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Biosystems Engineering (2004) 89 (1), 69–77doi:10.1016/j.biosystemseng.2004.05.001 Available online at www.sciencedirect.com PH } Postharvest Technology Modelling and Simulation of Heat Transfer in Stored Rough Rice with Aeration A. Iguaz 1 ; C. Arroqui 1 ; A. Esnoz 2 ; P. V ! ıırseda 1 1 Area de Tecnolog ! ııa de Alimentos, Universidad P ! uublica de Navarra, Escuela Technica Superior de Ingenieros Agronomos,Pamplona 31006, Spain; e-mail of corresponding author:
[email protected] 2 Area de Tecnolog ! ııa de Alimentos, Universidad Polit ! eecnica de Cartagena, Cartagena, Spain; e-mail:
[email protected] (Received 8 September 2003; received in revised form 6 May 2004; published online 26 June 2004) A mathematical model based on dynamic heat and mass balances was developed to simulate grain and airtemperature in a bin storage during rough rice forced aeration periods. The mathematical model includesseveral experimentally obtained expressions to determine thermo-physical grain properties. Model validationwas carried out by comparing predicted with experimentally measured grain temperatures in different pointsof a pilot silo, ventilated with cool air at constant air temperature and humidity. Predicted and measured datawere in close agreement. The model can be used to predict the development of grain temperature and the timeneeded to cool stored grain under different ventilation conditions. # 2004 Silsoe Research Institute. All rights reservedPublished by Elsevier Ltd 1. Introduction Self-reheating is the main reason for grain deteriora-tion during storage. As living substances, grain kernelscontinue respiring after the harvest and carbohydratesin the grain are degraded into CO 2 , heat and water. As aresult of the raised temperatures, microorganism andinsect growth is enhanced. One method to reduce thedeterioration of the stored grain is to cool it (Sinha,1971) using an aeration system. Cooling the grain until asafe temperature is reached, can inhibit insect andmould activity and minimise the use of chemicaltreatments. Grain in storage is also subject to moisturemigration caused by differences in grain temperature.An aeration system can also prevent deterioration byreducing the temperature gradients throughout the grainbulk which may cause moisture migration and pocketsof mouldy grain (Metzger & Muir, 1983). The aerationsystems used for the grain storage are operated inresponse to seasonal weather variations and usuallyaeration periods are intercalated with extended periodswhen ventilation is not required.Rice is a cereal which is especially difficult to processbecause most of the production is used for humanconsumption and grain breakage can affect seriouslymarket value. Fissures in rice kernels cause these kernelsto break. Rough rice can fissure before and duringharvesting, during drying, storage or milling (Abud-Archila et al. , 2000). As for the drying process, theproportion of fissured kernels increases with thetemperature and the evaporating capacity of the air(Aguerre et al. , 1986; Bonazzi et al. , 1997). Industrially,rough rice is dried carefully in various steps to minimisegrain breakage. Cool-air ventilation during rough ricestorage can contribute to a slightly decreased grainmoisture content and so a gentler drying is possible if cooling is performed immediately after drying.Accurate prediction of grain moisture and tempera-ture during storage are needed in order to develop andevaluate aeration strategies. Mathematical models basedupon grain thermo-physical properties are very useful topredict grain conditions in any point of a storage binand constitute an alternative to temperature andmoisture content recording. Sutherland et al. (1971)developed a model for heat and moisture transfer inairflow through wheat assuming that thermal andsorption equilibrium was reached in every location.The same assumption was used by Thompson (1972) ina model for simulating the storage of high moistureshelled corn using continuous aeration. As equilibriumis assumed, the model is limited to use at lowtemperature and low airflow conditions. In additionno validation of the model is performed. Based on thefinite difference method, Sharma and Muir (1973) ARTICLE IN PRESS 1537-5110/$30.00 69 # 2004 Silsoe Research Institute. All rights reservedPublished by Elsevier Ltd developed a model for the simulation of heat and masstransfer during ventilation of wheat and rapeseed. Themodel adequately predicted the performance of alaboratory grain cooler. A model for wheat storagewith and without aeration was developed by Metzgerand Muir (1983). The model simulated conductive heattransfer in radial and vertical directions and forcedconvective heat and moisture transfer in verticaldirection. Chang et al. (1993, 1994) developed a rigorousmodel for predicting the temperature and moisturecontent of wheat during storage with aeration. Themodel was based on the finite difference method andincluded terms that represent forced convective heat andmass transfer. Most of this models were developed forwheat or maize. However, relatively few models havebeen developed for rough rice. Kajunoso et al. (1995)simulated moisture changes in rough rice storageduring aeration. No experimental data of rough ricethermo-physical properties were used in this model.Instead, mass transfer coefficient was determined byfitting experimental moisture content measurements of aeration tests to simulated results. Thermal propertieswere calculated using literature expressions. Consideringthe variability of the thermo-physical properties of different varieties of rough rice (Iguaz et al . , 2003b),it would be interesting to include experimentallyobtained expressions to improve the accuracy of thestorage model.This work is part of a more general study that aims tomodel the whole process of rough rice including drying,cooling and storage. The authors previously developed amodel for the storage of rough rice during periods of noaeration (Iguaz et al ., 2004), and when used togetherwith the model developed here, it becomes possible tosimulate the whole storage process of rough rice.The objectives of this study are:(1) to develop a simulation model for predicting graintemperature in a rough rice storage bin withaeration, based on heat and moisture dynamicbalances;(2) to verify the validity of the expressions experimen-tally developed for the thermo-physical propertiesused in the model; and(3) to validate the simulation model with experimentaldata. ARTICLE IN PRESS Notation a specific surface contact, m 2 m 3 A area, m 2 c specific heat capacity, kJ 1 kg 8 C 1 D diameter of grain bin, m D AA average absolute difference E s standard error G mass flow rate, kg [DM]sm 2 k constant rate, s 1 h sup superficial convective heat transfer coefficient,kJm 2 8 C 1 h vap latent heat of vaporisation of moisture in thegrain, kJkg 1 h vol volumetric convective heat transfer coefficient,kJm 3 8 C 1 h w latent heat of vaporisation of pure water,kJkg 1 H height of grain bin, m M mass in the control volume, kg [DM] n number of the control volume n s sample size N number of the control volume at the top of thegrain column P atm atmospheric pressure, Pa P va vapour pressure, Pa P vs saturation vapour pressure, Pa Q conv convective heat, kJ Re reynolds number H R air relative humidity, % R drying rate, kgkg 1 [DM] s 1 t time, s T temperature, 8 C T * predicted temperature, 8 C V volume, m 3 v velocity, ms 1 W grain moisture content, kg [water]kg 1 [DM] Y absolute humidity of the air, kg [water]kg 1 [dry air] z height of the control volume, m e porosity r bulk density, kgm 3 Subscriptsa air as dry air E equilibrium g grain in inlet s dry grain v vapour w water wg wet grain A. IGUAZ ET AL. 70 2. Model development To develop the model, the cylindrical grain bin of height H in m and diameter D in m was longitudinallydivided into n control volumes of area A in m 2 andheight D z given by H/n as it is shown in Fig. 1 .The following assumptions were adopted in order tosimplify the model:(1) grain and air contained in each control volume arenot in equilibrium so there is heat and mass transferbetween them;(2) conduction heat transfer by grain-to-grain contactis negligible;(3) heat and mass transfer in the radial direction isnegligible compared to heat and mass transfer in theaxial direction;(4) heat and mass transfer between grain and air ineach control volume is adiabatic;(5) the effect of hysteresis in the sorption process isneglected;(6) no change in the grain dry matter or heatgeneration take place;(7) the air mass flow in the axial direction remainsconstant through the whole bin; and(8) the intergranular air volume and pressure in eachcontrol volume do not vary with time.According to these assumptions the dynamic massand heat balances for air and grain were established ineach control volume ( Fig. 2 ). The following equationswere obtained.2.1. Moisture balance in the grain The mass balance for the moisture of the graincontained in each control volume on a dry matter (DM)basis is given by: @ M g W @ t ¼ R w M g ð 1 Þ where: M g is the grain mass in the control volume inkg[DM]; W is grain moisture content in kgkg 1 [DM]; t is time in s; and R w is the drying rate in kgkg 1 [DM]s 1 .Developing Eqn (1), the following expression isobtained: M g @ W @ t þ W @ M g @ t ¼ R w M g ð 2 Þ As @ M g @ t ¼ 0, Eqn (2) can be written as @ W @ t ¼ R w ð 3 Þ 2.2. Moisture balance in the air The mass balance for the moisture of the aircontained in each control volume is given by @ M a Y ð Þ @ t ¼ G a Y in G a Y þ R w M g ð 4 Þ where: M a the air mass in the control volume in kg [dryair]; Y in is the absolute humidity of the air entering the ARTICLE IN PRESS Fig. 1. Schematic diagram of the model; n is the number of control volume; N is the number of the control volume at the topof the grain column; H, height of cylindrical grain bin; D z, heightof control volume ∆ z z + ∆ z z M a , Y , T a M g , W , T g G a , Y in , T a , in G a , Y, T a Inlet air Outlet air Fig. 2. Control volume of the grain storage bin; z is the height inthe grain column in m; M g , W and T g are the mass in kg[DM],the moisture content in kkg 1 [DM] and the temperature in 8 C respectively of the grain in the control volume; M a is the air massin the control volume in kg [dry air], Y and Y in are the absolutehumidity of the air in the control volume and entering the control volume respectively in kgkg 1 [dry air]; G a is the air mass flowrate entering the control volume in kg[dry air] 1 s; T a and T a, in are the temperature of the air in the control volume, and enteringthe control volume, respectively, in 8 C MODELLING AND SIMULATION OF HEAT TRANSFER IN RICE 71 volume control in kgkg 1 [dry air]; Y is the absolutehumidity of the air in the control volume in kgkg 1 [dryair]; and G a is the air mass flow rate in kg[dry air]s 1 .Developing Eqn (4), the following expression isobtained: M a @ Y @ t þ Y @ M a @ t ¼ G a Y in Y ð Þþ R w M g ð 5 Þ As @ M a @ t ¼ 0, Eqn (5) can be written as: @ Y @ t ¼ 1 M a G a Y in Y ð Þþ R w M g ð 6 Þ Considering that: M a ¼ A D z er a ð 7 Þ G a ¼ v a A r a ð 8 Þ M g ¼ A D z er g ð 9 Þ where: A is the area of the cylindrical grain bin in m 2 , z is the height of the control volume in m, e is the porosity, v a is air velocity in ms 1 , and r a is the density of humidair in kgm 3 and r g is bulk density of wet grain inkgm 3 , Eqn (6) can be rearranged and the followingexpression is obtained for the air humidity variation: @ Y @ t ¼ v a e Y Y in ð Þ D z þ r g r a e R w ð 10 Þ 2.3. Heat balance in the grain The equation for the enthalpy balance in the graincontained in each control volume is given by @ M g T g c g @ t ¼ h sup aV T a T g R w M g h vap þ c v T a T g ð 11 Þ where: T g is the grain temperature in 8 C; c g is the specificheat capacity of the grain in kJkg 1 8 C 1 ; h sup is thesuperficial convective heat transfer coefficient inkJm 2 8 C 1 ; a is the specific surface on contact betweengrain and air in m 2 m 3 ; V is the volume in m 3 ; T a is thetemperature of air in 8 C; h vap is the latent heat of vaporisation of moisture in the grain in kJkg 1 ; and c v isthe specific heat of vapour in kJkg 1 8 C 1 .Developing Eqn (11), the following expression isobtained: M g T g @ c g @ t þ M g c g @ T g @ t þ c g T g @ M g @ t ¼ h sup aA D zT a T g h vap þ c v T a T g R w M g ð 12 Þ Considering that @ M g @ t ¼ 0 and expressing specific heatof grain c g as ( c s + Wc wg ) where c s and c wg are thespecific heat capacity of the dry grain and water in thegrain respectively in kJ, grain temperature variation canbe calculated as @ T g @ t ¼ h sup A D z T a T g c s r g þ c wg W r g h vap þ c v T a T g c s þ c wg W R w T g c wg c s þ c wg W @ W @ t ð 13 Þ 2.4. Heat balance in the air The equation for the enthalpy balance in the aircontained in each control volume is given by @ M a T a c a ð Þ @ t ¼ G a T a ; in c a ; in G a T a c a h a aA D z T a T g þ c v T a R w M g ð 14 Þ where: T a,in is the temperature of the air entering thecontrol volume in 8 C and c a,in and c a are the specific heatcapacity of the air entering and contained in the controlvolume respectively in kJkg 1 8 C 1 .Developing Eqn (14), the following expression isobtained: M a T a @ c a @ t þ M a c a @ T a @ t þ c a T a @ M a @ t ¼ G a T a ; in c a ; in T a c a h a aA D z T a T g þ c v T a R w A D z r g ð 15 Þ Considering that @ M a @ t ¼ 0 and expressing specific heatof air c a as ( c as +Y c v ), where: c as is the specific heatcapacity of the dry air in kJkg 1 8 C 1 air temperaturevariation can be calculated as @ T a @ t ¼ 1 c a v a e D z T a ; in c a ; in T a c a h a a er a T a T g þ r g er a T a R w T a c v @ Y @ t ð 16 Þ 2.5. Heat transfer equations Several studies on forced convective heat transfer inaerated grain bins can be found in the literature.Exchanged heat between air and grain has been calculatedusing global or superficial heat transfer coefficients. Boyce(1965) proposed calculating convective heat transfer usinga global volumetric heat transfer coefficient, Q conv in kJs: Q conv ¼ h vol V T a T g ð 17 Þ where h vol is the volumetric convective heat transfercoefficient in kJm 3 8 C 1 and it was empiricallyobtained and calculated by the following expression: h vol ¼ 8 568 10 5 r a V e T a þ 273 16 P atm 0 6011 ð 18 Þ where: P atm is the atmospheric pressure in Pa. ARTICLE IN PRESS A. IGUAZ ET AL. 72
