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Mathematical Modeling of Thin Layer Drying Characteristics of Dika (Irvingia Gabonensis) Nuts and Kernels

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Mathematical Modeling of Thin Layer Drying Characteristics of Dika (Irvingia Gabonensis) Nuts and Kernels HOSTED BY Available online at www.sciencedirect.com Nigerian Food Journal ] (]]]]) ]]]–]]] www.elsevier.com/locate/nifoj Mathematical modeling of thin layer drying characteristics of dika (Irvingia gabonensis) nuts and kernels O.A. Aregbesolaa, B.S Ogunsinaa,n, A.E. Sofolahana, N.N. Chimeb aDepartment of Agricultural and Environmental Engineering, Obafemi Awolowo University, Ile Ife, Nigeria bDepartment of Agricultural and Bioresource Engineering, University of Nigeria, Nsukka, Nigeria Abstract The thin layer drying characteristics of dika kernels and nuts were investigated at four drying temperatures of 50, 60, 70 and 80 1C and the data was fitted to drying models. Non-linear regression analysis was used to determine model parameters, while coefficient of determination (R2) and standard error of estimate (SEE) formed the basis for determining the model of best fit. The Modified Henderson–Pabis drying model gave the best fit for the dika kernels while the two term model was best for the dika nuts. Effective moisture diffusivity ranged from 2.84 Â 10À10 m2/s to À À À 5.06 Â 10 11 m2/s for the kernels and from 1.22 Â 10 10 m2/s to 2.03 Â 10 10 m2/s for the nuts. The activation energies of dika kernels and nuts were 16.747 kJ/mol and 37.019 kJ/mol respectively. & 2015 Association of Vice-Chancellors of Nigerian Universitie. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Moisture content; Temperature; Moisture ratio; Activation energy; Moisture diffusivity 1. Introduction et al., 1996). As trade in dika kernels is on the increase, product quality standard and value addition are becoming The domestication of lesser known indigenous plants for prime criteria for setting price for farmers and traders. There is subsistence agriculture is playing a major role in enhancing therefore the need to understand unit operations involved in rural livelihoods, mitigating deforestation and environmental dika fruit processing. degradation in sub-Sahara Africa (Leakey et al., 2005). The The need to preserve more food during peak harvest period, dika tree (Irvingia gabonensis) has high utility value; the reduce post-harvest losses and equalize availability in-between leaves, the fruits, the bark, the hardwood and the roots have seasons make artificial drying inevitable in bulk handling several medicinal, food and industrial applications (Ndoye of modern food products (Doymaz et al., 2006). Artificial et al., 1997; Ayuk et al., 1999). Apart from the common use of dryers are rapid and provide uniform, hygienic dried product the kernels as a soup thickener in West Africa, the kernel oil and reduce losses (Karathanos and Belessiotis, 1997; Goyal and meal are potential base materials for pharmaceutical et al., 2007). binders, confectionery, edible fat, soap and cosmetics Thin layer drying studies provide the basis for understanding the (Ogunsina et al., 2012). Dika fruit processing involves unique drying characteristics of any particular food material. The fermentation of the fresh fruits in heaped piles for few days results of such studies have been widely used to simulate dryers and washing the rotten pulp to obtain the nuts. Afterwards, the under deep-bed drying conditions and for quantifying parameters nuts are sun-dried and cracked to obtain the kernels (Ladipo for the design of specialized drying equipment. In thin layer drying, the moisture content of a bio-material exposed to a stream of n drying air of known relative humidity, velocity and temperature Corresponding author. is monitored over a period of time. A number of mathematical E-mail address: [email protected] (B. Ogunsina). Peer review under responsibility of Association of Vice-Chancellors of models have been developed to simulate moisture movement and Nigerian Universities. mass transfer during the drying of many agricultural products. http://dx.doi.org/10.1016/j.nifoj.2015.04.012 0189-7241/& 2015 Association of Vice-Chancellors of Nigerian Universitie. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article as: Aregbesola, O.A., et al., Mathematical modeling of thin layer drying characteristics of dika (Irvingia gabonensis) nuts and kernels. Nigerian Food Journal (2015), http://dx.doi.org/10.1016/j.nifoj.2015.04.012 2 O.A. Aregbesola et al. / Nigerian Food Journal ] (]]]]) ]]]–]]] Table 1 Thin-layer drying models used for the study. Name Model Reference Newton MR¼exp(Àkt) Ayensu (1997) Page MR ¼ expðÞÀktn Diamante and Munro (1993) Modified page MR ¼ expðÞðÞÀkt n White et al. (1981) Henderson and Pabis MR ¼ a expðÞÀkt Akpinar et al. (2003) Logarithmic MR ¼ a expðÞþÀkt c Yagcioglu et al. (1999) Two term MR ¼ a expðk0tÞþ b expðk1tÞ Togrul and Pehlivan (2004) Diffusion MR ¼ a expðÞþÀkt ðÞ1Àa expðÞÀkbt Yaldiz and Erdekin (2001) Modified Henderson and Pabis MR ¼ a expðÞþÀkt b expðÞþÀgt c expðÞÀht Karathanos and Belessiotis (1999) 1.2 0.8 0.7 1 50 C 0.6 0.8 60 C 0.5 50 C 70 C 60 C 0.4 0.6 80 C 70 C 0.3 80 C 0.4 Moisture Ratio Moisture Content 0.2 0.2 0.1 0 0 0 1000 1500 2000 2500 0 500 0 500 1000 1500 2000 2500 -0.1 Time(min) Time(min) -0.2 0.8 1.2 0.7 1 50 C 0.6 60 C 70 C 0.8 50 C 0.5 80 C 60 C 0.6 70 C 0.4 80 C 0.4 0.3 Moisture Ratio Moisture Content 0.2 0.2 0.1 0 0 200 400 600 800 1000 1200 1400 1600 1800 Time(min) 0 0 500 1000 1500 2000 Fig. 2. Moisture ratio versus time. (a) Nut and (b) kernel. -0.1 Time(min) Fig. 1. Moisture content versus time. (a) Nut and (b) kernel. Although drying is a major unit operation in dika fruits These have been found very useful in understanding drying processing from nuts to kernels, the literature regarding the kinetics and optimization of drying conditions (Vega et al., 2007; drying characteristics of dika nuts and kernels are rarely Doymaz et al., 2006; Mwithiga and Ochieng-Olwal, 2005). available. Therefore, the objective of this work is to investigate Please cite this article as: Aregbesola, O.A., et al., Mathematical modeling of thin layer drying characteristics of dika (Irvingia gabonensis) nuts and kernels. Nigerian Food Journal (2015), http://dx.doi.org/10.1016/j.nifoj.2015.04.012 O.A. Aregbesola et al. / Nigerian Food Journal ] (]]]]) ]]]–]]] 3 the thin layer drying characteristics of dika nuts and kernels, fit content of sample (% db), t the drying time (min), and k is the the drying data into eight thin layer models and determine their drying constant (minÀ1). effective diffusivities and activation energies. Other thin layer drying models which are commonly used for agricultural products include Page, Diffusion, Henderson and Pabis, Modified Henderson–Pabis, modified Page, Lewis, 2. Theoretical background for modeling of drying data Midilli and Kucuk, Logarithmic, Two Term, Two Term exponential, Thompson, Wang and Singh amongst others The simplest model for describing thin layer drying char- (Özdemir and Devres, 1999; Kashaninejad et al., 2007; acteristics of agricultural products is in the form of the Hassan-Beygi et al., 2009). exponential model (Eq. (1)). It assumes negligible resistance to moisture movement to the surface of the material and that the resistance to moisture movement is concentrated on the 3. Effective diffusivity and activation energy surface of the material and is referred to as ‘simple lumped’ model (which is analogous to Newton's law of cooling) The effective diffusivity of a product can be estimated by (Temple and Boxtel, 1999) Fick's second diffusion law for slab geometry (Taheri- Garavand et al., 2011; Adabi et al., 2013) as follows: M ÀMe MR ¼ ¼ expðÞkt ð1Þ Mi ÀMe Mi ÀMe MR ¼ Mo ÀMe where MR is the moisture ratio, M the moisture content at any 1 8 X 1 ð2nþ1Þπ2D t time ‘t’ (% db), M the equilibrium moisture content (emc) at ¼ exp eff ð2Þ e π2 2 2 À ðÞ2nþ1 4H the conditions of the drying air (% db), Mi the initial moisture n 1 Table 2 Coefficients of thin layer drying models and goodness of fit for dika nuts. S/N Model Temp (1C) Parameters R2 SEE 1 Newton 50 K¼0.0051 0.9913 0.0316 60 K¼0.0053 0.9734 0.0520 70 K¼0.0066 0.9860 0.0385 80 K¼0.0061 0.9858 0.0384 2 Page 50 K¼0.0100, n¼0.8677 0.9954 0.0234 60 K¼0.0192, n¼0.7475 0.9965 0.0193 70 K¼0.0152, n¼0.8286 0.9937 0.0262 80 K¼0.0152, n¼0.8162 0.9973 0.0169 3 Modified page 50 K¼0.0050, n¼0.8677 0.9954 0.0234 60 K¼0.0050, n¼0.7475 0.9965 0.0193 70 K¼0.0064, n¼0.8286 0.9937 0.0262 80 K¼0.0059, n¼0.8162 0.9973 0.0169 4 Henderson and Pabis 50 K¼0.0050, a¼0.9799 0.9917 0.0312 60 K¼0.0045, a¼0.9145 0.9837 0.0415 70 K¼0.0063, a¼0.9676 0.9872 0.0375 80 K¼0.0055, a¼0.9414 0.9907 0.0317 5 Logarithmic 50 K¼0.0054, a¼0.9616, c¼0.0296 0.9941 0.0270 60 K¼0.0049, a¼0.8986, c¼0.0267 0.9854 0.0400 70 K¼0.0070, a¼0.9470, c¼0.0368 0.9911 0.0319 80 K¼0.0058, a¼0.9302, c¼0.0178 0.9914 0.0312 6 Two term 50 K0 ¼0.0095, k1 ¼0.0025, a¼0.5981, b¼0.4278 0.9989 0.0118 60 K0 ¼0.0216, k1 ¼0.0031, a¼0.3465, b¼0.6705 0.9987 0.0120 70 K0 ¼0.0126, k1 ¼0.0028, a¼0.6221, b¼0.4047 0.9988 0.0121 80 K0 ¼0.0238, k1 ¼0.0042, a¼0.2780, b¼0.7377 0.9988 0.0118 7 Diffusion 50 K¼0.0083, a¼0.6206, b¼0.2801 0.9984 0.0141 60 K¼0.0198, a¼0.3381, b¼0.1535 0.9986 0.0125 70 K¼0.0113, a¼0.6288, b¼0.2382 0.9982 0.0143 80 K¼0.0218, a¼0.2687, b¼0.1917 0.9987 0.0123 8 Modified Henderson and Pabisa 50 k¼0.0025, g¼0.0025, h¼0.0095, a¼0.2139, b¼0.2139, c¼0.5981 0.9989 0.0123 60 k¼0.0031, g¼0.0031, h¼0.0216, a¼0.3352, b¼0.3352, c¼0.3465 0.9987 0.0125 70 k¼0.0028, g¼0.0028, h¼0.0126, a¼0.2024, b¼0.2024, c¼0.6221 0.9988 0.0127 80 k¼0.0042, g¼0.0042, h¼0.0238, a¼0.3689, b¼0.3689, c¼0.2780 0.9988 0.0124 aH–P: Henderson–Pabis.
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