Papers by Keyword: Generalized Coordinates

Abstract: In this work, a numerical solution for the diffusion equation applied to solids with arbitrary shape considering convective boundary condition is presented. To this end, the diffusion equation, written in generalized coordinates, was discretized by the finite-volume method with a fully implicit formulation. The transport parameters and the dimensions of the solids are considered constant during all process. For each time step, the system of equations obtained for a given non-orthogonal structured mesh was solved by the Gauss-Seidel method. One computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (parallelepiped and finite cylinder). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. In order to verify the potential of the proposed numerical solution, we used experimental data of the drying of ceramic roof tiles for the following temperature: T = 55.6 °C. The analysis of the results and the statistical indicators enables to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature for the convective boundary condition.

Abstract: Drying is a method of preservation widely used to prolong the post-harvest life of several agricultural products. In this work, experiments were accomplished involving drying of whole bananas, using hot air at temperature of 40.0 ^ºC and constant velocity of 1.5 m s^-1. The mass loss in regular time intervals was measured using the gravimetric method. In order to describe the process, the liquid diffusion model was used, assuming variable volume and effective mass diffusivity [. Thus, the diffusion equation was numerically solved through the finite volume method, with a fully implicit formulation. Due to the geometry of the product, the diffusion equation was written in generalized coordinates, and then discretized, assuming boundary condition of the third kind [. To take advantage of the symmetry, bananas were considered as revolution solids, obtained by the rotation of an area in the plane (x,y) about the axis y. The area was obtained directly of the photography of a banana, which served to create a non-orthogonal structured grid with 32 x 40 control volumes. The thermo-physical parameters were obtained through an optimization algorithm, based on the inverse method. Once the thermo-physical parameters were known, the drying kinetics as well as the water distribution within the bananas in stipulated times were presented and analyzed. The statistical indicators enable to conclude the methodology proposed to describe whole banana drying presents good results.

Abstract: This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. For this end, the diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. The computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (orthogonal and non-orthogonal meshes). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. The developed computational code was applied in the simulation of the drying of ceramic roof tiles for the following temperature: 55.6 °C. The analysis of the results makes it possible to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature.

Abstract: The paper describes the definition of a set of generalized coordinates and forces (kinematic control parameters) necessary to satisfy a specific job. Specifically, the generation of a three dimensional curve with torsion described by a Frenet reference system. The method employed to accomplish this task is using the Original ADAMS program alias MCADA. The analysis results indicate that the method can be successfully applied when designing motion simulators; however, there are accuracy restrictions for high precision six axis machining.