Mathematical modeling of thin layer solar drying of sultana grapes

Thin layer solar drying experiments were conducted for Sultana grapes (cv. Thompson seedless) grown in Antalya, Turkey. An indirect forced convection solar dryer consisting of a solar air heater and a drying cabinet was used in the experiments. Air heated by the solar air heater was forced through the product by an electric fan. In order to examine the effect of drying air temperature and velocity on a thin layer drying of Sultana grapes, twenty-two experiments were performed. Eight different thin layer mathematical drying models were compared according to their coefficient of determination to estimate solar drying curves. The effects of drying air temperature and velocity on the model constants and coefficients were predicted by the regression models. According to the results, a two-term drying model could satisfactorily describe the solar drying curve of Sultana grapes with a correlation coefficient (r) of 0.979. The constants and coefficients of this model could be explained by the effect of drying air temperature and velocity.     

Drying kinetics of pumpkinseeds

The drying of pumpkinseeds was investigated in the present study. Pumpkinseed has a thin liquid film on its surface and has rough‐surfaced peel. The most important parameter affecting its drying kinetics and increasing the drying rate is the temperature of the drying air. Drying was carried out with the surrounding air first at ambient temperature, and secondly an experimental rig was built to increase air temperature by using solar energy. A single layer of the pumpkinseed was dried in two different ways by free and forced convection. In these methods, pumpkinseeds were either placed in the tray exposed to the natural environment or placed in sieves on the experimental rig. The drying curves and variation of drying rate curves obtained were dependent on product moisture content. The drying air velocity can take moisture until saturation has a secondary effect on the moisture transfer. In the analysis, pumpkinseed was considered like a measurable rectangular prism. Fick's analytical solution, including effective diffusion coefficient, was applied to the present model. The results obtained from the present analytical model were compared with the experimental data and a good agreement was found. Copyright © 2000 John Wiley & Sons, Ltd.     

Mathematical modelling of thin layer drying process of long green pepper in solar dryer and under open sun

An experimental study was performed to determine the thin layer drying characteristics in a solar dryer with forced convection and under open sun with natural convection of long green pepper. An indirect forced convection solar dryer consisting of a solar air collector and drying cabinet was used in the experiments. Natural sun drying experiments were conducted for comparison at the same time. The constant rate period is absent from the drying curves. The drying process took place in the falling rate period. The drying data were fitted to 13 different mathematical models. Among the models, the logarithmic model for forced solar drying and the Midilli and Kucuk model for natural sun drying were found best to explain the thin layer drying behaviour of long green peppers. The performance of these models was investigated by comparing the coefficient of determination (R), reduced chi-square (χ²) and root mean square error (RMSE) between the observed and predicted moisture ratios.     

市政污泥干燥特性的实验研究和模拟分析

采用薄层干燥的方式对嘉兴市某污水处理厂的脱水市政污泥在不同厚度和温度下的干燥特性进行实验研究,并通过引入薄层干燥模型,对薄层市政污泥干燥过程进行模拟分析。结果表明:厚度越小或干燥温度越高,污泥干燥速率越快。当温度从70℃上升到130℃时,最大干燥速率从0.025 87 g·(g·min)~(-1)上升到0.081 58 g·(g·min)~(-1);从节能角度考虑,温度过高会导致有更多的能量消耗在污泥干质上,不利于能量的有效利用;Midilli模型很好地描述了市政污泥含水率的变化与时间的关系;应用Fick扩散定律推导出70～130℃下薄层市政污泥干燥的水分有效扩散系数变化范围为5.96×10~(-9)～3.24×10~(-8) m~2·s~(-1),并利用Arrhenius方程建立有效扩散系数与温度的关系,得到薄层市政污泥水分扩散的活化能为31.32 kJ·mol~(-1)。     

Modelling of heat and mass transfer in a tunnel dryer

This work presents a numerical model for heat and mass transfer of granular products in a fixed-bed tunnel dryer. The drying process is simulated under real operating conditions based on a thin layer model and experimental drying kinetics. A simplified heat and mass transfer numerical model is developed based on the governing equations and the drying rate of a thin layer bed of granular products.The obtained system of non-linear partial differential equations is numerically solved by a finite volume method. The turbulent airflow and granular bed convection coefficient as well as the effective conductivity are estimated using the turbulent airflow over flat-plate correlations. Simulations are compared with experimental data from drying of grapes in a thin layer model.In order to study the effects of the air inlet conditions on the relative moisture content and the drying time and therefore to optimise the tunnel dryer operation, the influences of different parameters essentially the air flow characteristics and the fixed-bed dryer length are examined. The numerical code allows establishing the drying front propagation for several operating conditions.     

Silk cocoon drying in forced convection type solar dryer

The thin layer silk cocoon drying was studied in a forced convection type solar dyer. The drying chamber was provided with several trays on which the cocoons loaded in thin layer. The hot air generated in the solar air heater was forced into drying chamber to avoid the direct exposure of sunlight and UV radiation on cocoons. The drying air temperature varied from 50 to 75 °C. The cocoon was dried from the initial moisture content of about 60–12% (wb). The drying data was fitted to thin layer drying models. Drying behaviour of the silk cocoon was best fitted with the Wang and Singh drying model. Good agreement was obtained between predicted and experimental values. Quality of the cocoons dried in the solar dryer was at par with the cocoons dried in the conventional electrical oven dryer in term of the silk yield and strength of the silk. Saving of electrical energy was about 0.75 kWh/kg cocoons dried. Economic analysis indicated that the NPV of the solar dryer was higher and more stable (against escalation rate of electricity) as compare to the same for electrical oven dryer. Due to simplicity in design and construction and significant saving of operational electrical energy, solar cocoon dryer seems to be a viable option.     

Modeling and experimental studies on a domestic solar dryer

A domestic solar dryer with transparent external surfaces was designed, built and tested. Thin-layer drying models that describe the drying phenomena in a unified way, regardless of the controlling mechanism; have been used to estimate the drying period for several products. Temperature of the drying medium is one of the factors that affect the drying rate constant of the exponential model. This fact introduces a problem when used to predict the drying rate under solar drying conditions since the temperature of the drying medium is rarely constant. This paper aims to propose a solar dryer with a uniform temperature profile that meets the requirements of the exponential model over a wide range of cases, thus, providing a simple and accurate design tool. The dryer is characterized by collecting the maximum possible solar energy by having a longer drying period, and allows the fixed dryer to approach with its performance the tracked one with all technical and economical advantages of the tracking system. The performance was tested under different operational conditions and the drying characteristics were experimentally investigated by conducting the experiments on two local herbs, Jew's mallow and mint leaves. The dryer was able to reduce moisture of the tested products to the recommended level (6% wb) in about a 12 h period. The reliability of the exponential model was evaluated by comparing the experimental with the predicted curves. A reasonable agreement was found for the different tests carried out for the entire drying period.     

A new termination control method for a clothes drying process in a clothes dryer

This paper reports on a study of developing a new termination control method for a clothes dryer, using both mathematical modeling and experimental approaches. Drying models in a constant-rate drying period (CRDP) and a falling-rate drying period (FRDP) were developed, based on well-established drying theory and using a “semi-empirical” approach. Drying experiments with regard to drying of cotton fabrics in different drying environments were carried out. A new termination control method using the equilibrium moisture content in ambient environment as a termination point has been investigated. The effectiveness of this new method has been evaluated by both experimental and modelling approaches. The results of the evaluation have demonstrated that the new method is workable and can help achieve energy saving.     

Solar drying of wastewater sludge: A review

Drying constitutes an important process for wastewater sludge management, as it can reduce the mass and the volume of the product and consequently the cost of storage, handling and transport. During constant operating conditions, the drying kinetic of the sludge has shown mainly: a constant drying rate, one or two falling rate periods and a final short period with variations along the process of the physical properties of the product with the appearance of shrinkage and cracks phenomena. Solar drying was benefit as using free solar energy can reduce the cost of the operation. On the other hand, it plays an important role for the pathogen reduction until Environmental protection Agency (EPA) recommendations. In some studied cases, the value of 1000 CFU g⁻¹ DS, which represents the EPA Class A pathogen requirement, for fecal coliform was attained. The general design of used solar dryers was constituted of: a greenhouse made with transparent material and a floor, where the product is speared in thick layers. Furthermore, fans and ventilations can be used in order to have homogeneous distribution of the air inside the greenhouse with replacement of humidified air with fresh one. Automatic or handle mix of the product was used once or for several times a day. In order to increase the performances of the drying system, other ways such as heating the floor using solar water heater, infrared lamps, using heat pumps or adding thermal energy storage systems were also tested. Covered solar drying has given better results than open solar drying. However, the origin of the wastewater sludge affects the obtained results. Alternatively, modeling drying systems was effectuated using heat and mass balances, applied for the air and the dried product. Solar drying of wastewater sludge has given satisfactory results.     

Mathematical modelling of the thin layer solar drying of banana, mango and cassava

The main objectives of this paper are firstly to investigate the behaviour of the thin layer drying of plantain banana, mango and cassava experimentally in a direct solar dryer and secondly to perform mathematical modelling by using thin layer drying models encountered in literature. The variation of the moisture content of the products studied and principal drying parameters are analysed. Seven statistical models, which are empirical or semi-empirical, are tested to validate the experimental data. A non-linear regression analysis using a statistical computer program is used to evaluate the constants of the models. The Henderson and Pabis drying model is found to be the most suitable for describing the solar drying curves of plantain banana, mango and cassava. The drying data of these products have been analysed to obtain the values of the effective diffusivity during the falling drying rate phase.     

热泵干燥菊花特性实验研究

搭建热泵干燥实验台,研究干燥室内不同热风温度、循环风速和排湿时间对菊花干燥特性的影响,并感官评定成品品质。结果表明:热风温度越高、循环风速越大或排湿时间越长,含水率越低,热风温度对含水率的影响最为明显;热风温度越高或循环风速越大,干燥初始相对湿度越大,干燥到一定时间相对湿度反而越小,转折时间点均约为10h,干燥全过程排湿时间越长,相对湿度越小;热风温度、循环风速对干燥速率与对相对湿度的影响呈现相同的规律,转折时间点分别为15和17h;热风温度越高、循环风速越大或排湿时间越长,干燥周期越短。任何一种参数过高均会影响成品品质,需综合调控这三个参数才能得到最佳干燥品质。     

Defining firewood quality: A comparison of quantitative and rapid appraisal techniques to evaluate firewood species from a southern African savanna

The study analyses the firewood characteristics of 16 tree species from the dry semi-deciduous woodlands dominant in south central Africa. The important firewood characteristics used by rural people in Malawi were determined by the pair-wise comparison of preferred indigenous species. This was compared with a fuel value index based on the properties of basic density, moisture and ash content. Nine species were compared over the two techniques and the ordering was broadly similar, with the denser species of lower moisture content being highly ranked in both cases. The main criteria used by villagers to rank firewoods were drying rate, duration of ember production and low moisture content or weight when dry. Drying rates converged after the first month to a daily rate of 0.1–0.2% of dry weight. The procedures used in the study were low technology but accurate enough to establish the important indigenous species to be managed for wood-fuel production. The study recommends that future firewood management planning should recognise the role of indigenous quality criteria in rural people's choice of firewoods.     

Liquid diffusion model for drying a stack of rough rice

Drying of a stack of rough rice was experimentally and theoretically investigated. Stacks of rough rice having different heights were dried with forced convection of warm air. A theoretical model was developed for predicting the bulk drying kinetics of a stack of rough rice using the analytical solution of liquid diffusion equation based on Fick's law. Effective diffusion coefficients were obtained minimizing the sum of squared differences between the theoretical results and experimental data obtained for various drying conditions. Drying air temperature is the most effective factor on the total rate of moisture removal from the stack. The bulk drying rate of a stack of rough rice was considerably reduced as compared to that of a single layer as the height of the stack increased. Agreement between the theoretical and experimental result is very good. Copyright © 2003 John Wiley & Sons, Ltd.     

A general analysis of moisture migration caused by temperature differences in an unsaturated porous medium

An analysis was performed which describes the moisture migration in a slab of an unsaturated porous material for the condition that the temperature of one surface is suddenly increased to a higher value whereas the temperature of the other surface is maintained constant. The two surfaces are assumed impermeable to mass flow. The thermodynamic and transport properties occurring in the equations describing the temperature and moisture transport are assumed constant. In this way, very general relations are obtained for the moisture field as it changes in time. Before dry-out, a dimensionless parameter describing the moisture field is a function of equivalent Luikov and Fourier numbers only. The dependence on the Luikov number becomes noticeable solely for the early periods and for small values of the Luikov number. After the onset of dry-out, the moisture ratio depends in addition on the thermal mass diffusion coefficient. The results of the analysis presented in the Figs 1–7, should describe the actual moisture migration with good accuracy where the variation of the properties is small in the range of the independent variables occurring in a specific situation and they should be useful as a first approximation for other situations as well.     

玫瑰花热风干燥实验及模型研究

鲜花干燥后易于保存,有多种用途。研究得出玫瑰花干燥模型以预测干燥过程,指导生产。基于热风温度、风速等做6组试验,得出玫瑰花干燥曲线,研究不同温度、风速对玫瑰花热风干燥特性的影响,并利用Origin等软件对玫瑰花热风干燥数据进行拟合,进行线性分析及可靠性分析,找出最适合描述其干燥过程的薄层干燥模型。结果表明,Logarithmic方程较适合用来描述玫瑰花干燥过程。     

Solar heat pump drying and water heating in the tropics

In this study, the performance of a solar assisted heat pump dryer and water heater has been investigated. A simulation program has been developed. The predicted results are compared with those obtained from experiments under the meteorological conditions of Singapore. A coefficient of performance (COP) value of 7.0 for a compressor speed of 1800 rpm was observed. Maximum collector efficiencies of 0.86 and 0.7 have been found for evaporator–collector and air collector, respectively. A value of the specific moisture extraction rate (SMER) of 0.65 has been obtained for a load of 20 kg and a compressor speed of 1200 rpm. Results suggest that the total drying time of the product decreases with the increase in drying potential. Drying potential is directly proportional to the air flow rate, drying air temperature and inversely proportional to the air relative humidity. Three important parameters that affect the system performance are solar radiation, compressor speed and the total load placed in the drying chamber. Both SMER and COP decrease with increase in compressor speed.     

Experimental testing of a new solar dryer

Drying of agricultural products is an energy-intensive operation. High prices and shortages in fossil fuels increase the emphasis on using solar energy as an alternative energy source, especially in developing countries. In this respect, a new solar dryer, which consisted of a solar air heater and a drying chamber, was developed and used for drying various fruits and vegetables, i.e., sultana grapes, green beans, sweet peppers and chilli peppers and was successfully tested. In order to make a comparison, the traditional sun-drying experiments were employed. Results showed that the solar dryer reduced the drying time significantly and prevented mass losses, and essentially provided better product quality.     

Experimental studies on hemi cylindrical walk-in type solar tunnel dryer for grape drying

A walk-in type hemi cylindrical solar tunnel dryer has been built with heat protective north wall at College of Dairy and Food Science Technology, Udaipur, India for drying agricultural & horticulture product on large scale. In this paper attempt has been made to evaluate the performance of developed dryer to dry the seedless grapes (mutant:Sonaka). The study show that chemically untreated grapes took seven days to dry at 16% (wb) moisture content. The temperature gradient inside the tunnel dryer is about 10–28 °C during the clear day, which is quite sufficient to dry agricultural commodities.     

Thin layer convective solar drying and mathematical modeling of prickly pear peel (Opuntia ficus indica)

This paper presents the thin layer convective solar drying and mathematical modeling of prickly pear peel. For these purposes, an indirect forced convection solar dryer consisting of a solar air collector, an auxiliary heater, a circulation fan and a drying cabinet is used for drying experiments. Moreover, the prickly pear peel is sufficiently dried in the ranges of 32 to 36 °C of ambient air temperature, 50 to 60 °C of drying air temperature, 23 to 34% of relative humidity, 0.0277 to 0.0833 m³/s of drying air flow rate and 200 to 950 W/m² of daily solar radiation. The experimental drying curves show only a falling drying rate period. The main factor in controlling the drying rate was found to be the drying air temperature. The drying rate equation is determined empirically from the characteristic drying curve.Also, the experimental drying curves obtained were fitted to a number of mathematical models. The Midilli–Kucuk drying model was found to satisfactorily describe the solar drying curves of prickly pear peel with a correlation coefficient (r) of 0.9998 and chi-square (χ²) of 4.6572 10⁻⁵.     

Experimental investigation of forced convection and desiccant integrated solar dryer

An indirect forced convection and desiccant integrated solar dryer is designed and fabricated to investigate its performance under the hot and humid climatic conditions of Chennai, India. The system consists of a flat plate solar air collector, drying chamber and a desiccant unit. The desiccant unit is designed to hold 75 kg of CaCl₂-based solid desiccant consisting of 60% bentonite, 10% calcium chloride, 20% vermiculite and 10% cement. Drying experiments have been performed for green peas at different air flow rate. The equilibrium moisture content M_e is reached in 14 h at an air flow rate of 0.03 kg/m² s. The system pickup efficiency, specific moisture extraction rate, dimensionless mass loss, mass shrinkage ratio and drying rate are discussed in this paper.