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Abstract
The Biot number informs researchers about the controlling mechanisms employed for heat or mass transfer during the considered process. The mass transfer coefficients (and heat transfer coefficients) are usually determined experimentally based on direct measurements of mass (heat) fluxes or correlation equations. This paper presents the method of Biot number estimation. For estimation of the Biot number in the drying process, the multi-objective genetic algorithm (MOGA) was developed. The simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) and the maximization of the coefficient of determination R2 between the drying model and experimental data were considered. The Biot number can be calculated from the following equations: Bi = 0.8193exp(−6.4951T−1) (and moisture diffusion coefficient from D/s2 = 0.00704exp(−2.54T−1)) (RMSE = 0.0672, MAE = 0.0535, R2 = 0.98) or Bi = 1/0.1746log(1193847T) (D/s2 = 0.0075exp(−6T−1)) (RMSE = 0.0757, MAE = 0.0604, R2 = 0.98). The conducted validation gave good results.
Highlights
The dimensionless Biot number (Bi) is present in partial differential equations in cases when the surface boundary conditions are written in a dimensionless form
The analysis of Biot numbers enables researchers to answer questions regarding the controlling mechanisms employed for heat or mass transfer during the considered process [3]
Dincer [3] stated that the values of Bi for mass transfer can be divided into the following groups: Bi < 0.1; 0.1 < Bi < 100; Bi > 100 (external resistance is much lower than the internal resistance)
Summary
The dimensionless Biot number (Bi) is present in partial differential equations in cases when the surface boundary conditions (of the third kind) are written in a dimensionless form. The Biot number informs researchers about the relationship between the internal and external fluxes [1]. Assuming similarity between heat and mass transfer, the Biot number used for mass exchange is gained by equating internal and external mass fluxes at the interface [3,4] and the discussed number is defined as follows: hm L Bi = (1) D. The analysis of Biot numbers enables researchers to answer questions regarding the controlling mechanisms employed for heat or mass transfer during the considered process [3]. Dincer [3] stated that the values of Bi for mass transfer can be divided into the following groups: Bi < 0.1 (the surface resistance across the surrounding medium boundary layer is much bigger in comparison with the internal resistance to the mass diffusion within the solid body); 0.1 < Bi < 100 (the values of the internal and external resistance can be treated as comparable); Bi > 100 (external (surface) resistance is much lower than the internal resistance)
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