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Present study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.

The numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.

For the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.

The difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for predicting the internal boundary conditions for thermal analysis of mechanical structure. A few examples of heat transfer systems are given to illustrate the applicability of the method and the challenges that must be addressed in solving the inverse problem.

In this paper, the thermal network method and the finite difference method are used to model the two-dimensional heat conduction inverse problem of the tube structure, and the heat balance equation is arranged into an explicit form for heat load prediction. To solve the matrix ill-conditioned problem in the process of solving the inverse problem, a Tikhonov regularization parameter selection method based on the inverse computation-contrast-adjustment-approach was proposed.

The applicability of the proposed method is illustrated by numerical examples for different dynamically varying heat source functions. It is proved that the method can predict dynamic heat source with different complexity.

The modeling calculation method described in this paper can be used to predict the boundary conditions for the inner wall of the heat transfer tube, where the temperature sensor cannot be placed.

This paper presents a general method for the direct prediction of heat sources or boundary conditions in mechanical structure. It can directly obtain the time-varying heat flux load and thtemperature field of the machine structure.

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.

Intumescent coatings are nowadays a dominant passive system used to protect structural materials in case of fire. Due to their reactive swelling behaviour, intumescent coatings are particularly complex materials to be modelled and predicted, which can be extremely useful especially for performance-based fire safety designs. In addition, many parameters influence their performance, and this challenges the definition and quantification of their material properties. Several approaches and models of various complexities are proposed in the literature, and they are reviewed and analysed in a critical literature review.

Analytical, finite-difference and finite-element methods for modelling intumescent coatings are compared, followed by the definition and quantification of the main physical, thermal, and optical properties of intumescent coatings: swelled thickness, thermal conductivity and resistance, density, specific heat capacity, and emissivity/absorptivity.

The study highlights the scarce consideration of key influencing factors on the material properties, and the tendency to simplify the problem into effective thermo-physical properties, such as effective thermal conductivity. As a conclusion, the literature review underlines the lack of homogenisation of modelling approaches and material properties, as well as the need for a universal modelling method that can generally simulate the performance of intumescent coatings, combine the large amount of published experimental data, and reliably produce fire-safe performance-based designs.

Due to their limited applicability, high complexity and little comparability, the presented literature review does not focus on analysing and comparing different multi-component models, constituted of many model-specific input parameters. On the contrary, the presented literature review compares various approaches, models and thermo-physical properties which primarily focusses on solving the heat transfer problem through swelling intumescent systems.

The presented literature review analyses and discusses the various modelling approaches to describe and predict the behaviour of swelling intumescent coatings as fire protection for structural materials. Due to the vast variety of available commercial products and potential testing conditions, these data are rarely compared and combined to achieve an overall understanding on the response of intumescent coatings as fire protection measure. The study highlights the lack of information and homogenisation of various modelling approaches, and it underlines the research needs about several aspects related to the intumescent coating behaviour modelling, also providing some useful suggestions for future studies.

This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth.

A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform.

Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth.

A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.

This paper aims to present a novel approach for computing particle temperatures in simulations coupling computational fluid dynamics (CFD) and discrete element method (DEM) to predict flow and heat transfer in fluidized beds of thermally thick spherical particles.

An improved lumped formulation based on Hermite-type approximations for integrals to relate surface temperature to average temperature and surface heat flux is used to overcome the limitations of classical lumped models. The model is validated through comparisons with analytical solutions for a convectively cooled sphere and experimental data for a fixed particle bed. The coupled CFD-DEM model is then applied to simulate a Geldart D bubbling fluidized bed, comparing the results to those obtained using the classical lumped model.

The validation cases demonstrate that ignoring internal thermal resistance can significantly impact the temperature in cases where the Biot number is greater than 0.1. The results for the fixed bed case clearly demonstrate that the proposed method yields significantly improved outcomes compared to the classical model. The fluidized bed results show that surface temperature can deviate considerably from the average temperature, underscoring the importance of accurately accounting for surface temperature in convective heat transfer predictions and surface processes.

The proposed approach offers a physically more consistent simulation without imposing a significant increase in computational cost. The improved lumped formulation can be easily and inexpensively integrated into a typical DEM solver workflow to predict heat transfer for spherical particles, with important implications for various industrial applications.

Gas metal arc-based directed energy deposition (GMA-DED) process experiences residual stress (RS) developed due to heat accumulation during successive layer deposition as a significant challenge. To address that, monitoring of transient temperature distribution concerning time is a critical input. Finite element analysis (FEA) is considered a decisive engineering tool in quantifying temperature and RS in all manufacturing processes. However, computational time and prediction accuracy has always been a matter of concern for FEA-based prediction of responses in the GMA-DED process. Therefore, this study aims to investigate the effect of finite element mesh variations on the developed RS in the GMA-DED process.

The variation in the element shape functions, i.e. linear- and quadratic-interpolation elements, has been used to model a single-track 10-layered thin-walled component in Ansys parametric design language. Two cases have been proposed in this study: Case 1 has been meshed with the linear-interpolation elements and Case 2 has been meshed with the combination of linear- and quadratic-interpolation elements. Furthermore, the modelled responses are authenticated with the experimental results measured through the data acquisition system for temperature and RS.

A good agreement of temperature and RS profile has been observed between predicted and experimental values. Considering similar parameters, Case 1 produced an average error of 4.13%, whereas Case 2 produced an average error of 23.45% in temperature prediction. Besides, comparing the longitudinal stress in the transverse direction for Cases 1 and 2 produced an error of 8.282% and 12.796%, respectively.

To avoid the costly and time-taking experimental approach, the experts have suggested the utilization of numerical methods in the design optimization of engineering problems. The FEA approach, however, is a subtle tool, still, it faces high computational cost and low accuracy based on the choice of selected element technology. This research can serve as a basis for the choice of element technology which can predict better responses in the thermo-mechanical modelling of the GMA-DED process.

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.

In the present work, we focus on developing an in-house parallel meshless local Petrov-Galerkin (MLPG) code for the analysis of heat conduction in two-dimensional and three-dimensional regular as well as complex geometries.

The parallel MLPG code has been implemented using open multi-processing (OpenMP) application programming interface (API) on the shared memory multicore CPU architecture. Numerical simulations have been performed to find the critical regions of the serial code, and an OpenMP-based parallel MLPG code is developed, considering the critical regions of the sequential code.

Based on performance parameters such as speed-up and parallel efficiency, the credibility of the parallelization procedure has been established. Maximum speed-up and parallel efficiency are 10.94 and 0.92 for regular three-dimensional geometry (343,000 nodes). Results demonstrate the suitability of parallelization for larger nodes as parallel efficiency and speed-up are more for the larger nodes.

Few attempts have been made in parallel implementation of the MLPG method for solving large-scale industrial problems. Although the literature suggests that message-passing interface (MPI) based parallel MLPG codes have been developed, the OpenMP model has rarely been touched. This work is an attempt at the development of OpenMP-based parallel MLPG code for the very first time.

The purpose of this paper is to introduce an innovative strategy for the approximate solution of the heat flow problems in two- and three-dimensional spaces. This new strategy is very easy to implement and handles the restrictive variable that may ruin the physical nature of the problem.

This study combines Sawi transform (ST) and the homotopy perturbation method (HPM) to formulate the idea of Sawi homotopy perturbation transform method (SHPTM). First, this study implements ST to handle the recurrence relation and then incorporates HPM to derive the series solutions of this recurrence relation. ST has the advantage in that it does not require any assumptions or hypothesis for the evaluation of series solutions.

This strategy finds the results very accurate and close to the precise solution. The graphical observations and the surface solution demonstrate that SHPTM is a reliable and powerful scheme for finding the approximate solution of heat flow problems.

The study presents an original work. This study develops SHPTM for the approximate solution of two- and three-dimensional heat flow problems. The obtained results and graphical representation demonstrate that SHPTM is a very authentic and reliable approach.