Mathematical Modeling of Sun and Solar Drying Kinetics of Fermented Cocoa Beans

In this study, thin layer drying experiments were conducted to compute drying characteristics of fermented cocoa beans in open sun and indirect natural convection solar dryer. The drying experiments were conducted at the same time for comparison. Three different thin layers drying of the fermented beans were examined under field conditions for Akure, Nigeria. The drying process took place only in the falling rate period. The drying curves obtained from the experimental data were fitted to thirteen (13) different thin layer mathematical models. All the models were compared according to three evaluation parameters. These include coefficient of determination (R), Root mean square error (RMSE) and Chi-square (X).The results showed that increasing drying air temperature resulted to shorter drying times. The Vermal et al. model was found to be the most suitable for describing the drying curve of the convective indirect solar drying process of cocoa beans with R = 0.9562, X=0.0069 and RMSE=0.0067; while, the Midilli and Kucuk model, best described the drying curve of fermented cocoa beans under open sun with R = 0.9866, X=0.0024 and RMSE=0.0023. Keywords— Thin-layer drying, moisture content, modelling,cut test, pH, Cocoa beans.


INTRODUCTION
Drying is one of the oldest methods of food preservation (Doymaz, 2007). Agricultural and other products have been dried by sun and wind in the open air for thousands of years. The purpose is either to preserve them for later use, as in the case with food; or as an integral part of the production process as with tobacco and cocoa beans. It is necessary that the traditional techniques be replaced with industrial drying methods. (Ertekin and Yaldiz, 2004). Mathematical modelling and simulation of drying curves under different conditions is important to obtain an overall improvement of the quality of the final product. Simulation models of the drying process are used for developing new designs, improving existing drying systems, predicting the airflow over the product and for the control of the process. (Aghbashlo, et al., 2008). Thin layer drying equations are used to estimate drying kineticsfor several products and also to generalize drying curves. A critically important aspect of drying technology is mathematical modelling of the drying process. Modelling of drying process and kinetics is a tool for process control and necessary to choose suitable method of drying for specific product. Modelling is also essential for engineers to choose the most suitable climatic conditions in order to design appropriate drying equipment for perishable crops. The aim of this work is to study the drying process and select the most suitable model (in terms of fitting ability) to describe the thin-layer drying of cocoa beans. Although much information has been reported about modelling of thin layer drying (Togrul&Pehlivan, 2002) there is no information about modelling of thin layer drying of cocoa beans in Nigeria.

Drying experiments
In this study, fresh healthy cocoa pods (Amenlonado variety) were procured from Oda village, Akure South Local Government, Akure Ondo State. The drying experiments were carried out using mobile solar dryer in the Department of Agricultural Engineering, Federal University of Technology, Akure. Plate 1 shows the schematic diagram of the solar dryer used for the experimental work which consists of a solar collector and a drying chamber. The samples were weighed using a digital balance with 0.01g sensitivity every 60 minutes throughout the drying process. Three different thin samples of wet fermented cocoa beans were spread evenlyinto the solar dryer and in the open sun drier for the dehydration test. The experiment was replicated thrice and the mean value was used. Thermal drying method was used in the determination of moisture content of the samples.100g of sample were placed in oven at 105± 3 0 C and allowed to dry to a constant weight for 24 hours (Lagha-Benamrouche, S. and Madani, K., 2013). The moisture content (MC) was calculated by expressing the weight loss upon drying a fraction of the initial weight of sample used. The moisture content of the seeds was determined by gravimetric method which determines the mass loss from the sample by drying to constant weight (ASABE STANDARDS, 1993 and AOAC, 2000).
(%) = 3 − 0 is weight of empty crucible 1 is weight of crucible plus sample before drying 3 is weight of crucible plus sample after drying DM is dry matter and MCdb is the cocoa beans moisture content (g water/g dry base, d.b).

Plate.1: Mobile Solar dryer
2.2 Mathematical modelling of drying process Many researchers have worked on many thin layer models in the past and this study evaluate thirteen (13) of such models as shown in Table 1. The moisture ratio, MR is given as follows: Where MR is the dimensionless moisture ratio or unaccomplished moisture content, M, Me, Mo are moisture content (kg water/kg, dry matter) respectively.
The values of Me are relatively small compared to those of M or Mo hence error involved in its simplification as negligible. (Aghbashlo,Kianmerhrk&Samini-Akhljahani, 2008), hence moisture ratio is calculated = (4) For drying model selection, drying data were fitted into thirteen well known thin layer drying models which are given in Table 1.  The goodness of fit was determined using three parameters; coefficient of determination (R 2 ), reduced chi-square (x 2 ) and the root mean square error (RMSE) using equations (4) -(6) as in Sacilik and Elicin (2008).The statistical analyses were carried out using SPSS 13.0 software and non-regression technique.
Where MRexp,iis ith experimentally observed moisture ratio, MRpre,iis ith predicted moisture ratio, N is the number of observation, n is the number of model constants.

Drying Kinetics of Fermented cocoa beans
From the experimental data, the moisture content (%wb) of fermented cocoa beans for the solar dryer and open sun drying at any time are represented in Figures 1-3. It was clearly evident from these curves that the drying rate of fermented cocoa beans in the solar dryer was faster than that of the open sun drying. The moisture content of the fermented cocoa beans reached 6.5% dry basis in 32hours of drying in the solar dryer, whereas the final moisture of the same product dried by open sun drying was only 9.87% dry basis thus moisture content was not enough for safe storage. When it was dried under open sun drying, the duration of dry was about two (2) sunshine days to bring it to the same moisture level. This can be explained that the main factor influencing drying rate was the drying air temperature. Compared to open sun drying, solar dryer can generate higher air temperature and affected the significant increasing of evaporation rate of water and then result in lower final moisture content of drying samples. These results indicated that solar dryer was effective than open sun drying.

Mathematical modelling
The moisture content data at different experimental modes were converted to the more useful moisture ratio expression, and curve fitting computations with drying time were performed with the thirteen (13) drying models presented by previous workers (Table 1).The results of the statistical analyses undertaken on these models for the natural convention solar drying and the natural sun drying are given in Table 2