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Experimental investigations and modeling of vacuum oven process using several semi-empirical models and a fuzzy model of cocoa beans

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Abstract

An experimental study combined with a mathematical modeling of vacuum drying of cocoa beans was carried out to enhance the drying kinetics without compromising the quality of dried products. Experiments were conducted to compare the effects of variation of temperature and pressure on the drying process. The temperature was varied between 40 and 60 °C, while the pressure between 735 and 245 mmHg. The experimental study investigated and analyzed the effects of various process parameters on drying kinetics and quality (in terms of color and pH value). Results demonstrated that the cocoa beans dried at 50 °C temperature and 735 mmHg pressure had the highest drying kinetics, lowest acidity, and best color among all the temperature and pressure values. Compared to convective drying conducted at 60 °C temperature and atmospheric pressure (760 mmHg), vacuum oven drying consistently showed better drying performance with a higher quality of dried products. Modeling for vacuum drying kinetics of cocoa beans was performed with semi-theoretical drying kinetic and fuzzy models to verify the experimental results. The graphical representations of the results demonstrated a good fit between the fuzzy model and the experimental data compared with semi-theoretical drying kinetic models. Finally, a suitable model was proposed for optimum drying conditions compared with the fuzzy and drying kinetic models that could play an important role in designing future advanced dryers.

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Abbreviations

Deff:

Effective moisture diffusivity, m2/s

g:

Constant in the two term and Verma et al. models, s−1

g:

Constant in the C.L. Hii model, s−1

k:

Constant in the Newton, Henderson and Pabis, logarithmic, two term, and Verma et al. models, s−1

k:

Constant in the page and C.L. Hii models, s−n

K:

Thermal diffusivity, m2/s

L, a, b:

Reference color (lightness, redness and yellowness, respectively),

L*, a*, b*:

Target color (lightness, redness and yellowness, respectively),

mt:

Mass of sample at time t, g

mds:

Mass of dry solid, g

Me:

Equilibrium moisture content (dry basis), kg/kg

M0:

Initial moisture content (dry basis), kg/kg

Mt:

Moisture content at time t (dry basis), kg/kg

MR:

Moisture ratio,

pH:

Acidity/basicity,

P:

Pressure, mm Hg

R2 :

Coefficient of determination, −

T:

Temperature, °C

ΔE:

Change of color,

COG:

Center of gravity

FL:

Fuzzy logic

MF:

Membership function

MSE:

Mean square error

RMSE:

Root mean square error

SC:

Subtractive clustering

TSK:

Takagi-Sugeno-Kang

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Acknowledgments

The authors would like to thank the University of Sharjah for the financial support to conduct this study (Project no: 1602040652-P). Besides, the authors have the deepest gratitude to Assistant Professor Andrew Joseph Power at the University of Sharjah for his kind proofreading providing beneficial comments that significantly helped to improve the overall quality of this paper. The authors would also like to thank Eng. Salah Issa Elsayed for his technical supports provided during this study.

Funding

This research was funded by The University of Sharjah, 1602040652-P”.

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Authors and Affiliations

  1. Department of Sustainable and Renewable Energy Engineering, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    S. M. Atiqure Rahman & Mamdouh El Haj Assad

  2. College of Engineering at Wadi Addawaser, Prince Sattam Bin Abdulaziz University, Al-Kharj, Kingdom of Saudi Arabia

    Ahmed M. Nassef & Hegazy Rezk

  3. Computers and Automatic Control Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt

    Ahmed M. Nassef

  4. Electrical Engineering Department, Faculty of Engineering, Minia University, Minya, Egypt

    Hegazy Rezk

  5. Department of Biomedical Engineering, Military Institute of Science and Technology (MIST), Mirpur Cantonment, Dhaka, 1206, Bangladesh

    Md Enamul Hoque

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  1. S. M. Atiqure Rahman
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Correspondence to S. M. Atiqure Rahman.

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Rahman, S.M.A., Nassef, A.M., Rezk, H. et al. Experimental investigations and modeling of vacuum oven process using several semi-empirical models and a fuzzy model of cocoa beans. Heat Mass Transfer 57, 175–188 (2021). https://doi.org/10.1007/s00231-020-02943-5

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