### 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 × 10^{10}m^{2}/s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.

Original language | English |
---|---|

Pages (from-to) | 1673-1686 |

Number of pages | 14 |

Journal | Drying Technology |

Volume | 15 |

Issue number | 6-8 |

Publication status | Published - 1997 |

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### Keywords

- Diffusivity of moisture
- Distributed parameter model
- Identification

### ASJC Scopus subject areas

- Chemical Engineering (miscellaneous)

### Cite this

*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.

Research output: Contribution to journal › Article

*Drying Technology*, vol. 15, no. 6-8, pp. 1673-1686.

}

TY - JOUR

T1 - Parameter estimation of fick's law drying equation

AU - Wan Daud, Wan Ramli

AU - Ibrahim, Mahamad Hakimi

AU - Meor Talib, Meor Zainal

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Diffusivity of moisture

KW - Distributed parameter model

KW - Identification

UR - http://www.scopus.com/inward/record.url?scp=0031175495&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031175495&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031175495

VL - 15

SP - 1673

EP - 1686

JO - Drying Technology

JF - Drying Technology

SN - 0737-3937

IS - 6-8

ER -