## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Modeling of drying rate of non hygroscopic products: Application to the pozzolana drying

**ABSTRACT**

Polynomial model adopted for the moisture content influence to the drying rate of non hygroscopic products like the pozzolana presented some limits. This model was not universal and has diverged whether moisture content different to the appropriate experiment values has been used. Thus, a new exponential model based on the inverse of moisture content and respecting to the imposed boundaries conditions has been proposed. Model parameters were determined using the least square approximation method of Newton-Marquart. The predicted temporal variations of moisture content were provided from the Runge-Kutta fourth order integration scheme computed on the new model of drying rate. Moreover, two-way ANOVA method was performed on data analysis, at the parameters statistical significance and in residual analysis for the model fit quality. Model validations were done by comparisons among theoretical and experimental values and between predicted and polynomial models. Comparisons showed a good agreement with highest R2 and lowest reduced chi-square, MBE, RMSE and MAPE.

**KEYWORDS**

PAPER SUBMITTED: 2016-02-23

PAPER REVISED: 2016-06-14

PAPER ACCEPTED: 2016-07-25

PUBLISHED ONLINE: 2016-08-07

- Ramamonjisoa, B. O., Development of interactive software for the dimensionality and the energizing diagnosis of driers at partially solar heating (in french language), Ph. D. Thesis, University of Antananarivo, Madagascar, 1997
- Idlimam, A., et al. Experimental study for peel of grenadine drying kinetics(in french language), Review of the Renewable Energy, CER'07, Oujda, 7 (2007), 237, pp.237-240
- Khedhari, J., et al., Experimental determination of food product commodities drying rate (in french language), General Review of COMPLES, International Symposium Act, Perpignan, France, 1994
- Alidina, M. E., Feasibility technico-economic of a hybrid drier achieved from one metallic hangar. Application to the paddy drying, Thesis, University of Perpignan, France, 1991
- Sarr, J., et al., Experimental study of fish drying curves, Journal of Sciences, 3 (2003), 1, pp.1-9
- Schuk, P., et al., Drying of lacto-serums and derivative: role of the lactose and the water dynamics, Review of Milk -INRA EDP Sciences, 84 (2004), Mar., pp. 243-268
- Tagne, M. S., et al., Modeling and numerical simulation on the drying of Ayous woods and ebony. Experimental Validation, Review of the Renewable Energy, 13 (2010), 1, pp.13-24
- Darvishi, H., et al., Mathematical Modeling of Thin-Layer Drying of Shrimp, Global Journal of Science Frontier Research Mathematics & Decision Sciences, 12 (2012), 3, pp.83-89
- Andriazafimahazo, L.F.G., et. al., Modeling of corn drying rate (in french language), Africa Science, 5 (2009), 2, pp.173 - 183
- Rakotondramiarana, H. T., Theoretical study of thermal drying and digestion anaerobe of sludge in the purification stations. Adjustment of laboratory device pilots for linked experimental characterization to the drying and the sludge methanization (in french language), Thesis, University of Antananarivo, Madagascar, 2004
- Lahmari, N., et al., Drying method influence on dried tomatoes quality (Zahra variety), Review of the Renewable Energy, 15 (2012), 2, pp.285-295
- Henderson, S.M., A basic concept of equilibrium moisture, Agric. Eng, 1 (1952), 33, pp.29-32
- LAMBERT, P., et al., The pozzolana in technical road (in french language), Bull. Link Labo. P and Ch, Clermont -Ferrand, France, 64 (1973), 1277, pp.63-75
- Benkaddour, M., et al., Durability of the mortars to basis of natural and artificial pozzolana, Review Nature and Technology, 1 (2009), 1, pp.63-73
- Thikare, N.B. et al., Experimental Study of Fly Ash Mortar, International Journal of Modern Trends in Engineering and Research (I.J.M.T.E.R.), 2 (2015), 2, pp.94 - 98
- Bottini, M., Modeling of thermo-hydration for drying and concrete shrinkage (in french language), in: Modelings for the Civil Genius and the Geomaterials, (Ed. Code Aster) ), Reference manual Fascicle r7.01, Revision : 10084, EDF R&D, France, 2012, pp.1-15
- Ramamonjisoa, B. O., Contribution to the driers development of heating partially solar to La RĂ©union : Device adjustement for the drying rate measurement in thin layer and dimensionality abacuses calculation code (in french language), Thesis, La RĂ©union University, France, 1993
- Da Silva, E. C., Methods and numerical analysis (in french language), School of Engineer- Institute Polytechnic of Grenoble, Grenoble, 2007, pp.1-99
- Makowski, D., Evaluation of model parameters : general principles (in french language), Proceedings, INRA ACTA ICTA formation, U.M.R.A., La Rochelle, France, 2005, pp.1-52
- Billong, N. et al., Physicochemical Characteristics of Some Cameroonian Pozzolana for Use in Sustainable Cement Like Materials, Materials Sciences and Applications, 4 (2013), Oct., pp.14-21
- Shcherbakov, M. V., et al., A Survey of Forecast Error Measures, World Applied Sciences Journal (I.T.M. I.E. S.), 24 (2013), 28, pp.171-176
- Ostertagova, E., Ostertag, O., Methodology and Application of One-way ANOVA, American Journal of Mechanical Engineering, 7 (2013), 1, pp. 256-261
- Balbay, A., et al., Modeling of convective drying kinetics of pistachio kernels in a fixed bed drying system, Thermal Science, 17 (2013), 3, pp. 839-846
- Jarque, C. M., Bera, A. K., Efficient tests for normality, homoscedasticity and serial independence of regression residuals, North-Holland Publishing Company,(1980), 6, pp. 255-259
- Williams, J. M., Degrees of Freedom: A Correction to Chi Square For Physical Hypotheses, in : Chi Square df v. 1.23, (Ed. J. M. Williams), Redwood City, Cal., USA, 2010, pp. 1-47
- Chai, T., Draxler, R. R., Root mean square error (RMSE) or mean absolute error (MAE), Geosci. Model Dev, 7 (2014), 3, pp.1247-1250
- Luo, D., et al., Modeling of Efficient Hot Air Drying of Apple Snails (Pomacea canaliculata) for Use as a Fishmeal Protein Substitute, Adv. J. Food Sci. Technol, 3 (2015), 8, pp. 193-201
- Chouquet, C., Linear models (in french language), in : Probability and Statistics Laboratory IMAT, (Ed. P. Sabatier), Toulouse University, France, 2010, pp.1-50
- Wyllys, R. E., ANOVA: Analysis of Variance, in : Mathematical Notes for LIS 397.1, (Ed. Research in Library and Information Science), U.T.A.S.I., USA, 2003, pp.1-10
- Bessonneau, P., et al., Two-way ANOVA (in french language), in : Apllied Statistics and Biostatistics in Experimental Sciences, (Ed. Cogmaster A4), France, 2007, pp.1-16
- Gros, P., Use of linear model. Basis reminder-Validation models (in french language), in : Fremr Coast Laboratories, (Ed. P. Gros), Brest Center, France, 2000, pp.1-155
- Andrea, R., et al., Dos and don'ts of reduced chi-squared, in : Astro-ph.IM, (Ed. ArXiVe-prints : 1012.3754v1), Heidelberg, Germany, 2010, pp.1-12
- Polat, K., Kirmaci V., A Novel Data Preprocessing Method for the Modeling and Prediction of Freeze-Drying Behavior of Apples: Multiple Output-Dependent Data Scaling (MODDS), Drying Technology: An International Journal, 30 (2012), 2, pp.185-196
- Laub,C., et al., How Bad is Good?, in : A Critical Look at the Fitting of Reflectivity Models using the Reduced Chi-Square Statistic, (Ed. Davis), D.C.E.M.S., Cal. Univ., USA, 2015, pp. 1-11
- Taylor, J.R., An introduction to Error analysis, University Science Books, California, USA, 1997