Predicting the Drying Time of Banana Slices with Fick's Diffusion Equation

Najwa Muhammad

Abstract


Knowing how long a product must stay in the dryer is a basic question in food processing. In the falling-rate period of drying, introductory unit-operations courses offer two quick answers: a linear drying-rate model and the rule that drying time grows with the square of the slice thickness. The two answers do not agree. When the slice is twice as thick, the first predicts a drying time twice as long and the second predicts four times as long. This paper uses Fick's second law of diffusion to settle the question for a typical banana-slice dryer. The model includes a surface condition taken directly from the textbook drying-rate law, so that both quick rules appear as special cases of one equation, linked by a single number, the Biot number. The equation is solved by separation of variables (Fourier series) and checked independently with the Crank–Nicolson finite-difference method; the two solutions differ by less than 0.0001. For the banana example, the diffusion model predicts a falling-rate period of 10.1 h, compared with 3.6 h from the linear model and 6.7 h from the thickness rule, so within the model both quick rules underestimate the time. Doubling the slice thickness from 5 to 10 mm increases the predicted time about 3.3 times, which lies between the two quick rules. A simple estimate, obtained by adding the two quick-rule times, stayed within about 4% of the full model over the range of parameters tested. These are model predictions based on textbook parameters and still need to be checked against measured drying curves.


Keywords


Food Drying; Fick's Second Law; Fourier Series; Biot Number; Crank-Nicolson Method; Banana

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References


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DOI: https://doi.org/10.18860/jrmm.v6i2.47404

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