Leandro A. Sphaier

Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems

The present work summarizes the theory and describes the algorithm related to an open-source mixed symbolic-numerical computational code named unified integral transforms (UNIT) that provides a computational environment for finding hybrid numerical-analytical solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established methodology known as the generalized integral transform technique (GITT), together with the symbolic and numerical computation tools provided by the Mathematica system. The main purpose of this study is to illustrate the robust precision-controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multidimensional formulations of Burgers’ equation, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects in the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code, including the proposition of a progressive filtering strategy and a combined criteria reordering scheme, not previously discussed in related works, both aimed at convergence acceleration of the eigenfunction expansions.

Numerical Solution of Periodic Heat and Mass Transfer with Adsorption in Regenerators: Analysis and Optimization

A novel solution scheme for periodic heat and mass transfer problems with adsorption is proposed. The method consists of a combination of the finite–volume method and the numerical method of lines. The method is applied to a general transport problem for heat and mass regenerators. The equations are spatially discretized and the resulting ordinary differential equation (ODE) system is solved using a stiff ODE solver with user-prescribed precision. The solution algorithm is analyzed and optimized, showing that selecting suitable computational procedures and proper values for parameters associated with the numerical solution can lead to a significant reduction in computational time.

Unified Integral Transform Approach in the Hybrid Solution of Multidimensional Nonlinear Convection-Diffusion Problems

The present work summarizes the theory and describes the algorithm related to the construction of an open source mixed symbolic-numerical computational code named UNIT — Un ified I ntegral T ransforms, that provides a development platform for finding solutions of linear and nonlinear partial differential equations via integral transforms. The reported research was performed by making use of the symbolic computational system Mathematica v.7.0 and the hybrid numerical-analytical methodology Generalized Integral Transform Technique — GITT. The aim here is to illustrate the robust and precision controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source code. Test cases are selected based on nonlinear multi-dimensional formulations of the Burgers equations, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects and computational behaviors of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code.Copyright

Desiccant Cooling Cycle Tuning for Variable Environmental Conditions

The performance of desiccant cooling systems has been increasingly addressed, with applications spanning from thermal comfort to gas-turbine air cooling. Desiccant systems are particularly suitable regarding the environmental impact, due to the absence of refrigerants with ozone-depleting properties. Moreover, the use of low-grade waste heat as the primary energy source also characterizes a low global warming potential, when compared to vapor compression systems. Under this scenario, this study demonstrates how desiccant ventilation cycles can be tuned for environmental conditions while maintaining the conditioned space within acceptable thermal comfort conditions. The analysis is based on a simple numerical procedure for desiccant cooling simulation in which the overall system operation is calculated from individual cycle components’ characteristics. With the employed methodology, the conditioned space state is calculated for different environmental conditions and compared to a standard, previously set, comfort zone. The results show that, in addition to desiccant wheel performance, the effectiveness of evaporative coolers and the regenerator is of prime importance for achieving acceptable thermal comfort conditions.

Size effect on the thermal intensification of alumina-filled nanocomposites

This work comprises an experimental investigation of thermal intensification in polymeric nanocomposites. Polyester and epoxy resins were employed as continuous phases and alumina spherical nanoparticles with different diameters (30–40, 27–43, 150, and 200 nm) were used as fillers, in volumetric concentrations up to 10%. The thermal conductivities of the fabricated samples were measured using a guarded heat flow meter and the influence of filler size was investigated. Density measurements were performed for verifying the volume concentrations of particles in batches containing distinct sorts of nanoparticles. In addition, scanning electron micrographs of all samples were obtained. Results show that larger particles are responsible for larger agglomerates and greater thermal conductivity augmentation of the polymeric matrices, indicating that interfacial properties play a significant role in the effective thermal conductivity of nanocomposites.

One-Dimensional Formulation for Heat and Mass Transfer in Solid Desiccant Dehydration of Natural Gas

An analysis of heat and mass transfer in the dehydration of natural gas using solid desiccants has been carried out, leading to a mathematical model for the simulation of the dehumidification process of a wet gas stream flowing through a porous bed containing desiccant particles. The process is divided in two periods: one for adsorption, in which the gas stream is actually dehydrated, and another one for the regeneration of the desiccant material, both of which are cyclically applied. The mathematical model considers spatial dependence in the flow direction, such that heat and mass transfer resistances within particles are treated in a lumped capacitance fashion. The resulting formulation constitutes a system of four coupled equations for describing temperature and humidity fields within solid particles and in the gas stream. These equations are normalized in terms of physically meaningful dimensionless groups, and numerically solved for producing simulation results for different configurations. The results suggest that the duration of regeneration periods can be shorter than those for adsorption, and that this dependence is clearly influenced by the regeneration temperature. In addition, it is seen that larger operation pressures can lead to larger water concentration in the adsorbed phase, and hence higher dehumidification levels.

Integral Transform Analysis of Poisson Problems that Occur in Discrete Solutions of the Incompressible Navier-Stokes Equations

The present work presents an alternate method for solving the poisson equation for calculating the pressure field that appears in many discrete numerical solvers of the incompressible Navier-Stokes equations. The methodology is based on a pressure-correction scheme with a mixed approach that employs Integral Transform Technique for the calculation of the pressure field from a given discrete velocity field. Two solution schemes are analyzed, these being the single transformation and the double transformation. The poisson equation is solved with the two different schemes using a prescribed source term to simulate the discrete data that could arise in the solution process of the momentum equation and an numerical results are presented. An error analysis of these results show that the single-transformation scheme is computationally superior to the double transformation, and that good convergence rates can be obtained with few terms in the series. Moreover, it was also verified that the series solution employed for the Poisson equation maintains the original spatial order of the discretization.

Semi-Analytical Method for the Solution of the Poisson Equation Derived From the Navier-Stokes Using Integral Transforms

The present work proposes two methodologies using the Integral Transform Technique to solve the Poisson equation arising from the incompressible Navier-Stokes equations. The solution of this Poisson equation is very common in the formulations based on pressure-correction and are the main bottleneck of these approaches. The new formulation proposed in this work will allow the elimination of the pressure-velocity decomposition and also eliminate the sub-iterations of the usual pressure-correction methods. The results show a comparison in performance of both proposed approaches.Copyright