In this communication, a novel strategy is presented for addressing advection-conduction problems with solid <-> liquid phase change by using a modified implementation of the improved element-free Galerkin (IEFG) method. The approach involves a deferred inclusion of non-linear effects related to temperature-dependent material properties and the latent heat exchanged during phase change, incorporated within thermal load vectors. The temperature and solid phase fraction gradients needed to construct these thermal load vectors are computed iteratively within the non-linear solution process, delaying their assembly until required. This deferred approach eliminates the need for temperature derivatives of the solid or liquid fraction in the core problem formulation, a component that often complicates convergence when using conventional effective specific heat methods. A comprehensive description of the iterative process is given, along with the method for obtaining solid phase fraction gradients using a global reconstruction based on improved moving least squares (IMLS). The technique is rigorously validated through a 1-D advection-conduction phase change problem with an analytical solution and a 3-D application in direct chill casting of AA-1050 aluminium alloy. Outcomes demonstrate that this method not only enhances convergence over traditional effective specific heat techniques, but also achieves a substantial reduction in computational time.

A novel Overset Improved Element-Free Galerkin-Finite Element Method (Ov-IEFG-FEM) for solving transient heat conduction problems with concentrated moving heat sources is introduced in this communication. The method is a mesh-less/mesh-based chimera-type approach that utilises a coarse finite element mesh to discretise the problem geometry, while a separate set of overlapping nodes (patch nodes) moves with the heat source to capture the marked thermal gradients with higher accuracy using the Improved Element-Free Galerkin (IEFG) technique. Outside of the heat source area, where accuracy requirements are significantly lower, the thermal problem is solved using the Finite Element Method (FEM). The approach involves solving the problem over these two overlapping computational domains and transferring numerical information between the approximations performed on both. Such transfer of information occurs through immersed boundaries that are properly defined, enabling straightforward achievement of accurate results. The proposed Ov-IEFG-FEM is conceived to provide an enriched solution by appropriately coupling the temperature fields computed on the patch nodes and the coarse background mesh using IEFG and FEM, respectively. A comprehensive explanation concerning the appropriate coupling between the temperature fields of both the coarse background finite element mesh and the fine arrangement of moving patch nodes for the IEFG computations, is also provided in this communication. Numerical experiments demonstrate the method effectiveness in accurately and efficiently solving transient heat conduction problems with concentrated moving heat sources.

Forced convection heat transfer problems are successfully solved in this work via a simple staggered approach based on the improved element-free Galerkin (IEFG) formulation, which involves a fluid-dynamic analysis conducted in the framework of Navier–Stokes equations written in terms of velocity via a reduced integration penalty method (RIPM). Subsequently, the velocity field achieved from the solution of the Navier–Stokes equations is used in the IEFG-based solution of the internal energy balance formulated in terms of temperature. The proposed approach is tested in the solution and analysis of forced convection heat transfer problems concerning (i) the simultaneously (thermally and fluid-dynamically) developing flow between parallel plates and, (ii) the confined recirculating flow in non-isothermal lid-driven square cavities (also including viscous dissipation effects). A comprehensive parametric analysis developed in terms of characteristic dimensionless numbers is conducted for both problems, providing reliable benchmark results that will be useful to assess the performance of numerical techniques to model forced convection heat transfer phenomena. The versatility and reliability of the proposed approach are also demonstrated in the solution of a more complex problem with curved geometry, such as the non-isothermal lid-driven semicircular cavity with a circular obstacle. The accuracy and feasibility of solving forced convection heat transfer problems via the mesh-less procedure proposed in this communication are proven by comparison with results achieved via mesh-based techniques, and also with analytical solutions available in the literature. The outcomes demonstrate that the appropriate implementation of such numerical technique allows the achievement of accurate and stable results in a straightforward and remarkably simple manner, even under markedly advection-dominated flow conditions in both thermal and fluid dynamics problems.

A novel approach to solve the transient heat conduction problem with moving boundary and solid + liquid phase change involved in the start-up stage of direct chill casting (DCC) processes is introduced in this work, which is based on the improved element-free Galerkin (IEFG) method. The procedure is developed under a temperature-enthalpy mixed formulation of the internal energy balance, but the construction of improved moving least squares (IMLS) is required only to approximate temperature. The reliability and suitability of this approach have been first proven in a 1-D alloy solidification benchmark problem with exact solution, and subsequently used to solve a more complex three-dimensional applied ther-mal problem concerning the start-up stage of the DCC process of an aluminium alloy slab. The domain growth conditioned by the bottom block (moving boundary) is modelled moving down the nodes used to represent the problem domain at each time step, and adding a new nodes plane at the domain upper boundary. Outcomes have revealed the usefulness of this technique to overcome the difficulties concern-ing solid + liquid phase change marked non-linearities and moving boundaries involved in the transient analysis of DCC heat transfer problems, allowing the achievement of accurate and stable results in a re-markably simple manner. (c) 2023 Elsevier Ltd. All rights reserved.

This work introduces the sequential quasi-Newton method (SQNM) to solve the inverse design problem of estimating the transient boundary heat fluxes that produce desired evolutions of the solidus and liquidus isotherms in alloys' solidification processes. This is an unprecedented application for sequential gradient-based methods. The final goal is monitoring and controlling the evolution of the mushy zone in a near real-time fashion, which is of high technological interest to the foundry industry. We assess the performance of the SQNM in solving several inverse design problems in one- and two-dimensional domains. The method satisfactorily estimates the boundary heat fluxes using relatively few future measurements. However, some instabilities have been detected in the SQNM-predicted heat fluxes. To alleviate this issue, we proposed a modified version of SQNM, say mSQNM, that employs an inexact line search strategy to find the optimal step length during the iterative estimation procedure. We finally show how mSQNM improves the estimation of the boundary heat fluxes.

A novel overlapping nodes scheme developed in the framework of an improved element-free Galerkin (IEFG) formulation is introduced in order to solve the transient heat conduction problem with a moving heat source involved in arc welding processes, in an accurate and remarkably simple manner. The proposed approach consists in solving the aforementioned problem over two overlapping arrangements of nodes, which transfer temperature and heat flux information each other through properly defined immersed boundaries. A fine arragement of nodes (patch nodes) moves with the heat source over a coarse background nodes distribution, and the solution is enriched via an appropriate coupling of the temperature approximations computed over both arrangements. The patch nodes are conceived to achieve an accurate computation of the temperature distribution and corresponding heat fluxes in the heat source vicinity, whose effects cannot be properly captured by the coarse background arrangement. A detailed explanation concerning the appropriate coupling between the temperature fields of both the background and patch nodes, is also provided in this communication. The outcomes of this study reveal that the proposed Overset-IEFG (Ov-IEFG) formulation allows the achievement of very accurate, smooth and stable solutions for both temperature and heat flux fields, without the need of resorting to post-processing or additional local reconstruction techniques.

In this communication, we introduce an online sequential implementation of a gradient-based method for reconstructing transient heat transfer coefficients in the context of non-linear one-dimensional heat conduction problems. Such a method employs a quasi-Newton updating strategy for computing the descent direction, in contrast with the traditional approach based on the conjugate gradient method. We denote the resulting procedure as the sequential quasi-Newton method (SQNM). The performance of the proposed algorithm was tested in the reconstruction of triangle-, sine-, and square-wave functions that models different transient heat transfer coefficients and compared with the results obtained using a standard sequential function specification method. The SQNM was capable of properly reconstruct the aforementioned exact functions independently of the location of the temperature sensors within the body. The proposed strategy is fast, robust, and reliable, which demonstrates the suitability of employing the sequential gradient-based implementation, together with the quasi-Newton updating strategy, for reconstructing transient heat transfer coefficients in the context of one- and two-dimensional non-linear heat conduction problems. Thus, the proposed method is a novel alternative strategy to other online inverse estimation procedures.

In this work, we propose the extension of total variation regularization strategies in principle formulated to be implemented in image processing and signal analysis research fields, to the solution of one-dimensional linear inverse heat conduction problems concerning the estimation of surface heat fluxes. Three solution procedures are considered in the current study, and these include the lagged diffusivity fixed point iteration, the iteratively reweighted least-squares, and the split Bregman iteration methods. The performance of such procedures is tested using four cases, and the regularization parameter is selected via the L-curve criterion. The results are compared to the reconstruction obtained via a classical Tikhonov-like strategy. The main outcome is that the staircase effect dominated all the reconstructions. Despite it deteriorated the quality of the solutions in some specific cases, it did not prevent the appropriate fulfillment of the reconstruction task. The results achieved in this communication have been useful to demonstrate the suitability and reliability of extending total variation approaches to the solution of linear inverse heat conduction problems concerning the estimation of surface heat fluxes, as an appropriate and novel alternative to standard procedures.

The present work introduces the optimization-based approach for the design of metadevices to manipulate the heat flux in transient regime. It consists of solving a continuous, nonlinear, constrained, large-scale optimization problem where the objective function (to be minimized) is the error in accomplishing a given heat flux manipulation task along a transient heat conduction process. The response of the metadevice is modeled by using the finite element method, and its design is characterized by a set of parameters defining the material at all the finite elements in the device. These parameters are the design variables of the optimization problem, being chosen from an admissible design set in order to guarantee the feasibility of the optimal solution. As an example, this optimization-based approach is applied to the design of a heat flux shielding metadevice. Compared to a metadevice designed under the classical thermodynamics transformation approach and intuition, the current device performs the shielding task with considerably higher success. In order to highlight the versatility of the proposed optimization-based design method, this approach is also applied to the design of metadevices to satisfy multiple different simultaneous tasks, particularly shielding and cloaking.

The present work has been conducted in order to propose an alternative solution for the heat transfer problem involved in direct-chill casting (DCC) processes, employing the element-free Galerkin (EFG) method. The internal energy balance has been solved on the basis of this global weak formulation under an Eulerian description. The EFG formulation has been adapted to a three-dimensional steady thermal problem on an aluminum alloy slab. Additionally, the advection dominated problem involved in the casting direction during the liquid-solid phase change has been stabilized by extending adequately the implementation of the stream upwind Petrov–Galerkin (SUPG) scheme to the EFG formulation. A detailed explanation concerning the suitable numerical procedure to achieve such an extension, has also been provided. The feasibility and reliability of this novel approach has been depicted by comparison with both finite element method (FEM) and finite volume method (FVM) based solutions. The results have demonstrated that a proper extension of the SUPG scheme to the EFG method allows the achievement of stable numerical solutions, when predicting the three-dimensional temperature distribution during the phase-change heat transfer phenomena involved in slab DCC processes.

Topology optimization refers to the problem of designing a structure by distributing a limited volume of material inside a fixed domain (the so-called design domain) in order to optimally accomplish a certain objective (frequently, to maximize the stiffness of the structure). In most cases, the loads on the structure are assumed to be given. However, in the case of self-weight and surface pressure, the loads are design-dependent. In thermal problems, design-dependent loads appear with boundary heat flux and convection. Until today, design-dependent boundary conditions thermal problems are mostly dealt by regularization of the heat flux through the solid/void interface, leading to large errors in typical topology optimization thermal problems like the design of heat exchangers where the optimal design has a high surface/volume ratio. In this work, we introduce a density-based topology optimization method for the solution of heat conduction problems with boundary convection, avoiding the regularization of the thermal loads along the solid/void interface. The conductivity of the material in a finite element of the design domain is defined as a function of a volume density that is continuous in the interval [0,1], which is the design variable of the optimization problem, following the classical SIMP method. Then, the contribution to boundary convection of each element interface is determined by a Surface density, continuous in [0,1] as well as the classical volume density. This new density is completely determined by the volume densities of the neighbor elements, so that the treatment of boundary convection does not require additional design variables. Finally, we provide examples to highlight the advantages of the current method with respect to the existing topology optimization method with regularized thermal loads.