3D Heat Research Articles

Quantitative 2D propagation of smallness and control for 1D heat equations with power growth potentials

Quantitative 2D propagation of smallness and control for 1D heat equations with power growth potentials

Cerebroventricular deformation and vector mapping, a topographic visualizer for surgical interventions in pediatric hydrocephalus.

Hydrocephalus is a challenging neurosurgical condition due to nonspecific symptoms and complex brain-fluid pressure dynamics. Typically, the assessment of hydrocephalus in children requires radiographic or invasive pressure monitoring. There is usually a qualitative focus on the ventricular spaces even though stress and shear forces extend across the brain. Here, the authors present an MRI-based vector approach for voxelwise brain and ventricular deformation visualization and analysis. Twenty pediatric patients (mean age 7.7 years, range 6 months-18 years; 14 males) with acute, newly diagnosed hydrocephalus requiring surgical intervention for symptomatic relief were randomly identified after retrospective chart review. Selection criteria included acquisition of both pre- and posttherapy paired 3D T1-weighted volumetric MRI (3D T1-MRI) performed on 3T MRI systems. Both pre- and posttherapy 3D T1-MRI pairs were aligned using image registration, and subsequently, voxelwise nonlinear transformations were performed to derive two exemplary visualizations of compliance: 1) a whole-brain vector map projecting the resulting deformation field on baseline axial imaging; and 2) a 3D heat map projecting the volumetric changes along ventricular boundaries and the brain periphery. The patients underwent the following interventions for treatment of hydrocephalus: endoscopic third ventriculostomy (n = 6); external ventricular drain placement and/or tumor resection (n = 10); or ventriculoperitoneal shunt placement (n = 4). The mean time between pre- and postoperative imaging was 36.5 days. Following intervention, the ventricular volumes decreased significantly (mean pre- and posttherapy volumes of 151.9 cm3 and 82.0 cm3, respectively; p < 0.001, paired t-test). The largest degree of deformation vector changes occurred along the lateral ventricular spaces, relative to the genu and splenium. There was a significant correlation between change in deformation vector magnitudes within the cortical layer and age (p = 0.011, Pearson), as well as between the ventricle size and age (p = 0.014, Pearson), suggesting higher compliance among infants and younger children. This study highlights an approach for deformation analysis and vector mapping that may serve as a topographic visualizer for therapeutic interventions in patients with hydrocephalus. A future study that correlates the degree of cerebroventricular deformation or compliance with intracranial pressures could clarify the potential role of this technique in noninvasive pressure monitoring or in cases of noncompliant ventricles.

Numerical Study of the Influence of Regenerator Structure on the Performance of Hot Blast Stoves

The properties and arrangement of checker bricks in regenerators are crucial for the heat exchange process of hot blast stoves. In this study, a 3D fluid flow heat transfer model is established to analyze the influence of three regenerator layered structures on the combustion and air supply performance of hot blast stoves. The results show that a “silica bricks–high-alumina bricks–clay bricks” three-layer arrangement in regenerators produces a “thermal conduction hindrance effect” at the interface between silica and high-alumina bricks during the 2 h combustion period, which raises the local temperature and improves air supply performance. Compared to the “silica bricks–clay bricks” and “high-alumina bricks–silica bricks–clay bricks” structures, this setup increases the maximum air supply temperature difference to 23 and 64 K, respectively, and extends the effective air supply time by 80 and 320 s, respectively. However, the “thermal conduction hindrance effect” diminishes over longer combustion periods, and by 4 h, the performance across all structures becomes increasingly consistent. Additionally, the study suggests that the temperature level and distribution in the upper part of the regenerator are the key factors determining the air supply performance of hot blast stoves.

Experimental investigation of tailoring functionalized carbon-based nano additives infused phase change material for enhanced thermal energy storage

The advancement of phase change materials (PCMs) as potential thermal energy storage (TES) materials for building envelopes holds promise for efficient energy utilization. However, the PCMs have a major drawback during energy storage, which is lower thermal conductivity, leading to inadequate heat transfer performance and energy storage density. The foremost objective is to formulate a nanocomposite by dispersing functionalized multi-walled carbon nanotubes in salt hydrate PCM with the presence of surfactant. A two-step technique is employed to formulate the nanocomposites with different weight concentrations (0.2, 0.4, 0.6 and 0.8 %) of carbon-based nanoparticles and these nanocomposites are thoroughly characterized to explore the thermophysical properties. Resulting the nanocomposite demonstrates a significant improvement in thermal conductivity, increasing by 91.45 %, which can be attributed to the well-developed thermal networks with the PCM matrix. The nanocomposite samples exhibit extreme thermal stability up to 477 °C with a slight enhancement of 4.6 %. Optical investigations further confirmed that the transmissibility of PCM decreased to 8.3 % from 62.8 %, indicating an enhanced absorption capability due to the dark color nature of the nanoparticles. Moreover, the formulated nanocomposite demonstrated both chemical and thermal stability, with negligible changes in melting enthalpy even after 300 cycles of heating and cooling operations. Additionally, a numerical simulation analysis of 2D heat transfer was performed using Energy 2D software to demonstrate the efficacy of thermal conductivity in heat transfer. The thermally energized nanocomposite is suitable for medium-temperature TES applications such as photovoltaic thermal systems, building applications, textiles, electronic cooling, and desalination systems.

Bayesian inversion for in-situ thermal characterisation of walls in the presence of thermal anomalies

This paper develops a Bayesian inverse modelling framework for the in-situ characterisation of walls' thermal performance in the presence of thermal anomalies subject to uncertainty. For any given wall, the proposed framework uses in-situ contact measurements of temperature and heat flux in order to approximate the (posterior) distribution of a set of parameters which are inputs of a 3D heat transfer model of the wall that accounts for the presence of unknown anomalies. The set of inputs that we infer include (i) the geometry of the thermal anomaly as well was its material properties, (ii) the as-built thermophysical properties of the clear part (i.e. without anomaly) of the wall (iii) surface resistances and (iv) modelling errors that arise from unaccounted sources of uncertainty in the boundary conditions. The geometry of the unknown thermal anomaly is parameterised with a level-set function that is inferred within the proposed Bayesian approach. In order to incorporate prior statistical information of the thermal anomaly, a Gaussian process conditioned on measurements from thermal images is employed to build a prior on the level-set function. The posterior distribution of inferred inputs is approximated via the implementation of an Ensemble Kalman Inversion algorithm that provides stable and accurate approximations of the posterior. This paper also proposes a methodology that uses the inferred 3D model to derive a thermally equivalent 1D model of the wall that is suitable for its integration with existing building energy performance software. The proposed inverse modelling technique is experimentally validated by characterising the thermal performance of an insulation panel in the presence of a thermal anomaly. Our computations show that the proposed approach produces a 3D model that accurately describes thermal performance, and a derived equivalent 1D model that effectively reproduces the dynamic thermal performance of the insulation panel in the presence of the thermal anomaly.

Distribution of the acoustobrightness temperature satisfies heat equation

Passive acoustic thermometry (PAT), a method proposed for medical applications, involves direct measurement of the acoustobrightness temperature which is the intensity of the thermal acoustic radiation expressed in degrees. The hypothesis has been proposed that the acoustobrightness temperature measured on the surface of the object under study obeys the 2D heat equation whose parameters coincide or are uniquely connected with the parameters of the 3D heat equation governing the deep temperature of the object. Since in PAT a noise signal is measured, the achievement of an acceptable error level (0.5–1 K) requires a considerable integration time (about a minute). The proposed hypothesis will enable linking together the data obtained by acoustothermometric sensors separated in space, at different points in time. This, in turn, will lower the dimensionality of the problem of temperature distribution reconstruction and enable reducing the integration time without loss of accuracy. The proposed hypothesis has been confirmed experimentally and with the aid of computer simulation for the case where local hyperthermia of soft tissues of the human organism is modeled.

A comparison of Finite difference schemes to Finite volume scheme for axially symmetric 2D heat equation

In this work, we compare finite difference schemes to finite volume scheme for axially symmetric 2D heat equation with Dirichlet and Neumann boundary conditions. Using cylindrical coordinate geometry, we describe a mathematical model of axially symmetric heat conduction for a stationary, homogeneous isotrophic solid with uniform thermal conductivity in a hollow cylinder with an exact solution in a particular case. We obtain the numerical solution of the PDE adapting finite difference and finite volume discretization techniques. Compared to the exact solution, we explore that the numerical schemes are the sufficient tools for the solution of linear or nonlinear PDE with prescribed boundary conditions. Furthermore, the numerical solution discrepancies in the results obtained from Explicit, Implicit and Crank-Nicolson schemes in Finite Difference Method (FDM) are extremely close to the exact solution in the case of Dirichlet boundary condition. The solution from the Explicit scheme is slightly far from the exactsolution and the solutions from Implicit and Crank-Nicolson schemes are extremely close to the exact solution in the case of Neumann boundary condition. Likewise, the numerical solutions obtained in the Finite volume method (FVM) are extremely close to the exact solution in the case of the Dirichlet boundary condition and slightly away from the exact solution in the case of the Neumann boundary condition.

High-efficiency thermal-electric conversion enabled by water-solid triboelectric nanogenerators within a 3D pulsating heat pipe

At present, effective strategies for obtaining electric energy from harvesting and converting thermal energy have attracted great attention in the field of new energy. According to the working principle of electrostatic induction and triboelectrification, the triboelectric nanogenerators (TENGs) technology is regarded as a promising energy harvester. Herein, we propose a novel thermal-electric generator that combines a liquid-solid TENG and a 3D pulsating heat pipe (3D-PHP). The liquid-solid TENG consists of copper foil and polytetrafluoroethylene (PTFE) tubes, and 50 % deionized water is filled into the 3D-PHP. Based on phase change heat transfer, water columns in the 3D-PHP will pulsate and flow through a liquid-solid TENG, leading to the generation of electric energy. The minimum thermal resistance of this 3D-PHP with TENGs is only 0.131 K/W at a heating power of 200 W, indicating it has excellent heat transfer performance. The peak output voltage and power generated by the developed 3D-PHP generator are up to 14 V and 1.05 μW, respectively. Finally, the harvested electricity is successfully applied to power a digital thermometer. These findings will offer a promising strategy for harvesting thermal energy from electronic equipment and systems involving high-flux heat production and dissipation.

The dimension coupling method for 3D transient heat conduction problem with variable coefficients

In this study, a dimension coupling method (DCM) is presented to study the variable coefficients transient heat conduction problems. The dimension splitting method (DSM) is introduced to split the 3D domain into some 2D domains, which are discretized by selecting the improved element-free Galerkin (IEFG) method; thus the corresponding discretized equation in each 2D domain is derived, and the finite element method (FEM) is employed to deal with these discretized equations in a third direction, and the time-dependent term is discretized by selecting the finite difference method (FDM), thus the final solved equation of the transient heat conduction problems is obtained. In the first example, the convergence is proved by increasing the nodes and meshes on the influence of relative errors. Some numerical results illustrate that the proposed method can substantially enhance the computational efficiency of the IEFG method. When an exact solution of the numerical example is a nonlinear function about splitting direction with natural boundary condition is given, the proposed method has shorter computing time than the hybrid element-free Galerkin (HEFG) method when dealing with this situation.

Understanding the dynamics of in-situ micro-rolling in directed energy deposition using thermo-mechanical finite-element analyses

Rolling in Directed Energy Deposition (DED) has shown promising improvements in build quality by providing compressive deformations. The rolling dynamics and associated boundary conditions are crucial for how these deformations impact the stress–strain profiles on the deposited part and substrate. This study investigates these impacts by developing a fully coupled dynamic-thermo-mechanical finite-element model in Abaqus for in-situ micro-rolling in DED. Single bead analyses have been done with a 2D heat flux moving ahead of the roller at a fixed offset. Two rolling boundary condition cases with varying friction at the roller-bead interface have been examined: (i) only translation defined with rotation calculated from roller-bead interaction and (ii) translation with a defined rotation corresponding to a no-slip condition. In the first case, analyses have shown that the surface stress–strain conditions and rolling load variation are susceptible to interfacial friction. With increasing friction, the surface conditions deteriorate and variations in rolling load increase. However, beyond the surface, the overall stress–strain profiles remain similar. The surface stress–strain profile and rolling load variation have been smoothened in the second case because of the defined rotation. Further, a comparison has been made between the results of dynamic-explicit analyses and static-implicit analyses to quantify the roller’s inertia effects. The stress–strain profiles predicted by both analyses have marginal differences but with 16 % over-prediction in rolling load by dynamic-explicit analyses. These results imply that the roller’s inertia marginally affects the deposited part’s stress–strain evolution but has a notable role in rolling load. Also, providing an external drive to the roller corresponding to the second case can effectively minimise the deteriorating effects of roller-bead interfacial friction.

Panoramic heat map for spatial distribution of necrotic lesions.

In this study, we aimed to visualize the spatial distribution characteristics of femoral head necrosis using a novel measurement method. We retrospectively collected CT imaging data of 108 hips with non-traumatic osteonecrosis of the femoral head from 76 consecutive patients (mean age 34.3 years (SD 8.1), 56.58% male (n = 43)) in two clinical centres. The femoral head was divided into 288 standard units (based on the orientation of units within the femoral head, designated as N[Superior], S[Inferior], E[Anterior], and W[Posterior]) using a new measurement system called the longitude and latitude division system (LLDS). A computer-aided design (CAD) measurement tool was also developed to visualize the measurement of the spatial location of necrotic lesions in CT images. Two orthopaedic surgeons independently performed measurements, and the results were used to draw 2D and 3D heat maps of spatial distribution of necrotic lesions in the femoral head, and for statistical analysis. The results showed that the LLDS has high inter-rater reliability. As illustrated by the heat map, the distribution of Japanese Investigation Committee (JIC) classification type C necrotic lesions exhibited clustering characteristics, with the lesions being concentrated in the northern and eastern regions, forming a hot zone (90% probability) centred on the N4-N6E2, N3-N6E units of outer ring blocks. Statistical results showed that the distribution difference between type C2 and type C1 was most significant in the E1 and E2 units and, combined with the heat map, indicated that the spatial distribution differences at N3-N6E1 and N1-N3E2 units are crucial in understanding type C1 and C2 necrotic lesions. The LLDS can be used to accurately measure the spatial location of necrotic lesions and display their distribution characteristics.

Influence of different Reynolds numbers and new geometries on water jacket cooling performance in a CI engine

Physical damage and emission increases that may occur in the engine due to uncontrolled temperature increases are prevented by cooling systems. In this study, the water jacket (WJ) of the F-Type F8Q706 engine was examined for different Reynolds numbers and geometries. With a combined examination approach, engine tests, 1D engine model, 3D in-cylinder combustion (ICC) model, and 3D WJ CFD studies are presented together, for the first time. Accordingly, a 3D WJ CFD model was developed using in-cylinder parameters calculated from 1D and 3D ICC which were verified by tests. Engine powers in 1D and 3D models, heat transfer, liner temperature, and heat flux in WJ models were compared. The engine powers at 2500 rpm with wide-open throttle are as follows: 1D (33.610 kW), 3D ICC (32.075 kW), engine catalog test (30.890 kW), and a literature test (29 kW). In the WJ model, instead of the Reynolds number 22,128.97, values of 18,440.81–15,367.34–12,806.11–1067.76–8893.14–7410.95–6175.79 were used. In this case, heat transfer decreased by 11.224%–20.844%–29.940%–38.168%–45.723%–52.874%–59.340%. Liner temperature increased by 3.962%–7.505%–10.879%–13.958%–16.800%–19.470%–21.822%. As the Reynolds number decreased, heat transfer decreased, and liner temperature increased. In the WJ, uncontrolled temperature increases were seen in areas farthest from the water inflow. Unlike studies using nanofluids, a new WJ geometry with 169 fins was developed for cooling performance. Nanoparticles cause damage to elastomeric system elements, clogging, and corrosion in lines. This geometry increased heat transfer by 42.01% and reduced liner surface temperatures by 48.28% for 22,128.966 Re. Repeated analyses showed that the fins increased heat transfer.

A reality-augmented adaptive physics informed machine learning method for efficient heat transfer prediction in laser melting

Physics informed neural network (PINN) method is proposed to alleviate problems in many science and engineering scenarios when data-collection is difficult, or traditional numerical calculations are lack of convenience because more time-consuming numerical calculations are required whenever one or more parameters of the process is changed. However, for advanced manufacturing processes like laser melting (LM), a basis of laser metal additive manufacturing, involve many complex physical phenomena (e.g. melting, convection, solidification, vaporization and interface evolution), the full equations of which are too complex to be solved by current PINN. This paper proposes a reality-augmented adaptive physics informed machine learning (RAA-PIML) method to meet the objectives of precise and fast predictive LM. It applies adaptive function, integrating heat transfer law and boundary condition equations to loss function, which has fast convergence and strong physics-based constraints. The reality-augmented data are acquired by few experiments and an accurate 3D heat transfer model covering turbulence. The conducted experimental results demonstrate that the developed solution exhibits higher efficiency than simulation, and superior performance than state-of-the-art methods, which shows outstanding potential in industry applications.

Adaptive identification of linear infinite-dimensional systems

We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an adaptive update law (a differential equation in time) driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown linearly-varying (in space) coefficient.

Three-dimensional analysis reveals diverse heat wave types in Europe

Heat waves are among the most studied atmospheric hazards but commonly investigated near-surface temperature patterns provide only limited insight into their complex structure. Here we propose and evaluate a novel approach to the analysis of heat waves as three-dimensional (3D) phenomena, employing the ERA5 reanalysis in three European regions during 1979–2022. Four types of heat waves based on their vertical cross sections of temperature anomalies are introduced: near-surface, lower-tropospheric, higher-tropospheric, and omnipresent. The individual heat wave types differ in length, predominant occurrence within summer, and soil moisture preconditioning. While near-surface heat waves may persist for more than 2 weeks, those located mainly in higher troposphere are shortest (5 days at most). This demonstrates that warm advection must be accompanied by a downward propagation of positive temperature anomalies through air subsidence and diabatic heating to maintain long-lasting heat waves. We also show that soil-moisture preconditioning is crucial for near-surface heat waves only, thus pointing to different driving mechanisms for the individual 3D heat wave types.

Investigation of novel type of cylindrical lithium-ion battery heat exchangers based on topology optimization

The in-depth research on the heat exchanger for lithium-ion batteries is of significant importance due to its crucial role in ensuring the safe operation of electric vehicle (EV) power systems. To enhance the thermal and flow characteristic of the heat exchangers, the novel heat exchangers for 18650-cylinderical lithium-ion batteries have been proposed by topology optimization with the minimization of pressure drop and the lowest average temperature (∏1) and the minimization of pressure drop and the lowest temperature difference (∏2) as two different optimal goals. The topology optimization based on the variable density method is utilized to get two-dimensional (2D) optimal channels, and then the optimized results are extended to three-dimensional (3D) heat exchangers. The 3D heat exchangers are named TOHE-1 which is gotten by stretching the topology channels with ∏1 as optimal goal and TOHE-2 which is gotten by that with ∏2 as optimal goal. Subsequently, a detailed thermodynamic analysis is performed to assess the effect of the type of heat exchangers, channel heights, weight factor of topology optimization function, mass flow rates and discharge rates on the cooling effect of the batteries. The results show that compared with the traditional channel heat exchangers, the heat transfer coefficient of topological heat exchangers have increased by 49.92%, while reducing pressure drop by 27.81%. Meanwhile, compared to TOHE-1, heat transfer coefficient of TOHE-2 is increased by 9.70%, while pressure drop is saved by 4.70%. Other studies have indicated that for a 4 C discharge of the battery, a topological heat exchanger with a channel height of 1.5 mm, a thermal performance weight factor of 0.1, and a mass flow with 3.3 × 10−3 kg s−1 is the optimum heat dissipation scheme. Finally, the numerical studies are verified by conducting the convective heat transfer experimental tests.

A Bayesian Spatiotemporal Modeling Approach to the Inverse Heat Conduction Problem

Abstract This study introduces a Bayesian spatiotemporal modeling approach to solve inverse heat conduction problems (IHCPs), employing penalized splines within a spatiotemporal forward model. The complexity and ill-posed nature of IHCPs, characterized by potential nonexistence, nonuniqueness, or instability of solutions, pose significant challenges for traditional methods. Addressing this, our study presents a spatiotemporal forward model that incorporates spatial, temporal, and interaction terms, accurately capturing the intricate dynamics inherent in IHCPs and using this information as a leverage to solve the inverse problem. We adopted a Bayesian inference framework for the subsequent parameter estimation problem and developed a Gibbs sampling algorithm to sample from the posterior distribution of the model's parameters, enhancing the estimation process. Through case studies on a one-dimensional (1D) heat simulation and a pool boiling experiment using multisensor thermocouple data for heat flux reconstruction, we demonstrate the model's superiority over traditional methods. The inclusion of the spatiotemporal interaction term significantly enhances model performance, indicating its potential for broader application in solving IHCPs. The application of this method in both simulated and real-world scenarios highlights its effectiveness in capturing the spatiotemporal complexities of IHCPs. This work contributes to the field by offering a robust methodology for addressing the spatial and temporal complexities inherent in IHCPs, supported by a comprehensive Bayesian inference framework and the use of a Gibbs sampling algorithm for parameter estimation.

Empirical loss weight optimization for PINN modeling laser bio-effects on human skin for the 1D heat equation

The application of deep neural networks towards solving problems in science and engineering has demonstrated encouraging results with the recent formulation of physics-informed neural networks (PINNs). Through the development of refined machine learning techniques, the high computational cost of obtaining numerical solutions for partial differential equations governing complicated physical systems can be mitigated. However, solutions are not guaranteed to be unique, and are subject to uncertainty caused by the choice of network model parameters. For critical systems with significant consequences for errors, assessing and quantifying this model uncertainty is essential. In this paper, an application of PINN for laser bio-effects with limited training data is provided for uncertainty quantification analysis. Additionally, an efficacy study is performed to investigate the impact of the relative weights of the loss components of the PINN and how the uncertainty in the predictions depends on these weights. Network ensembles are constructed to empirically investigate the diversity of solutions across an extensive sweep of hyper-parameters to determine the model that consistently reproduces a high-fidelity numerical simulation.

Maximizing liquid-cooled heat sink efficiency with advanced topology-optimized fin designs

Direct-to-chip liquid cooling offers significant advantages in managing higher power densities compared to traditional air-cooling methods. This approach utilizes nearly half the power required by server fans and air conditioners, enhances cooling efficiency in data centers. The effectiveness of this cooling strategy is intricately linked to the layout of the cold plate fins. In this research, a density-based topology optimization method is implemented in generating free-forming and non-intuitive fin structures. A pseudo-optimization model, which approximates the 3D heat sink as two 2D thermally coupled problem is selected and optimized with ‘pressure drop’ and ‘average junction temperature’ as objective function and constraint, respectively. Several fin layouts with inlet flow velocities and temperature constraints are generated. Three-dimensional numerical simulations reveal that the average junction temperature with the topology-optimized fin pattern is ∼2°C higher, and the pressure drop is significantly lower compared to size-optimized straight channel. Building on this, an inverted topology-optimized design is introduced along the channel length, inspired by the wavy nature of sectional fins. The average junction temperature with the inverted TO design is 3 to 4°C lower compared to the straight design, with a similar pumping power of 0.023 W. The TO fin layout capitalizes on frequent re-initialization of boundary layers, secondary flow-induced mixing, and the formation of Dean vortices along the channel length. Further refinement leads to the derivation of drop-oblique-trapezoidal and oval-shaped (DOTO) fins. These fins reduce average junction and wall temperatures by ∼23% compared to the inverted TO design, owing to the persistent effects of fluid dynamic phenomena along the channel length. Comparison with benchmarked designs indicates that DOTO fins reduce the average junction temperature by 3 to 6°C compared to size-optimized offset strip fins and step fins, with a similar pumping power of 0.083 W. The study indicates that optimizing DOTO fins dimensions can further enhance heat sink performance.

Graphics‐Processing‐Unit‐Accelerated 3D Online Heat Transfer and Solidification Model for Continuously Cast Slab

A graphics‐processing‐unit (GPU)‐accelerated 3D heat‐transfer and solidification model is proposed to predict the temperature field and solidification field for continuously cast slab. The fully 3D model is developed based on the finite difference method and implemented on the compute unified device architecture (CUDA)/C++ platform. The model is verified by solving the 1D Stefan problem and validated by surface temperature measurements. The model is proven to be 18.91 times faster for the coarsest mesh of 35 million nodes and 22.92 times faster for the finest mesh of 50 million nodes than a central‐processing‐unit (CPU)‐based parallel version with 28 threads. The corresponding relative calculational times are 0.19 and 0.32, which indicate that the model has great computation efficiency. The model is proven to be robust enough for the dynamic continuous casting (CC) process via a test of dynamic casting speed. Further analysis of the nonuniform heat transfer and solidification shows that the model is able to predict the nonuniform heat transfer efficiently. In the studied cases, a higher casting speed will lead to a remarkable enhancement of the unevenness of heat transfer and solidification in general.