A comprehensive hybrid analytical-numerical solution is presented for a viscoelastic cantilever Euler-Bernoulli beam with an eccentric damped tip mass, subjected to external excitation, viscous damping, and an arbitrary base motion that undergoes translation and small rotation. The solution is obtained using the Generalized Integral Transform Technique (GITT), based on the application of an implicit filter and an eigenfunction expansion supported by a biharmonic-type eigenvalue problem, yielding a fast and straightforward implementation. A numerically stabilized eigenproblem formulation is proposed, ensuring robust convergence and accurate eigenfunctions. This hybrid solution, presented in a state-space framework, is validated experimentally against damped and undamped natural frequencies, and verified numerically through time-varying free and forced transverse deflection. A physical analysis is presented through four studies: (i) parametric maps of the first two complex eigenvalues, highlighting the distinct modal roles of viscoelastic damping and viscous damping, tip mass magnitude, and eccentricity; (ii) the combined effect of tip-mass eccentricity and internal damping on free and forced vibration; (iii) the influence of tip-mass damping and viscoelastic damping on free and forced vibration; and (iv) a Frequency Response Function (FRF) evaluation considering viscoelastic damping and viscous damping. The resulting formulation delivers fast-convergent solutions, providing closed-form base actions and frequency-response characterizations. The accompanying time- and frequency-domain results, together with compact eigenvalue maps, supply benchmark-quality references that clarify damping and eccentricity effects and support design, identification, and model assessment in linear vibration.

This study proposes a hybrid numerical-analytical solution based on the Generalized Integral Transform Technique (GITT) on the modal analysis of non-uniform and non-homogeneous Euler-Bernoulli cantilever beams carrying an eccentric tip mass. The eigenvalue problem given by the physical problem is expanded in terms of eigenfunctions of an auxiliary self-adjoint biharmonic eigenvalue problem, yielding a physically consistent analytical representation. The resulting solution exhibits excellent agreement with benchmark results reported in the literature, covering both uniform and homogeneous beams and tip-massed Axially Functionally Graded (AFG) beams. Detailed modal analyses are provided for every configuration examined. Several new case studies are introduced, in which the proposed structural design displays rapid and monotonic convergence for AFG beams with eccentric tip masses, covering also a stepped beam with abrupt, piecewise-constant sections, underscoring its accuracy and efficiency for complex, gradient-dependent structural systems.

PurposeThis study aims to theoretically and experimentally analyze conjugated conductive-convective heat transfer in laminar flow within rectangular microchannel heat sinks.Design/methodology/approachA three-dimensional steady-state conjugated heat transfer problem was solved using the generalized integral transform technique (GITT), uniquely reformulating the channel and substrate regions as a single domain with variable properties. This single-domain modeling strategy enables seamless treatment of multi-region problems without the complexity of multiple coupled integral transformed domains or mesh-based discretization with interfaces refinement typically required in conventional numerical methods. Experimental data, obtained from a custom-built thermohydraulic circuit using water and water/ethylene glycol (50 Wt.%) as working fluids, were used to validate the model.FindingsThe GITT solutions achieved a root-mean-square error of at most 10-2 and, upon comparison to experimental measurements, demonstrated good predictive accuracy. Unlike conventional microchannel correlations, the results captured the critical influence of the substrate on heat flux distribution, revealing deviations that arise primarily from lengthwise heat conduction effects.Originality/valueThis work introduces a novel application of GITT with single-domain modeling to practical heat sink configurations, offering a robust, efficient and accurate hybrid numerical-analytical framework. Compared to traditional discretization-based approaches, this method simplifies the treatment of conjugated problems and significantly reduces computational cost while faithfully capturing substrate conduction effects that are often overlooked in standard simulations and classical correlations.

Despite the proven feasibility and cost-effectiveness of nuclear desalination in small modular reactors (SMRs), the exclusive use of waste heat for this purpose remains virtually unexplored. This work investigates coupling an SMR (NuScale) to a direct contact membrane distillation (DCMD) desalination plant with heat recovery and feed recycle. Both the reactor waste heat and the low-pressure (LP) steam extraction from the reactor turbine were considered as heat sources. The DCMD hollow fiber module was modeled as a porous medium with satisfactory accuracy. Key parameters affecting system performance, identified through factorial analysis, include membrane porosity, module length, feed superficial velocity, and fiber inner radius. Single and multiobjective optimization analyses revealed the feasibility of producing up to 3,810 m3/d of water without any reactor power loss, and up to 8,832 m3/d, with a 2.28 MWe power loss, using steam extraction. DCMD demonstrated competitiveness, especially when the reactor's primary purpose is electricity generation.

The present work seeks to develop, through a genetic algorithm (GA), a procedure for optimization of the geometry of micro-channel heat exchangers used to dissipate the residual heat from high concentration photovoltaic panels (HCPV) to prevent the cells from overheating. In addition to the proper thermal management of the photovoltaic cell, the possibility of reuse of the dissipated thermal energy in a secondary process (e.g. desalination through membrane distillation) was also included during the optimization process. The methodology combines the open-source computational fluid dynamics software, OpenFOAM, for computational simulation of conjugate flow and heat transfer within the micro-channel heat sink, and the Python programming language, for the development of the procedure that couples the HCPV panel model with that of the heat sink, including the genetic algorithm to solve the optimization problem. In addition to the thermal parameters, the pressure drop inside the micro-heat exchanger is also considered in the optimization process. Although only single-phase flows are handled now, the algorithm can be extended to other flow regimes. As key findings, one can stress that the algorithm devised in-house works well in the optimization of the number vs dimensions of straight microchannels, for single-phase flows. The results also show that the number of channels should be maximized when the maximum electric power generation is required. On the other hand, when heat recovery is also a concurrent objective, the algorithm leads to the opposite solution, i.e., the number of channels should be minimized, so the efficiency of the secondary process can be attended.

The thermal reliability of two different high-power insulated gate bipolar transistor (IGBT) modules was studied under both conduction and switching regimes by experimental and numerical approaches. Indeed, the reliability of semiconductor devices is tightly linked to the junction temperatures reached in the IGBT, which is a function of the diode chips present in such devices and its operating condition. However, measurements of the semiconductor temperatures are often difficult to be done, thus requiring modeling and simulation tools to accurately evaluate the instantaneous temperature under different thermal loads. For this reason, a transient 3D heat transfer numerical model of two different IGBT power devices was proposed using the Finite Element Method, assuming that heat is dissipated on the IGBT by natural convection and radiation. These simulations were validated with experimental measurements, obtained through infrared thermography, performed for the IGBT modules either opened or enclosed, varying the heat source, the module orientation and under conduction or switching regime. For the switching regime, power losses due to the gate-closing and gate-opening transitions between conducting and non-conducting states were taken into consideration. The heat losses were modeled assuming the time-dependent heat dissipation obtained by previous electrical simulations, and it was compared with time-averaged heat source solutions. Results showed that averaging the heat source can significantly reduce the computational time, allowing quick design explorations. Overall, the numerical model led to deviations of less than 16% over the transient heating and at steady-state. Finally, the impact of a heat sink attached to the IGBT was studied, demonstrating that the proposed model can be used for accurate and quick investigations of potential failures and for the development of more efficient IGBT devices.

Membrane distillation (MD) has emerged as a promising thermal separation technology aimed mainly at water desalination, compatible with low-grade heat sources such as waste heat from thermal engines, solar collectors, and high concentration photovoltaic panels. This study presents a comprehensive theoretical-experimental evaluation of direct contact membrane distillation (DCMD) and air gap membrane distillation (AGMD), focusing on the influence of different membrane materials (PVDF, PTFE, and PE) and operational parameters on performance. Ex-periments were conducted in a flat-sheet MD module under varying NaCl concentrations (7 to 70 g/L), feed temperatures (65–85°C), and flow rates (0.2–0.8 L/min). The DCMD configuration achieved significantly higher permeate flux, with PTFE membranes achieving up to 33.59 kg/m²h at 85°C, attributed to the high hydrophobicity (contact angle: 143.4°) and porosity (85%). Con-versely, AGMD exhibited lower distillate fluxes (maximum 24.77 kg/m²h with PE) but outper-formed DCMD in specific energy consumption (SEC), achieving values as low as 1390.14 kWh/m³ with PTFE at 85°C, in a setup without any heat recovery from either the feed or distillate streams. The thermal efficiency of AGMD reached 0.54, 17% higher than DCMD with the same membrane. Salinity impacted performance differently: PTFE exhibited consistent flux across NaCl concen-trations, while PE showed a reduction of 31.3% at 70 g/L. The proposed heat and mass transfer reduced model showed good agreement with experimental data, with deviations within ±15%, effectively capturing the influence of operational parameters. These findings underscore the trade-offs between DCMD's higher fluxes and AGMD's higher energy efficiencies, offering quantitative insights to guide the design and optimization of MD systems for desalination and wastewater treatment.

A fast and robust computational model of a spiral-wound vacuum-enhanced air gap membrane distillation (V-AGMD) module at the pilot-scale is proposed and implemented. In contrast with data-driven models available in the literature, a physics-based approach is adopted for more reliable generalization beyond the validation dataset. A total of 86 experimental results, of which 41 are described in this work and 45 come from independent sources available in the literature, are used in the validation effort with quite favorable results. With the confidence on the robustness of the methodology due to the wide range of operational parameters and the use of spiral-wound modules of four different sizes included in the validation comparisons, a physical analysis is conducted varying the air gap pressure, the number of feedwater channels, the feedwater flow rate, and the membrane area. Improvements of up to 60% in both water productivity and energy efficiency can be achieved by intensifying the vacuum in the air gap or decreasing the number of feedwater channels. These parameters achieve performance gains due to less resistance in the air gap for vapor to migrate through it, in the former case, and a reduced temperature polarization effect, in the latter case. Smaller flow rates favor energy efficiency at the expense of water productivity by simultaneously decreasing transport-phenomena-related irreversibility and the partial pressure difference across the membrane and the air gap. In addition, this tradeoff between energy efficiency and driving force is shown to lead to an optimum value for the membrane area beyond which the permeate flow rate through the membrane starts to fall due to the small driving force. An illustrative case is predicted to achieve energy efficiency metrics, such as a gain-output ratio of 12.7, competitive with multi-effect distillation.

The generalized integral transform technique (GITT) is advanced to deal with conduction heat transfer in anisotropic heterogeneous media. A formal solution for exact integral transformation of conduction in anisotropic media is extended to account for heterogeneities expressed as space variable equation coefficients and source terms. The proposed eigenfunction expansion is based on biorthogonal eigenvalue problems, which results in an exact integral transformation for a class of linear problems and in a coupled transformed ordinary differential system for nonlinear situations. An algorithm is proposed for the associated eigenvalue problems, also handled through the GITT, by considering simpler biorthogonal eigenvalue problems of known analytical solution, leading to transformed algebraic eigenvalue problems. A single domain reformulation strategy is adopted to merge the information from multiple regions and materials, either isotropic or anisotropic, into one single diffusion equation. A two-dimensional transient test case is considered that presents an abrupt transition between isotropic and anisotropic materials yielding a marked change in thermal behavior in a defined region of interest formed by the anisotropic inclusion. Convergence behavior of the integral transform solution is illustrated, and the fully converged results are employed as a benchmark to inspect the accuracy of a commercial finite element code for automatically defined mesh refinement levels.

An analysis based on integral transforms is undertaken for transient three-dimensional conjugated conduction-convection heat transfer, with a focus on mini or micro channels-based devices. The numerical-analytical approach Generalized Integral Transform Technique (GITT) is combined with a single domain reformulation, providing accurate, robust, and cost-effective simulations for determining temperature distributions within the domain. The fluid and solid subdomains are represented as one single region, while the integral transformation is carried out using a three-dimensional eigenvalue problem encompassing the thermophysical properties and velocity field abrupt spatial variations. The steady state problem solution is employed as a filter and solved through an integral transformation based on the corresponding two-dimensional eigenvalue problem defined for the channel cross section. The transformed ordinary differential systems for both the steady and homogeneous transient problems are handled analytically, requiring only the numerical solution of the associated matrix eigensystem analysis. Converged numerical results for dimensionless temperature distributions are then critically compared with a finite element solution and a previously proposed GITT solution that implements a partial transformation scheme under a pseudo-transient formulation, both for the conjugated problem with thermally developing laminar flow in a rectangular channel.

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.