Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz, and diffusion–convection equations

Four methods that solve the Poisson, Helmholtz, and diffusion–convection problems on Cartesian grid by collocation with radial basis functions are presented. Each problem is split into a problem with an inhomogeneous equation and homogeneous boundary conditions, and a problem with a homogeneous equation and inhomogeneous boundary conditions. The former problem is solved by collocation with multiquadrics, whereas the latter problem is solved by collocation with either multiquadrics or fundamental solutions. It is found that methods that make use of fundamental solutions for collocation yield more accurate solutions that are less sensitive to the shape parameter of multiquadrics and node arrangement. Additional collocation appears to improve the quality of solutions.     

Solutions of partial differential equations with random Dirichlet boundary conditions by multiquadric collocation method

Problems described by deterministic partial differential equations with random Dirichlet boundary conditions are considered. Formulation of the solution to such a problem by the global collocation method using multiquadrics is presented. The quality of the solution to a stochastic problem depends on both its expected value and its variance. It is proposed that the shape parameter of multiquadrics should be chosen to optimize both the accuracy and the variance of the solution. Test problems described by the Poisson, the Helmholtz, and the diffusion–convection equations with random Dirichlet boundary conditions are solved by the multiquadric collocation method. It is found that there is a trade-off between solution accuracy and solution variance for each problem.     

Design of Porous Banana Foam Mat to Resist Moisture Migration Using a 2-D Stochastic Pore Network and Its Textural Property

The high porosity of dried banana foam allows it to quickly adsorb moisture from the air during storage, leading to a loss of quality and textural properties. Therefore, the main purpose of this research was to design and study banana foam structure at the pore level to limit moisture migration using a 2-D stochastic pore network. A 2-D network formed by the interconnection of cylindrical pores was used to represent the voids inside the banana foam and the moisture movement inside the individual pore segments during adsorption was described by Fick's law. The pore network was divided into two layers with different banana foam densities and the top surface of the network was exposed to humid air. The upper layer was assigned with pore sizes from the banana foam density of 0.31 g/cm³, having a void area fraction of 0.22, or from a density of 0.21 g/cm³, having a void area fraction of 0.31; the lower layer was assigned specifically with the pore sizes from the banana foam density of 0.26 g/cm³, having a void area fraction of 0.26. The predictions agreed well with the experimental results, with an R² value above 0.95. The two-layered banana foam mat with high banana foam density (characterized by mostly small pores) on the upper layer could limit the transport of moisture, with a rate relatively lower than that of a single-layered banana foam mat, and also exhibited more crispiness than the single banana foam. However, when the low banana density was in the upper layer, the two-layered sample adsorbed moisture quickly and its texture was less crispy.     

Evolution of mechanical properties of parboiled brown rice kernels during impinging stream drying

Information on mechanical properties of parboiled brown rice kernels upon impinging stream drying, which is important for effective control of kernel fissure and head rice yield, is reported. Experiments were performed at the drying temperatures of 130, 150, and 170°C; inlet air velocity of 20?m/s; impinging distance of 5?cm and paddy feed rate of 40?kg_{dry_paddy}/h. Parboiled paddy was dried for up to seven cycles. Between each drying cycle, the paddy was tempered for a period of either 0 (without tempering) or 30?min. The moisture evaporation rate was noted to be very high during the first two drying cycles and rapidly dropped in the later drying cycles. When tempering was included after a particular drying cycle, the drying rate in a subsequent cycle was higher than without tempering. At the kernel moisture contents immediately after drying of 25.3–47.5% (d.b.), the drying temperature and existence of tempering did not affect the mechanical properties although microcracks were formed in the kernels. However, both factors played a more important role on the mechanical properties when the kernels were evaluated at 16% (d.b.). The head rice yield correlated well with the tensile strength of the kernels.     

DESORPTION ISOTHERMS AND DRYING CHARACTERISTICS OF SHRIMP IN SUPERHEATED STEAM AND HOT AIR

Desorption isotherms for shrimp were determined at the temperatures of 50, 60, 70 and 80°C. Amongst the moisture equilibrium predictions between the BET and GAB models, the latter has a better predictable capability. The GAB parameters are correlated with the temperatures by the Arrhenius expression. Drying characteristics of shrimp in drying media at the temperature range of 120-180°C for superheated steam and of 70-140°C for hot air have been examined. Drying rate and effective diffusion coefficient are used to quantify quantitatively the difference between the superheated steam and the hot air dryings. The temperature is more important effect on drying rate and effective diffusion coefficient in the superheated steam than in the hot air. Inversion temperature exists between 140 and 150°C. Comparing to the hot air, the shrimp dried by the superheated steam shows a lower degree of shrimp shrinkage. In addition, product colours are slightly different to those from the commercial sources.     

MOBILE FLUIDIZED BED PADDY DRYER

The objectives of this research are to design, construct and test a mobile fluidized bed paddy dryer with a drying capacity of 2.5-4.0 t/h. Suitable drying conditions are recommended as follows : drying capacity 3.8 t/h, bed velocity 2.8 m/s, average drying air temperature 144 °C, bed height 13.5 cm, fraction of air recycled 0.8. Residence time of paddy was approximately 1.3 minutes. Test results showed that moisture content of paddy was reduced from 32.6 % dry-basis to 25.8 % dry-basis. Consumption of electrical power and diesel fuel was 12.9 kW and 21.71 1/h respectively. Primary energy consumption was 910.9 MJ/h. The dryer could evaporate water 218.8 kg/h. Specific primary energy consumption was 4.2 MJ/kg-water evaporated. Cost of paddy drying was 1.48 baht/kg-water evaporated of which 0.53 was fixed cost and 0.95 was energy cost (US$1 =34baht).     

Drying and Urease Inactivation Models of Soybean Using Two-dimensional Spouted Bed Technique

The most important factors for examining the quality of soybeans in the animal feed industry are moisture and urease inactivation. Mathematical models for soybean drying and urease inactivation using two-dimensional spouted bed are developed and validated with experimental data. The influences of initial moisture content, inlet air temperature, air recycle on the drying rate, urease inactivation, and energy consumption are also studied. The results revealed that the increase in initial moisture content slightly affected the drying rate and urease inactivation while the inlet air temperature caused a significant effect. To obtain a high drying rate and save energy consumption, the recycle air ratio should be kept in a range of 80-90%.     

Characteristics of Rice Dried in Superheated-Steam Fluidized-Bed

Characteristic properties of rice in a superheated-steam fluidized-bed dryer have been investigated using RVA, DSC, and SEM. The experimental results have shown that the reduction in moisture content from 41-42.5 to 25% d.b. using steam temperatures of 150-170°C was initially linear with drying time followed by the exponential decay when the moisture content was below 25% d.b. During the latter period, the water transport was controlled by the internal diffusion. Condensation of steam, along with the use of high temperature, enabled the development of gel layer as obvious from SEM. The formed gel layer caused the very low effective diffusivity when compared with the case of no gel formation in paddy kernel. The pasting properties and DSC measurements have shown that paddy dried at a higher temperature and a thinner bed depth provided a greater extent of gelatinization during the drying time, the first factor showing a profound effect. Kinetics of gelatinization is reasonably described by the zero-order reaction. For the paddy quality, the head rice yield was 70% higher than the reference value and color of white rice became yellow and low luminous after reducing moisture content to 18% d.b. The percentage of white belly was less than 1.5%.     

The method of fundamental solutions for solving free boundary saturated seepage problem

The problem of seepage flow through a dam is free boundary problem that is more conveniently solved by a meshless method than a mesh-based method such as finite element method (FEM) and finite difference method (FDM). This paper presents method of fundamental solutions, which is one kind of meshless methods, to solve a dam problem using the fundamental solution to the Laplace's equation. Solutions on free boundary are determined by iteration and cubic spline interpolation. The numerical solutions then are compared with the boundary element method (BEM), FDM and FEM to display the performance of present method.