Approximation error model (AEM) approach with hybrid methods in the forward-inverse analysis of the transesterification reaction in 3D-microreactors

This work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized Integral Transform Technique (GITT) is applied using approximate non-converged solutions of the 3D model, by adopting low truncation orders in the eigenfunction expansions. Second, the Coupled Integral Equations Approach (CIEA) provides a reduced mathematical model for the average concentrations, which leads to inherently approximate solutions. The AEM approach through the Bayesian framework is illustrated in the simultaneous estimation of kinetic and diffusion coefficients of the transesterification reaction. For this purpose, the fully converged GITT results with higher truncation orders for the 3D partial differential model are employed as reference results to define the approximations errors. The results highlight that either the non-converged solutions via GITT or the reduced model solution obtained via CIEA, when taking into account the model error, are robust and cost-effective alternatives for the inverse analysis of nonlinear convection–diffusion-reaction problems

Hybrid Approach in Microscale Transport Phenomena: Application to Biodiesel Synthesis in Micro-reactors

A hybrid engineering approach to the study of transport phenomena, based on the synergy among computational, analytical, and experimental methodologies is reviewed. The focus of the chapter is on fundamental analysis and proof of concept developments in the use of nano- and micro-technologies for energy efficiency and heat and mass transfer enhancement applications. The hybrid approach described herein combines improved lumped-differential modeling, hybrid numericalanalytical solution methods, mixed symbolic-numerical computations, and advanced experimental techniques for micro-scale transport phenomena. An application dealing with micro-reactors for continuous synthesis of biodiesel is selected to demonstrate the instrumental role of the hybrid approach in achieving improved design and enhanced performance

Meniscal allograft transplantation in rabbit

This study evaluated the technique for meniscal allograft transplantation using allografts preserved in glycerin 98% in rabbits. Euthanasia was performed at 70 days to compare the transplanted (TM1 to TM16) versus the contralateral meniscus (OM1 to OM16). Sixteen menisci, 8 transplanted and 8 contralateral, were submitted to gross examination, histomorphometric analysis for identification and quantification of cellular type, and for quantification and distribution of collagen fibers. A revascularization study was conducted in all of the other samples. Lengths of the OM varied from 0.9 to 1.0 cm and two TM were smaller. All TM were completely attached to the synovial membrane, except for one case that presented partial fixation. Both, TM and OM had similar amounts of chondrocytes, fibroblasts and fibrocytes, and at the horns, chondrocytes were predominant. The collagen fibers in TM were well organized throughout the body, and disorganized at the horns. These fibers in OM were organized. The amounts of collagen type I and III, and the vascularization of the perimeniscal tissue and of the edge were similar in OM and TM. These results demonstrated graft integration and thus this transplantation technique and preservation method may be recommended