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The generalized integral transform technique (GITT) is reviewed as a computational–analytical methodology in linear and nonlinear convection–diffusion problems, based on eigenfunction expansions extracted from characteristic differential operators, coefficients, and boundary conditions present in the original partial differential problem formulation. Here, the emphasis is on the employment of nonclassical eigenvalue problems as the expansion basis, which do not fall into the more usual framework of Sturm–Liouville problems. The goal is to enable or improve the eigenfunction expansions convergence, by incorporating more information from the original operators into the chosen eigenvalue problem, while requiring the handling of such a more involved expansion base. In this concern, the proposed differential eigenvalue problem can itself be handled by the GITT, leading to an algebraic eigensystem analysis. Different classes of nonclassical eigenvalue problems are then reviewed and associated with typical applications in heat and mass transfer. Representative test cases are then chosen to illustrate the extended methodology and demonstrate the convergence rates attainable by this enhanced hybrid solution path.

Submitted by Jairo Amaro (jairo.amaro@sibi.ufrj.br) on 2019-07-04T16:00:45Z No. of bitstreams: 1 2010_COTTA_CNME_v26_p1417-1434-min.pdf: 590631 bytes, checksum: 810055efdc402f6d2a744085fcefbe9e (MD5) Made available in DSpace on 2019-07-04T16:00:45Z (GMT). No. of bitstreams: 1 2010_COTTA_CNME_v26_p1417-1434-min.pdf: 590631 bytes, checksum: 810055efdc402f6d2a744085fcefbe9e (MD5) Previous issue date: 2010-10-28 Indisponível. A hybrid numerical–analytical solution based on the generalized integral transform technique is proposed to handle the two‐dimensional Navier–Stokes equations in cylindrical coordinates, expressed in terms of the streamfunction‐only formulation. The proposed methodology is illustrated in solving steady‐state incompressible laminar flow of Newtonian fluids in the developing region of a circular tube. The flow modeling also considers two limiting inlet conditions, namely, uniform velocity profile representing a parallel flow, and zero vorticity that characterizes irrotational inlet flow. The integral transform analysis for such a full cylindrical region brings up singularities at the channel centerline, and, as previously described in a work dealing with the boundary‐layer formulation, a way to alleviate this difficulty is to adopt a recently introduced fourth‐order eigenvalue problem as the basis for the eigenfunction expansion. A thorough convergence analysis of the proposed expansion is then undertaken, for different values of Reynolds number, and a set of reference results for the velocity distributions and friction factors are then presented in tabular and graphical forms.

This paper deals with the solution of an inverse heat conduction problem, aiming at the identification of the interface thermal contact conductance, which can be directly associated to the quality of the adhesion between layers of multilayered composite materials. The inverse problem is solved within the Bayesian framework, with a Markov chain Monte Carlo method. A total variation prior is used for the spatially distributed contact conductance. The feasibility of the approach is evaluated with simulated temperature measurements for cases with contact failures of different sizes.

Heat regenerators can be found in a considerable number of engineering applications, and are either used as pair of fixed matrices or as single rotary matrix. These matrices are composed of numerous channels, traditionally of about a few millimeters in diameter. The thermal design of heat regenerators is usually done considering models that rely on well-established simplifying assumptions. Most of these assumptions are valid for mini- and larger scale channels; nevertheless, with the growing tendency towards miniaturization, mini- to micro-scale channels come into play. As a result some classical simplifying assumptions may no longer be applied to reduced-size channels. One such effect is that of rarefaction, in which the mean free path of the molecules can no longer be considered negligible. In this context, this paper proposes an investigation on how rarefaction and additional effects encountered in regenerative heat exchange (such as a transient regime and thermal wall storage) can influence the heat transfer coefficient. The obtained results can be of assistance in achieving better thermal designs for miniaturized heat exchangers.Copyright © 2011 by ASME

The analysis of two-dimensional laminar flow in the entrance region of arbitrarily shaped ducts is undertaken by application of the Generalized Integral Transform Technique (GITT) in the solution of the steady Navier-Stokes equations for incompressible flow. The streamfunction-only formulation is adopted, and a general filtering solution that adapts to the irregular contour is proposed to enhance the convergence behavior of the eigenfunction expansion. The case of a wavy-wall channel is then considered more closely in order to report some numerical results illustrating the expansions convergence behavior. In addition to reporting results of streamfunction, the product of friction factor-Reynolds number is also calculated and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel.Copyright © 2007 by ASME

Hybrid numerical—analytical algorithms, based on the generalized integral transform technique, developed to handle transient two- and three-dimensional heat and fluid flow in cavities filled with a porous material, are reviewed. To illustrate the approach, specific situations of both horizontal and vertical cavities are more closely considered, under the Darcy flow model. The problem is analyzed with and without the time derivative term in the flow equations, using a vorticity-vector potential formulation, which automatically reduces to the streamfunction-only formulation for two-dimensional situations. Results for rectangular (2D) and parallelepiped (3D) cavities are presented to demonstrate the convergence behavior of the proposed eigenfunction expansion solutions and comparisons with previously reported numerical solutions are critically performed.