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The purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.

Through analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.

The accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.

The application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

Laser-based powder bed fusion (LPBF) is a new method for forming thin-walled parts, but large cooling rates and temperature gradients can lead to large residual stresses and deformations in the part. This study aims to reduce the residual stress and deformation of thin-walled parts by a specific laser rescanning strategy.

A three-dimensional transient finite element model is established to numerically simulate the LPBF forming process of multilayer and multitrack thin-walled parts. By changing the defocus amount, the laser in situ annealing process is designed, and the optimal rescanning parameters are obtained, which are verified by experiments.

The results show that the annealing effect is related to the average surface temperature and scan time. When the laser power is 30 W and the scanning speed is 20 mm/s, the overall residual stress and deformation of the thin-walled parts are the smallest, and the in situ annealing effect is the best. When the annealing frequency is reduced to once every three layers, the total annealing time can be reduced by more than 60%.

The research results can help better understand the influence mechanism of laser in situ annealing process on residual stress and deformation in LPBF and provide guidance for reducing residual stress and deformation of LPBF thin-walled parts.

Among the various applications involving the use of microwave energy, its growing utility within the mining industry is particularly noteworthy. Conventional grinding processes are often overburdened by energy inefficiencies that are directly related to machine wear, pollution and rising project costs. In this work, we numerically investigate the effects of microwave pretreatment through a series of compression tests as a means to help mitigate these energy inefficiencies.

We investigate the effects of microwave pretreatment on various rock samples, as quantified by uniaxial compression tests. In particular, we assign sample heterogeneity based on a Gaussian statistical distribution and invoke a damage model for elemental tensile and compressive stresses based on the maximum tensile stress and the Mohr–Coulomb theories, respectively. We further couple the electromagnetic, thermal and solid displacement relations using finite element modeling.

(1) Increased power intensity during microwave pretreatment results in decreased axial compressive stress. (2) Leveraging statistics to induce variable compressive and tensile strength can greatly facilitate sample heterogeneity and prove necessary for damage modeling. (3) There exists a nonlinear trend to the reduction in smax with increasing power levels, implying an optimum energy output efficiency to create the maximum degradation-power cost relationship.

Previous research in this area has been largely limited to two-dimensional thermo-electric models. The onset of high-performance computing has allowed for the development of high-fidelity, three-dimensional models with coupled equations for electromagnetics, heat transfer and solid mechanics.

Selective laser melting and electron beam melting processes are well-known for the additive manufacturing of metal parts. Metal powder bed fusion (MPBF) is a common term for them. The MPBF process can empower the manufacturing of intricate shapes by reducing the use of special tools, shortening the supply chain and allowing small batches. However, the MPBF process suffers from many quality issues. In literature, several works are recorded for qualification of the MPBF part. The purpose of this study is to recollect those works done for quality control and report their helpful findings for further research and development.

A systematic literature review was conducted to highlight the major quality issues in the MPBF process and its root causes. Further, the works reported in the literature for mitigation of these issues are classified and discussed in five categories: experimental investigation, finite element method-based numerical models, physics-based analytical models, in-situ control using artificial intelligence (AI) and machine learning (ML) methods and statistical approaches. A comparison is also prepared among these strategies based on their suitability and limitations. Additionally, improvements in MPBF printers are pointed out to enhance the part quality.

Analytical models require less computational time to simulate the MPBF process and need a smaller number of experiments to confirm the results. They can be used as an efficient process parameter planning tool to print metal parts for noncritical applications. The AI-ML based quality control is also suitable for MPBF processes as it can control many processing parameters that may affect the quality of the MPBF part. Moreover, capabilities of MPBF printers like thinner layer thickness, smaller beam diameter, multiple lasers and high build temperature range can help in quality control.

This study converts the piecemeal data on MPBF part qualification methods into interesting information and presents it in tabular form under each strategy. This tabular information provides the basis for further quality improvement efforts in the MPBF process.

This study references researchers and practitioners on recent quality control efforts and their significant findings for a better quality of MPBF part.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

This paper aims to propose a method to quickly set the heating zone temperatures and conveyor speed of the reflow oven. This novel approach intensely eases the trial and error in reflow profiling and is especially helpful when reflowing thick printed circuit boards (PCBs) with bulky components. Machine learning (ML) models can reduce the time required for profiling from at least half a day of trial and error to just 1 h.

A highly compact computational fluid dynamics (CFD) model was used to simulate the reflow process, exhibiting an error rate of less than 1.5%. Validated models were used to generate data for training regression models. By leveraging a set of experiment results, the unknown input factors (i.e. the heat capacities of the bulkiest component and PCB) can be determined inversely. The trained Gaussian process regression models are then used to perform virtual reflow optimization while allowing a 4°C tolerance for peak temperatures. Upon ensuring that the profiles are inside the safe zone, the corresponding reflow recipes can be implemented to set up the reflow oven.

ML algorithms can be used to interpolate sparse data and provide speedy responses to simulate the reflow profile. This proposed approach can effectively address optimization problems involving multiple factors.

The methodology used in this study can considerably reduce labor costs and time consumption associated with reflow profiling, which presently relies heavily on individual experience and skill. With the user interface and regression models used in this approach, reflow profiles can be swiftly simulated, facilitating iterative experiments and numerical modeling with great effectiveness. Smart reflow profiling has the potential to enhance quality control and increase throughput.

In this study, the employment of the ultimate compact CFD model eliminates the constraint of components’ configuration, as effective heat capacities are able to determine the temperature profiles of the component and PCB. The temperature profiles generated by the regression models are time-sequenced and in the same format as the CFD results. This approach considerably reduces the cost associated with training data, which is often a major challenge in the development of ML models.

3D steady heat conduction analysis considering heat source is conducted on the fundamental of the fast multipole method (FMM)-accelerated line integration boundary element method (LIBEM).

Due to considering the heat source, domain integral is generated in the traditional heat conduction boundary integral equation (BIE), which will counteract the well-known merit of the BEM, namely, boundary-only discretization. To avoid volume discretization, the enhanced BEM, the LIBEM with dimension reduction property is introduced to transfer the domain integral into line integrals. Besides, owing to the unsatisfactory performance of the LIBEM when it comes to large-scale structures requiring massive computation, the FMM-accelerated LIBEM (FM-LIBEM) is proposed to improve the computation efficiency further.

Assuming N and M are the numbers of nodes and integral lines, respectively, the FM-LIBEM can reduce the time complexity from O(NM) to about O(N+ M), and a full discussion and verification of the advantage are done based on numerical examples under heat conduction.

(1) The LIBEM is applied to 3D heat conduction analysis with heat source. (2) The domain integrals can be transformed into boundary integrals with straight line integrals by the LIM. (3) A FM-LIBEM is proposed and can reduce the time complexity from O(NM) to O(N+ M). (4) The FM-LIBEM with high computational efficiency is exerted to solve 3D heat conduction analysis with heat source in massive computation successfully.

The purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.

The present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe₃O₄) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.

The influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.

The findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.

Tribological research is complex and multidisciplinary, with many parameters to consider. As traditional experimentation is time-consuming and expensive due to the complexity of tribological systems, researchers tend to use quantitative and qualitative analysis to monitor critical parameters and material characterization to explain observed dependencies. In this regard, numerical modeling and simulation offers a cost-effective alternative to physical experimentation but must be validated with limited testing. This paper aims to highlight advances in numerical modeling as they relate to the field of tribology.

This study performed an in-depth literature review for the field of modeling and simulation as it relates to tribology. The authors initially looked at the application of foundational studies (e.g. Stribeck) to understand the gaps in the current knowledge set. The authors then evaluated a number of modern developments related to contact mechanics, surface roughness, tribofilm formation and fluid-film layers. In particular, it looked at key fields driving tribology models including nanoparticle research and prosthetics. The study then sought out to understand the future trends in this research field.

The field of tribology, numerical modeling has shown to be a powerful tool, which is both time- and cost-effective when compared to standard bench testing. The characterization of tribological systems of interest fundamentally stems from the lubrication regimes designated in the Stribeck curve. The prediction of tribofilm formation, film thickness variation, fluid properties, asperity contact and surface deformation as well as the continuously changing interactions between such parameters is an essential challenge for proper modeling.

This paper highlights the major numerical modeling achievements in various disciplines and discusses their efficacy, assumptions and limitations in tribology research.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2023-0076/