Optimization Mathematical Model of the Cooling Process in Hard Candies

SERGIO F. MUSSATI; MARÍA A. REINHEIMER

Lisboa

Conferencia; EngOpt 2010 - 2nd International Conference on Engineering Optimization; 2010

IST – Instituto Superior Técnico- Technical University of Lisbon & IDMEC/IST - Institute of Mechanical Engineering

In this paper a mathematical model of the transient heat transfer in the cooling of hard candies is proposed in order to determine optimal process parameters. Precisely, a mathematical model previously developed by authors of this paper has been extended to determine optimal operating policies aiming to prevent product defects. In fact, the previous model was recently used to study the influence on the main operating parameters on the cooling process efficiency by simulations. From the quality product point of view, simulation results showed that there is a strong trade-off between the main process parameters. Cooling air flow velocities, residence time in the cooling equiptment and the thermal conductivity of product influence on the number of decomised products as nonconforming. For example, high air velocities, especially at the beginning of the process, increase the product fragility for the wrapping stage. The most practical way of avoiding misshapen candies is by minimizing the difference of temperature between the centre and the surface on candy. Therefore, a mathematical model based on the finite element method is here proposed to determine the optimal operating policies to minimize the temperature difference. gPROMS modeling tool is used to implement the proposed model. A Centered Finite Difference Method (CFDM) of the second order is applied to the spatial (radial) partial derivates. A sensitivity analysis on the radial discretization is considered. Also, detailed discussions of results are presented through several case studies. temperature between the centre and the surface on candy. Therefore, a mathematical model based on the finite element method is here proposed to determine the optimal operating policies to minimize the temperature difference. gPROMS modeling tool is used to implement the proposed model. A Centered Finite Difference Method (CFDM) of the second order is applied to the spatial (radial) partial derivates. A sensitivity analysis on the radial discretization is considered. Also, detailed discussions of results are presented through several case studies. temperature between the centre and the surface on candy. Therefore, a mathematical model based on the finite element method is here proposed to determine the optimal operating policies to minimize the temperature difference. gPROMS modeling tool is used to implement the proposed model. A Centered Finite Difference Method (CFDM) of the second order is applied to the spatial (radial) partial derivates. A sensitivity analysis on the radial discretization is considered. Also, detailed discussions of results are presented through several case studies. temperature between the centre and the surface on candy. Therefore, a mathematical model based on the finite element method is here proposed to determine the optimal operating policies to minimize the temperature difference. gPROMS modeling tool is used to implement the proposed model. A Centered Finite Difference Method (CFDM) of the second order is applied to the spatial (radial) partial derivates. A sensitivity analysis on the radial discretization is considered. Also, detailed discussions of results are presented through several case studies. temperature between the centre and the surface on candy. Therefore, a mathematical model based on the finite element method is here proposed to determine the optimal operating policies to minimize the temperature difference. gPROMS modeling tool is used to implement the proposed model. A Centered Finite Difference Method (CFDM) of the second order is applied to the spatial (radial) partial derivates. A sensitivity analysis on the radial discretization is considered. Also, detailed discussions of results are presented through several case studies.