis of process parameters showed that infrared burner temperature, distance of infrared burner from the grain bed, grain initial moisture content and grain heating time significantly affected kernel temperature. Burner temperature and burner height had no significant effect on grain final moisture content.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

THE DRYING OF SOYBEAN SEEDS IN COUNTERCURRENT AND CONCURRENT MOVING BED DRYERS

ABSTRACT

The aim of this work was to analyze the simultaneous heat and mass transfer between air and soybean seeds in countercurrent and concurrent moving bed dryers by simulation. The technique chosen was based on modeling from mass and energy conservation equations for the fluid and particulate phases. The equilibrium, heat transfer and mass transfer equations were taken from specific studies. The equation representing drying kinetics was obtained by means of a thin-layer study, whereas the equilibrium equations was chosen from rival model discrimination, based on nonlinearity measures. Hence, the model parameters were defined by the respectives studies. The profiles for temperature and humidity of the fluid and the temperature and moisture of the seeds were obtained by numerical solution of the model. This model consisted of ordinary differential equations and the solution was obtained by a specific code. The simulated results indicated a significant.     

Modelling the Bulk Cooling of Alfalfa Pellets

ABSTRACT

Cooling of alfalfa pellets after being made is one o f the unit operations in the pelleting of alfalfa. Using the thermal properties and drying diffusion coeficient together with other properties reported in refereed journals. a combined heat and mass transfer model was developed for the cooling of alfalfa pellets in deep beds. The model utilized the distributed heat and mass transfer equations to describe the temperature and moisture of the pellets. The distributed model interacts with the cooling air through a convective boundary condition for the temperature and a time–varying exponential surface condition for the moisture. Coupling o f the heat and mass transfer processes was carried out at the surface of the pellet using evaporative surface condition. The model was validated with field experimental data from a double–deck crossflow cooler. The simulated pellet and air temperatures were within 5⁰C of the collected field data while predicted moisture from the model was within 0.3% o f the experimental data.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

Moisture Changes in Grain During Aeration Under Warm Humid Conditions

ABSTRACT

Two mathematical models (an equilibrium model and a combined model) were evaluated, which described the moisture and heat transfer in low temperature drying and aeration. The predicted moisture contents from both models were compared with the experimental data. Comparisons indicated that the combined model was more accurate than the equilibrium model. The combined model is based on the idea that the partial pressure difference is the driving force in moisture transfer. A series of simulation was performed using the combined model to evaluate the effect of air temperature, air relative humidity, and the temperature difference between grain and air on the moisture changes in stored rough rice. The simulation results proved the concept of using the partial pressure difference to describe the moisture transfer in stored grain. A minimum of 5.6°C in     

Modeling Superheated Steam Vacuum Drying of Wood

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^-1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

DETERMINATION OF MASS DIFFUSIVITY COEFFICIENT OF SWEET POTATO

Abstract

Using Luikov's heat and mass transfer equations and a finite element formulation, the drying process of an anisotropic biological product (sweet potato) was investigated. The model was used to determine the coefficients of heat and mass transfer, the mass diffusivity normal and parallel to the fibers of sweet potato samples. These parameters were estimated by minimizing the deviation of experimental data and numerical predictions.

Laboratory experiments with three different configurations were conducted to measure the temperature and moisture content of sweet potato samples during drying. Numerical simulation showed good agreement with the measured values.     

Moisture adsorption isotherms and thermodynamics properties of sucuk (Turkish dry-fermented sausage)

Moisture adsorption isotherms of sucuk were determined using the isopiestic method at 10 °C, 20 °C and 30 °C and within the range of 0.2-0.9 water activity. The isotherms of sucuk exhibited Type II behavior according to BET classification. The adsorption data were analyzed using mathematical equations of Halsey, Caurie, Peleg, Smith, Oswin, Henderson, Modified-BET, GAB, Ferro-Fontan and Harkins-Jura. The best fit of experimental data was obtained with Peleg equation in the range of temperatures and water activities investigated. Thermodynamic properties such as differential enthalpy and entropy, enthalpy-entropy compensation, spreading pressure, net integral enthalpy and entropy were determined from moisture adsorption isotherm data of sucuk. The net isosteric heat of sorption and differential entropy decreased with increasing moisture contents in an exponential function. The spreading pressure increased with increasing water activity, and decreased with increasing temperature. The net integral enthalpy decreased with increased moisture content. The integral entropy increased with moisture content, but it was negative in value. The enthalpy-entropy compensation theory was applied to water adsorption of sucuk.     

MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

ABSTRACT

A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.     

SIMULATION OF THE HEAT AND MOISTURE TRANSFER PROCESS DURING DRYING IN DEEP GRAIN BEDS

Grain drying is a simultaneous heat and moisture transfer problem. The modelling of such a problem is of significance in understanding and controlling the drying process. In the present study, a mathematical model for coupled heat and moisture transfer problem is presented. The model consists of four partial differential equations for mass balance, heat balance, heat transfer and drying rate. A simple finite difference method is used to solve the equations. The method shows good flexibility in choosing time and space steps which enable the simulation of long term grain drying/cooling processes. A deep barley bed is used as an example of grain beds in the current simulation. The results are verified against experimental data taken from literature. The analysis of the effects of operating conditions on the temperature and moisture content within the bed is also carried out     

Stochastic Modelling of Grain Moisture Content.in Near-Ambient Drying

ABSTRACT

A stochastic analytical model was developed to describe the mass transfer in a thin layer of grain ventilated with unheated air. As an excitation to the drying system, a stochastic analytical model of variations in ambient air temperature and relative humidity during the drying period, based on a sine function. was used. Mean. carrelation function, variance and the standard deviation were determined for main moisture content treated as a random process. The stochastic models of variations in air temperature and relative humidity were fined to the observed historical data. The standard deviation and m ean of grain moisture content calculated from the developed analytical model were compared to changes in mean and the standard deviation obtained from the numerical deterministic model of mass transfer and hourly weather data from 17 year.     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

ABSTRACT

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

a rview of: UNIFIED ANALYSIS AND SOLUTIONS OF HEAT AND MASS DIFFUSION

ABSTRACT

The objective of this study is the formulation of a finite element model that could be used to analyze the stress crack formation in a viscoelastic sphere resulting from temperature and moisture gradients during the drying process. Numerical solutions to the simultaneous moisture and heat diffusion equations describing moisture removal and heat intake process for the sphere are obtained. The distribution and gradients of temperature and moisture developed inside the sphere during drying are established. The calculated temperature and moisture gradients are used in a finite element analysis of the thermo-hydro viscoelastic boundary value problem to simulate the stresses in the body.

The model is used to solve a sample problem of drying a soybean kernel. The simulated drying curve for the soybean model is obtained and compared favorably with the experimental results reported in the literature. Tangential stress, as a criteria for failure, is shown to change from compressive to tensile stress as it approaches the surface. It reaches its peak value at the surface in one hour and then decays slowly. The effect of different drying conditions is studied and the results are discussed.