Chemical Engineering Science 63 (2008) 5503--5512 Contents lists available at ScienceDirect Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces Modeling coupled transport phenomena and mechanical deformation of shrimp during drying in a jet spouted bed dryer Chalida Niamnuy a , Sakamon Devahastin a, ∗ , Somchart Soponronnarit b , G.S. Vijaya Raghavan c a Department of Food Engineering, Faculty of Engineering, King Mongkut's University of Technology Thonburi, 126 Pracha u-tid Road, Tungkru, Bangkok 10140, Thailand b School of Energy, Environment and Materials, King Mongkut's University of Technology Thonburi, 126 Pracha u-tid Road, Tungkru, Bangkok 10140, Thailand c Department of Bioresource Engineering, McGill University, Macdonald Campus, 21111 Lakeshore, Ste. Anne de Bellevue, Canada H9X 3V9 ARTICLE INFO ABSTRACT Article history: Received 1 May 2008 Received in revised form 22 July 2008 Accepted 29 July 2008 Available online 3 August 2008 Keywords: Biomaterials Finite element method Heat and mass transfer Shrinkage Shrimp Strain Stress Virtual work principle Heat and mass transfer in highly shrinkable and irregular-shape biomaterials such as shrimp during convective drying represents a complicated phenomenon since it is important to consider not only the transport phenomena occurring during drying but also the various changes of the drying materials. In order to describe drying of biomaterials adequately, a mathematical model that considers both of the above-mentioned aspects is needed. In this study, the formulation and validation of a mathematical model describing coupled transport phenomena and mechanical deformation of shrimp undergoing drying in a representative convective dryer, i.e., a jet spouted bed dryer, was conducted. The model consists of coupled heat conduction and mass diffusion equations along with the elastic solid mechanics equations. Governing equations and initial as well as boundary conditions were solved numerically using a finite element method via COMSOL Multiphysics TM software (version 3.3a). The simulated results, in terms of the shrimp moisture content, mid-layer temperature and shrinkage, were compared with the experi- mental results also obtained in this study and good agreement between the theoretical simulation and experimental results was observed in general. The model was also used to predict the principal stress distributions within shrimp during drying. Moreover, the effect of including deformation in the model was also illustrated by comparing the simulated results with those obtained from the model assuming no deformation. © 2008 Elsevier Ltd. All rights reserved. 1. Introduction One of the most important steps in the production of dried shrimp is drying. Since shrimp is a biomaterial with irregular shape and is highly shrinkable during drying, simultaneous heat and mass transfer as well as strain–stress formation in three dimensions need to be considered during drying. During drying moisture in the pores of shrimp is lost leading to a decrease in the volume of the pores and the apparent volume of shrimp. If shrinkage takes place uniformly in internal bodies, the strain behavior would be quite simplified. However, moisture gradients within shrimp lead to non-uniform shrinkage generating stresses inside the shrimp body (drying-induced stresses) causing non-uniform deformation and may influence negatively the texture and rehydration behavior of the dried product (Kowalski and Rybicki, 2007). The ability to predict the stress–strain behavior, and hence deformation, of a drying biomaterial, in general, and shrimp, in * Corresponding author. Tel.: +66 2 470 9246; fax: +66 2 470 9240. E-mail address: sakamon.dev@kmutt.ac.th (S. Devahastin). 0009-2509/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2008.07.031 particular, is of great interest. Tsukada et al. (1991) and Akiyama and Hayakawa (2000) developed a two-dimensional model to sim- ulate transient heat and moisture transfer as well as stress distri- bution in axi-symmetric foods such as hydrated starch undergoing drying. A simultaneous heat and moisture transfer model was cou- pled with the virtual work principle. Good agreement between the theoretical and experimental results was observed and the models had potential to predict deformation and cracking of foods and bio- materials undergoing drying. Kowalski (1996, 2000) and Kowalski et al. (2000) presented a mathematical model describing the shrink- age phenomenon and drying-induced stresses of materials under- going drying processes. The models were constructed using the methods of continuum mechanics and the principles of irreversible thermodynamics. The models could describe the distributions of temperature and moisture content as well as the mechanical behavior of moist materials during drying. Although the heat and mass transfer coupled with mechanical models are useful for eval- uation of the thermal, mass and mechanical responses of foods as influenced by different drying processes, most published works have performed on products with regular shape and only one- or two-dimensional transport processes.