Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Exact and analytic-numerical solutions of lagging models of heat transfer in a semi-infinite medium

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Dynamic investigation of an ancient masonry bell tower with operational modal analysis: a non-destructive experimental technique to obtain the dynamic characteristics of a structure

This paper shows the results of an experimental analysis on the bell tower of “Chiesa della Maddalena” (Mola di Bari, Italy), to better understand the structural behavior of slender masonry structures. The research aims to calibrate a numerical model by means of the Operational Modal Analysis (OMA) method. In this way realistic conclusions about the dynamic behavior of the structure are obtained. The choice of using an OMA derives from the necessity to know the modal parameters of a structure with a non-destructive testing, especially in case of cultural-historical value structures. Therefore by means of an easy and accurate process, it is possible to acquire in-situ environmental vibrations. The data collected are very important to estimate the mode shapes, the natural frequencies and the damping ratios of the structure. To analyze the data obtained from the monitoring, the Peak Picking method has been applied to the Fast Fourier Transforms (FFT) of the signals in order to identify the values of the effective natural frequencies and damping factors of the structure. The main frequencies and the damping ratios have been determined from measurements at some relevant locations. The responses have been then extrapolated and extended to the entire tower through a 3-D Finite Element Model. In this way, knowing the modes of vibration, it has been possible to understand the overall dynamic behavior of the structure.

An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Non-covalent immobilization of RhDuphos on carbon nanotubes and carbon xerogels

The immobilization of the chiral complex RhDuphos, by electrostatic or π–π (adsorption) interactions, on carbon nanotubes and carbon xerogels is investigated. To promote such interactions, the supports were either oxidized or heat treated to create carboxylic type surface groups or an apolar surface, respectively. The catalysts were tested in the hydrogenation of methyl 2-acetamidoacrylate. The prepared hybrid catalysts are less active than the homogeneous RhDuphos, but most of them show a high enantioselectivity and the one prepared with the oxidized carbon xerogel is also reusable, being able to give a high substrate conversion, keeping as well a high enantioselectivity. The anchorage by electrostatic interactions is more interesting than the anchorage by π–π interactions, as the π–π adsorption method produces a modification of the metal complex structure leading to an active hybrid catalyst but without enantioselectivity. The creation of carboxylic groups on the support surface has led to some hindering of the complex leaching.