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The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation.

The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme.

A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification.

A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.

The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis.

The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials.

An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented.

This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.

The purpose of this paper is to employ the Generalized Integral Transform Technique in the analysis of conjugated heat transfer in micro-heat exchangers, by combining this hybrid numerical-analytical approach with a reformulation strategy into a single domain that envelopes all of the physical and geometric sub-regions in the original problem. The solution methodology advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures, and fluid temperature measurements obtained through micro Laser Induced Fluorescence.

The methodology is applied in the hybrid numerical-analytical treatment of a multi-stream micro-heat exchanger application, involving a three-dimensional configuration with triangular cross-section micro-channels. Space variable coefficients and source terms with abrupt transitions among the various sub-regions interfaces are then defined and incorporated into this single domain representation for the governing convection-diffusion equations. The application here considered for analysis is a multi-stream micro-heat exchanger designed for waste heat recovery and built on a PMMA substrate to allow for flow visualization.

The methodology here advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures and fluid temperature measurements obtained through Laser Induced Fluorescence. A very good agreement among the proposed hybrid methodology predictions, a finite elements solution from the COMSOL code, and the experimental findings has been achieved. The proposed methodology has been demonstrated to be quite flexible, robust, and accurate.

The hybrid nature of the approach, providing analytical expressions in all but one independent variable, and requiring numerical treatment at most in one single independent variable, makes it particularly well suited for computationally intensive tasks such as in optimization, inverse problem analysis, and simulation under uncertainty.

The purpose of this paper is to provide an analysis of two‐dimensional laminar flow in the entrance region of wavy wall ducts as obtained from the solution of the steady Navier‐Stokes equations for incompressible flow.

The study is undertaken by application of the generalized integral transform technique 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.

A few representative cases are considered more closely in order to report some numerical results illustrating the eigenfunction expansions convergence behavior. The product friction factor‐Reynolds number is also computed and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel.

The proposed methodology is fairly general in the analysis of different channel profiles, though the reported results are limited to the wavy channel configuration. Future work should also extend the analysis to geometries represented in the cylindrical coordinates with longitudinally variable radius.

The error‐controlled converged results provide reliable benchmark results for the validation of numerical results from computational codes that address the solution of the Navier‐Stokes equations in irregular geometries.

Although the hybrid methodology is already known in the literature, the results here presented are original and further challenges application of the integral transform method in the solution of the Navier‐Stokes equations.

Different possibilities for the enhancement of convergence rates in eigenfunction expansions are investigated in the realm of integral transform solutions for partial differential equations. A representative parabolic problem is chosen to illustrate two schemes and their combinations; a filtering technique and an integral balance approach. Numerical results are presented to confirm the relative merits in each proposed procedure.

This teaching case was based on both primary and secondary sources of information. An interview with the entrepreneur and protagonist of the case was conducted, recorded and fully transcribed. Also, secondary data (digital and print media) were obtained from the interviewee, before, during and after the interview, as well as on governmental, institutional and company websites.

The Ninho da Águia Farm is a family business located in Minas Gerais and specialized in coffee production. Although founded in 1969 by Aides Gomes Monteiro, it was only when his surfer son Clayton Barbosa Monteiro took over the business that the small farm started focusing on specialty coffee, quality beans and international markets. With no formal education, Clayton managed to implement several managerial, organizational and strategic changes in the company, including its internationalization. Understanding the logic behind the development of the farm can help students understand several important concepts in International Business in relation to international entrepreneurs and effectuation/causation decision-making logics.

This teaching case was designed for graduate courses in international business/international strategy. But because of the richness of the case, it could also be used in other courses (e.g. marketing or international marketing). However, should this be the case, different teaching notes would be necessary.

Starting from the knowledge-based view as a theoretical perspective, this study aims to examine how an emerging market multinational enterprise (EMMNE) engages in reverse knowledge transfer (RKT) processes and how such processes are managed by headquarters. Therefore, this paper captures the perspective of top management concerning RKT and the processes used to create, transfer and integrate knowledge.

The study uses a longitudinal design based on the case method of investigation. The case selected for the study was a Brazilian company theoretically sampled for being a domestically, regionally and globally important, information-rich company that operates in an industry in which technology plays a crucial role. The company was also selected for having had asset-seeking motives in at least some of its foreign market entries and for having successfully absorbed foreign-acquired capabilities.

The study provides counterfactual evidence to the springboard perspective, considering timing and speed of the internationalization and catch-up processes and the size of acquisitions. The study also highlights differences to other emerging market multinational enterprises, concerning the internationalization trajectory and catch-up moves, and to traditional MNEs, regarding RKT challenges and practices.

The main limitations of the study relate to the case study method, which does not allow for statistical generalization, although it does support analytical generalization.

The study contributes to the literature by shedding light on the process by which a Latin American multinational firm developed technological capabilities to compete globally, focusing on the symbiotic, self-nurturing relationship between internationalization processes and technology acquisition and integration processes. Moreover, the work provides novel theoretical insights regarding timing, location, size and execution of the RKT activities. Finally, the paper contributes to the understanding of the relational aspects of the RKT process by focusing on building human relationships as the major force behind knowledge integration and examining the resistance of the acquired companies from developed markets to adopt the parent company’s best practices, or to contribute to its integrated knowledge, when the parent company is an EMMNE.

Students should learn gradual process of internationalization and commitment; reasons for internationalization; and role of networks.

This case is about Bazzar, a small company that sells sauces, toppings and desserts made only with high-quality Brazilian ingredients. The case dilemma refers to market entry strategies and commitment, although other IB topics are addressed.

Originally designed for MBA courses.

CSS 5: International Business

Teaching Notes are available for educators only.

Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect to the co‐ordinate system chosen to represent the geometry under consideration. A quite general formulation of a two‐dimensional steady‐state diffusion problem is initially considered, and a formal solution is provided. The original partial differential equation is analytically transformed into an infinite system of ordinary differential equations for the transformed velocity field in the flow direction. On truncation to a sufficiently large finite order, adaptively chosen to meet prescribed accuracy requirements, well‐established numerical schemes for boundary value problems are utilized, readily available in scientific subroutines libraries. Illustrates convergence rates for a few typical duct geometries and critically examines previously reported numerical solutions.