Heat Transfer Boundary Conditions Research Articles

A new analytical model for transient heat transfer modeling of geothermal monotube heat exchangers

In this study, we present a new analytical model for the analysis of transient heat transfer (the model is solved after Laplace transformation) in geothermal monotube heat exchangers (GHE). The model accounts for various factors, including the heat exchanger's geometric parameters, the nature of the fluid (air and water), flow characteristics (laminar and turbulent), and heat transfer boundary conditions. Initially, the model's performance is validated by comparing its results with those obtained from computational fluid dynamics simulations using OpenFOAM. This validation process ensures the reliability and accuracy of the model. Additionally, an analysis of the heat transfer mechanisms and key modeling parameters identified from the comparison is provided. In the subsequent section, the analysis is extended by comparing the proposed model to four existing analytical models available in the literature. These reference models employ distinct approaches to simulate heat transfer to the ground. By examining a range of cases, the performance of the model is systematically evaluated against these conventional methods. This work closes by an analysis of the analytical models and the impact on the accuracy of the results highlighting the advantages of the proposed method in geothermal applications.

Predicting transformer temperature field based on physics‐informed neural networks

AbstractThe safe operation of oil‐immersed transformers is critical to the safety and stability of the power grid. As the operating time increases, the failure rate of oil‐immersed transformers shows an increasing trend, posing serious challenges to safe operation. It is necessary to investigate the internal state of the oil‐immersed transformer to improve the digital degree and achieve digitalisation and intelligent operation and maintenance. A physics‐informed neural network (PINN) for oil‐immersed transformers was introduced to reconstruct the temperature distribution inside the transformer. According to the approach, the loss function of the network would be optimised by incorporating physical constraint loss terms including heat transfer equations, initial conditions and boundary conditions. The results show that the method proposed can be used to reconstruct and predict the temperature field of transformers in a few seconds with satisfactory accuracy. In conclusion, the PINN proposed outperforms deep neural networks in terms of accuracy, reliability and interpretability, especially in data‐poor cases.

Theoretical and numerical investigation of introduced errors in surface temperature measurements of pistons applied in internal combustion engine

DMP (Differences in Material Properties) often exists between temperature sensors and combustion chamber components of ICE (Internal Combustion Engine), resulting in IEs (Introduced Errors) in the temperature measuring process. In this paper, we present a comprehensive theoretical analysis of the correlation between introduced errors on chamber components and the DMP. The analysis process considers the characteristics of the chamber's heat transfer BC (Boundary Condition). Then, simulations are used to investigate the introduced error of hardness plug and thermocouple sensors on the top surface of an ICE aluminum alloy piston. The theoretical analysis results indicate that heat transfer BC can be segmented into the time-averaged and fluctuation parts, and IEs are linearly superimposed under these two parts of BCs. The heat conductivity impacts the time-averaged error and the product of heat conductivity, density, and heat capacity impacts the fluctuation error. The experimental and simulation results indicate that the max time-average error of the hardness plug on piston is 2.4 °C, with a fluctuation introduced error of 3.6 °C and a total introduced error of 6 °C; and the time-average introduced error of thermocouple sensor is 9.4 °C, with a fluctuation error of 5.8 °C and a total introduced error of 15.2 °C. Finally, a fluctuation error correction method is proposed to reduce error. After correction, the error is reduced by 71 % and 66 % for hardness plug and thermocouple, respectively.

A between-wall heat transfer simulation approach based on the lattice Boltzmann method and its application in tube heat transfer analysis

Between-wall heat transfer is a fundamental physical process. As a typical coupling heat and mass transfer process, between-wall heat transfer-based problems can be solved conveniently on the basis of advanced computation methods among which the lattice Boltzmann method (LBM) has been widely used in the analysis of simple heat and mass transfer cases. To investigate the applicability of LBM in more complex solid-fluid coupling heat transfer analysis, a 3D fluid-solid-fluid model was established in this work to carry out between-wall heat transfer simulations using the doubled-population LBM. Three independent simulation regions were coupled in the heat transfer model, and the heat flux was taken as the physical quantity that transferred from the region at high temperature to that at low temperature through solid wall. The simulation results satisfactorily agree with that obtained using the commercial code FLUENT. Furthermore, an equivalent fluid-wall-fluid heat transfer model was established for simulation of heat transfer between internal and external fluids through a circular tube. All the boundaries are complete quadrilaterals on which heat transfer boundary conditions can be conveniently applied. The proposed between-wall model based on LBM can be easily established and applied in cases with internal heat source or mass force.

Formation Rate and Energy Efficiency of Ice Plug in Pipelines Driven by the Cascade Utilization of Cold Energy

Ice plug technology is an effective method for isolating the pipeline system, which are promising methods utilized in the nuclear, chemical, and power industries. To reduce the cold energy consumption and temperature stress, the multi-stage (1–10) of time-dependent thermal boundary conditions was proposed for the formation of ice plug, while the gradient cooling wall temperature of multi-stage was applied. A numerical model considering the liquid–solid phase change, heat transfer, and time-dependent thermal boundary condition has been established. The effects of the ratio of length and diameter of the cooling wall lc/d (1–9) on the formation rate and heat flux of ice plug in the pipe has been investigated. The fastest formation rate of ice plug with 800 mm in the axial direction (7.47 cm3/s) was observed in the pipe with the lc/d of 5. The formation rate of ice plug and the ice formation volume under unit energy consumption VE under various stages (1–10) of cooling wall temperature have been compared. The VE of eight temperature stages (1.45 cm3/kJ) was 1.16 times than the VE of one temperature stage, which satisfied the freezing rate at the same time. This investigation provides insight for proposing an energy-saving system for the formation of ice plug.

Optimizing heat transfer rate and sensitivity analysis of hybrid nanofluid flow over a radiating sheet: Applications in solar-powered charging stations

In a solar collector system, absorbing radiation through solar panel and transforming it into heat, the role of nanofluid is vital. However, the combined effect of CuO and Cu water hybrid nanofluid efficiently carries the fascinated heat away from the solar collector. Further, it helps improve in efficiency of the thermal solar thermal system by enhancing heat transfer and thermal losses. Based upon the advanced properties, the study aims at the behavior of a conducting hybrid nanofluid comprised of CuO and Cu nanoparticles through a nonlinear stretching surface filled with a porous matrix. Essentially, the use of thermal radiation with dissipative heat and convective heat transfer boundary conditions are important in enhancing heat transfer properties. The assemble of diversified similarity rules is useful for the transformation of the governing equations into dimensionless form. Further, numerical technique with the help of built-in function bvp4c in MATLAB is employed for the solution of the designed model equipped with different constraints. A robust statistical analysis i.e. response surface methodology (RSM) combined with analysis of variance (ANOVA) is used to optimize the heat transfer rate. Sensitivity analysis for the associated factors united to the response of heat transfer is obtained and presented briefly. Finally, the parametric behavior is important to describe following the pattern of the graph. Further, the important outcomes are; the enhanced volume fraction of the nanoparticles augments the fluid velocity as well as the temperature significantly. Thermal radiation has influential behavior in enhancing the heat transport phenomenon of hybrid nanofluid.

Analytical Model of Quantitative Texture Prediction Considering Heat Transfer Based on Single-Phase Material in Laser Powder Bed Fusion

Laser powder bed fusion (LPBF) is widely used in metal additive manufacturing to create geometrically complex parts, where heat transfer and its affected temperature distribution significantly influence the parts’ materials’ microstructure and the resulting materials’ properties. Among all the microstructure representations, crystallographic orientations play a paramount role in determining the mechanical properties of materials. This paper first developed a physics-based analytical model to predict the 3D temperature distribution in PBF considering heat transfer boundary conditions; heat input using point-moving heat source solutions; and heat loss due to heat conduction, convection, and radiation. The superposition principle obtained temperature distributions based on linear heat sources and linear heat loss solutions. Then, the temperature distribution was used to analytically obtain the texture grown on a substrate with random grain orientations considering columnar-to-equiaxed transition (CET). Thus, the link between process parameters and texture was established through CET models and physical rules. Ti-6Al-4V was selected to demonstrate the capability of the analytical model in a single-phase situation. By applying advanced thermal models, the accuracy of the texture prediction was evaluated based on a comparison of experimental data from the literature and past analytical model results. Hence, this work not only provides a method of the fast analytical simulation of texture prediction in the single-phase mode for metallic materials but also paves the road for subsequent studies on microstructure-affected or texture-affected materials’ properties for both academic research and industrial applications. The prediction of single-phase material texture has never been achieved before, and the scalability has been expanded.

Pool Fires Within a Large Under-Ventilated Environment: Experimental Analysis and Numerical Simulation Using OpenFOAM

Experimental analyses and numerical simulations are carried out on a test case involving an heptane pool fire within a large under-ventilated environment. During the experiments, the temperature history at several locations within the room is monitored by means of thermocouples, and the fire radiative heat transfer estimated through a plate thermocouple. The experimental layout is then replicated numerically and tested using OpenFOAM CFD code. The study is a preliminary analysis performed for code validation purposes on a full-scale fire scenario. The results of the simulations are compared to the experimental results and critically analysed, finding a reasonable agreement overall. Critical issues in fire modelling are also highlighted. In fact, due to the problem complexity and the limitations of the numerical models available some important aspect that can significantly influence the outcome of the simulations must be calibrated a posteriori, somewhat limiting the general predictive applicability of the fire models. Primarily, these are the heat release rate history, the combustion efficiency, and, to a lesser extent, the convective heat transfer boundary condition at the wall.

The Robin boundary condition for modelling heat transfer

The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice.

Unraveling the surface heat flux heterogeneity in cone calorimetry of cylindrical charring material: Insights from experiments and 2D modeling

Although originally designed for planar samples, cone calorimeter is frequently used for the flammability assessment and pyrolysis modeling of non-planar objects, like electrical cables. Prescribing the boundary conditions for the numerical models of such objects requires knowledge about the radiative and convective heat fluxes along the sample circumference. In this work, we performed gasification and flaming experiments and 2D numerical simulations on birch cylinders. During the gasification of a single-rod, the char front propagated faster vertically than horizontally, while similar rates were observed in the flaming condition. With five rods, ∪- and ∩-shaped char fronts were observed in gasification and flaming conditions, respectively. From the simulations, we extracted detailed heat flux distributions, with main deviation from flat samples being the steep reduction in incident radiation between the top and sides of the cylinders. Moreover, in five-rod configurations, radiative flux to the sides of the central rod increases up to 10 (gasification) and 20 kW m−2 (flaming). On the outermost rod, the descending flame induces downward-moving waves of heat fluxes with amplitudes 20 kW m−2 for convection and 15 kW m−2 for radiation. Simplified expressions for the heat transfer boundary conditions were tabulated for practical engineering applications.

Numerical Model of Simultaneous Multi-Regime Boiling Quenching of Metals

This work presents a heat transfer and boiling model that computes the evolution of the temperature field in a representative steel workpiece quenched from 850 or 930 °C by immersion in water flowing at average velocities of 0.2 or 0.6 m/s, respectively. Under these conditions, all three boiling regimes were present during cooling: stable vapor film, nucleate boiling, and single-phase convection. The model was based on the numerical solution of the heat conduction equation coupled to the solution of the energy and momentum equations for water. The mixture phase approach was adopted using the Lee model to compute the rates of water evaporation–condensation. Heat flux at the wall was calculated for all regimes using a single semi-mechanistic model. Therefore, the evolution of boiling regimes at every position on the wall surface was automatically determined. Predictions were validated using laboratory results, namely: (a) videorecording the upward motion of the wetting front along the workpiece wall surface; and (b) cooling curves obtained with embedded thermocouples in the steel probe. Wall heat flux calculations were used to determine the importance of the simultaneous presence of all three boiling regimes on the heat flux distribution. It was found that this simultaneous presence leads to high heat flux variations that should be avoided in production lines. In addition, it was determined that the corresponding inverse heat conduction problem to estimate the active heat transfer boundary condition must be set-up for 2D heat flow.

ON ONE PROBLEM OF OPTIMAL CONTROL OF VIBRATIONS OF A PLATE-STRIP IN A TEMPERATURE FIELD

The problem of optimal control of elastic vibrations of an isotropic plate-strip under the influence of temperature and force fields is studied. The function of changing the external load on the plane of the plate is represented as a control function. Optimal control is also carried out by the distribution function of the temperature of the external field over the plate. The well-known classical hypotheses of thermo-elastic bending of the plate are accepted. The equations of transverse vibrations of the plate and heat conduction in the plate are solved under the boundary conditions of heat transfer and the stress state on the planes of the plate. The method of Fourier series, the method of representing moment relations, the well-known method of minimizing the functional are used.

The use of Thermography to Determine the Boundary Conditions of Heat Exchange on The Inner Surfaces of Translucent Enclosing Structures

The paper presents an approach to determining the boundary conditions of heat transfer (heat transfer coefficients) on the inner surfaces of translucent enclosing structures using thermal imaging data. To implement this approach, it is necessary to use additional equipment in the form of sheets of paper. A sheet of paper is installed close to and perpendicular to the investigated surface of the structure. At the same time, the profile of the sheet of paper exactly repeats the geometry of the surface under study. Based on the results of thermal imaging, thermograms and temperature graphs are constructed on characteristic areas of the inner surface of the translucent enclosing structure. They are used to determine the thickness of the boundary layer of air adjacent to the inner surface of the translucent enclosing structure. These data are used later to calculate the heat transfer coefficient at the inner surface of these structures. The presented approach was implemented in the course of field studies of heat transfer conditions at the internal surfaces of four PVC windows.

The influence of MCrAlY coating application and its thickness on the heat transfer during water spray cooling

The main purpose of the paper was to determine the influence of NiCoCrAlY coating application and its thickness on the heat transfer during water spray cooling under surface boiling conditions. The scope of the research included: sensor preparation, measurements of the sensor temperature during cooling, and numerical calculations to determine the intensity of sensor cooling. The intensity of heat removal was determined by the average values of the heat flux on the cooled surfaces. The inverse method for the heat conduction equation was used to determine the heat transfer boundary conditions. Temperature measurements during cooling were carried out for an initial sensor temperature of 500°C, 700°C and 900°C and a liquid pressure 0.1 MPa, 0.2 MPa. Due to this, it was possible to select a coating thickness that contributed to the greatest extent to the increase in the intensity of heat dissipation from the hot surface. The highest values of the heat flux were obtained during the cooling of the sensor with a 134.5 μm coating.

Assessment of the Performance of FireFOAM in Simulating a Real-Scale Fire Scenario Using High Resolution Data

An assessment of the performance of FireFOAM in simulating a large-scale compartment fire scenario is presented in this study, using the Edinburgh Tall Building Fire Test I (2017) as the basis for evaluation. Different mesh geometries and sizes are tested, and both theory-based and experiment-based validation approaches are employed. The theory-based validation revealed that the implemented finite volumes method is generally conservative, but unaccounted deviations of up to 20% for the heat release rate were observed due to errors in numerically modelling subgrid phenomena, particularly with tetrahedral meshes. In the experiment-based validation, the simulated data showed good agreement with experimental measurements for flow patterns inside the compartment, neutral plane height, and temperatures outside the ceiling jet. However, there were relatively large errors in incident radiation in the hot gas zone, thermal boundary layer transient temperatures, and compartment inflow/outflow velocities. Systematic errors were attributed to deficient heat transfer boundary conditions and under-estimated air entrainment. The study also identified ways to improve run-time efficiency by implementing parallel processing or reducing solid angles in FVDOM, although using large meshes (30 cm and 40 cm cell size) resulted in faster run-times at the cost of accuracy.

Towards an automated framework for the finite element computational modelling of directed energy deposition

In the present work, a comprehensive framework for finite element-based computational modelling of Directed Energy Deposition (DED) process is presented. The proposed approach can be fully automated and implemented on a complex real-life part geometry to accurately predict a thermo-mechanical response during the full-scale deposition process. The discrete material deposition modelling in Finite Element Analysis (FEA) leads to artificial increases in temperature gradients in the melt pool domain. A new method is therefore proposed that aims to mitigate these gradients. Additionally, an easy-to-implement free-surface detection algorithm to accurately prescribe the evolving heat transfer boundary conditions is presented. A three-dimensional sequentially coupled thermo-mechanical model of the process is then validated against experimental data obtained in a deposition case study. The simulation results show good agreement with the in-situ temperature measurements taken during the actual deposition. In addition, result analysis showed that the largest tensile residual stresses form in the hoop and axial direction on the outer domain of the thin-wall cylindrical part near the base plate while the inward material is compressed.

Численное моделирование и верификация точечного лазерного нагрева нержавеющей стали AISI 316L

The paper considers the laser spot heating process in the AISI 316L stainless steel sample and its three-dimensional mathematical model. It proposes an option in this process numerical simulation by introducing a laser radiation source specified as the super Gaussian distribution with refined and experimentally selected dimensionless coefficients. Boundary conditions of convection and radiative heat transfer, as well as the Marangoni convection on the melting pool free surface, were taken into account. Metal phase transition from solid to the liquid aggregation state was realized within the solidus and liquidus temperature ranges due to effective functions of heat capacity and viscosity. Geometrical characteristics of the melt pools obtained during a number of practical experiments were compared with the data determined by numerical solution. It is shown that the results in both the options quantitatively and qualitatively coincide with the insignificant error. Conclusions are made on the error in the numerical solution.

A local absorbing boundary condition for 3D seepage and heat transfer in unbounded domains

AbstractFor the parabolic problems in an infinite space, previous methods basically focused on the one‐ and two‐dimensional artificial boundary. Here, a high‐order local absorbing boundary condition (ABC) used for the fluid seepage and heat transfer in unbounded one‐ and two‐dimensional domains is extended to the relative three‐dimensional analysis. The local ABCs are first derived for the problem in an isotropic media and then stretched to the case in an orthotropic media. The function including time‐related variables in Laplace‐Fourier space is approximated through the Gauss‐Legendre quadrature formula. By using the inverse Laplace‐Fourier transformation, the local ABCs in Laplace‐Fourier space are inverted into the ones in time space. The numerical examples indicate that the local ABCs can provide satisfactory results with high computational efficiency, especially for the long‐term analysis. Moreover, the relationship among the diffusion coefficient, maximum simulation time and approximation order value is also investigated.

A coupled computational framework for the transient heat transfer in the typical pyrotechnic device

Propellant combustion in pyrotechnic devices produces high-temperature, high-pressure gas. The component is moved by high-pressure gas, which subsequently impacts the energy absorber and causes it to compress and deform. The temperature difference between the high-temperature gas and the wall causes transient heat transfer. Propellant combustion, transient heat transfer, and structural response are coupled, but previous studies had to independently analyze them. Therefore, a multi-physical field numerical model is developed based on the commercial software ABAQUS in this paper, which couples energetic material combustion, transient heat transfer, and structural response. In the user subroutine VUAMP, a lumped-parameter model is used to predict the parameter distribution of combustion products. This determines the load applied on the thin-walled tube and the boundary conditions of transient heat transfer. In ABAQUS, the transient heat transfer and structural response are investigated by the direct thermo-dynamic coupling method. The coupling effect between multiple physical fields is realized by real-time parameter exchange. The rationality and accuracy of the coupling model are verified by comparison with the experiment. The results show that the coupling model can effectively simulate the complex coupling process after considering the transient heat transfer and the interaction between multiple physical fields. Taking a pyrotechnic device as the research object, the pressure load accuracy obtained by the coupled model is improved by 5.1%, and the structure response obtained is also closer to the experiment result. At the same time, more characteristic parameters of the structure field and temperature field are obtained.

Three-dimensional thermoelastic analysis of orthotropic laminated cylindrical shells subjected to uniformly localized thermal boundary conditions

Accurate evaluation of three-dimensional (3D) thermal-elastic analysis of laminated cylindrical shells under different loads has a significant impact on their safety design. In this study, we present a 3D thermoelastic solution of laminated orthotropic cylindrical shells subjected to uniformly localized thermal boundary conditions. For a homogeneous orthotropic layer, a thinning layer approach is introduced to deal with the heat conduction equation and the elastic equation. Based on the eigenequation method and pseudo-Stroh formalism, general solutions for physical quantities of a homogeneous layer are derived. The propagator matrix method is used to deal with multilayered media. A closed form solution for the laminated cylindrical shells is obtained. A numerical example of a 3-layered cylindrical shell subjected to convective heat transfer boundary conditions is presented to verify the solutions’ correctness. An excellent convergence of the current approach is found and the physical quantities predicted by the current method agree well with the numerical results by the finite element method. Finally, the numerical solutions of a 3-layered orthotropic cylindrical shell subjected to uniformly localized thermal boundary conditions are obtained by the current method. The closed form solution presented in this article can be used for 3D thermoelastic analysis of laminated cylindrical shells under complex boundary conditions.