Parameter estimation of fick's law drying equation

Wan Ramli Wan Daud, Mahamad Hakimi Ibrahim, Meor Zainal Meor Talib

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best. In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical tune is governed by the constant diffusivity Fick's law diffusion equation (the constraint). Although the estimation of Pick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Pick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Pick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms. The drying of oil palm kernels are used as a case study. It is found that the estimated diffusivities of moisture in oil palm kernels range from 0.5 to 5.0 × 1010m2/s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.

Original languageEnglish
Pages (from-to)1673-1686
Number of pages14
JournalDrying Technology
Volume15
Issue number6-8
Publication statusPublished - 1997

Fingerprint

Fick's laws
Parameter estimation
drying
Drying
diffusivity
eccentrics
curves
Palm oil
oils
Moisture
Derivatives
calcium oxides
trucks
moisture
moisture content
regression analysis
inspection
Lime
estimating
Inspection

Keywords

  • Diffusivity of moisture
  • Distributed parameter model
  • Identification

ASJC Scopus subject areas

  • Chemical Engineering (miscellaneous)

Cite this

Wan Daud, W. R., Ibrahim, M. H., & Meor Talib, M. Z. (1997). Parameter estimation of fick's law drying equation. Drying Technology, 15(6-8), 1673-1686.

Parameter estimation of fick's law drying equation. / Wan Daud, Wan Ramli; Ibrahim, Mahamad Hakimi; Meor Talib, Meor Zainal.

In: Drying Technology, Vol. 15, No. 6-8, 1997, p. 1673-1686.

Research output: Contribution to journalArticle

Wan Daud, WR, Ibrahim, MH & Meor Talib, MZ 1997, 'Parameter estimation of fick's law drying equation', Drying Technology, vol. 15, no. 6-8, pp. 1673-1686.
Wan Daud WR, Ibrahim MH, Meor Talib MZ. Parameter estimation of fick's law drying equation. Drying Technology. 1997;15(6-8):1673-1686.
Wan Daud, Wan Ramli ; Ibrahim, Mahamad Hakimi ; Meor Talib, Meor Zainal. / Parameter estimation of fick's law drying equation. In: Drying Technology. 1997 ; Vol. 15, No. 6-8. pp. 1673-1686.
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