Analytical Heat Transfer Model Research Articles

Physics-guided spatiotemporal approach for melt pool size prediction in laser powder bed fusion

ABSTRACT This study first proposes a physics-guided spatiotemporal graph. The melt pool temporal feature nodes and spatial feature nodes are extracted from melt pool images based on spatiotemporal correlations. These feature points are treated as graph nodes, and the edge weights in the graph are calculated based on an analytical heat transfer model. It supplements the physical information of accumulated heat. Based on this, the graph convolutional network (GCN) is used to extract spatiotemporal information of heat transfer, and the long short-term memory (LSTM) is used to capture the evolution patterns of the melt pool. Thus, a melt pool spatiotemporal feature extraction model is constructed for melt pool size prediction. The model achieves prediction errors within 12% for the melt pool area and 8.5% for the melt pool perimeter. Subsequently, interpretability analysis indicates that the physics-guided approach enhances the model's learning ability for the cumulative contribution of heat from neighboring tracks.

Qualitative Analysis of the Heat Transfer in a Package of Square Steel Sections

During the heat treatment of square or rectangular steel sections, a heated charge, arranged in regular packages, is placed inside a furnace. This type of charge forms a porous medium through which a complex heat flow occurs during heating. Several heat transfer mechanisms act simultaneously within this medium: conduction through the section walls, conduction and natural convection within the gas, thermal radiation between the section walls, and complex heat transfer (mainly contact conduction) at the joints between the adjacent sections. This article presents a qualitative analysis of heat transfer, aiming to determine the contribution of individual heat transfer mechanisms to the overall process. For this purpose, an analytical model of complex heat transfer within the package was employed, based on the thermo-electric analogy. The results from experimental studies were used to calculate the natural convection and heat transfer at the joints. It was assumed that the material of the sections was low-carbon steel, and the gas was air. Calculations were performed for the temperature range of 25 °C to 700 °C, considering three different geometrical configurations of the sections. It was shown that the effective thermal conductivity (ETC) of the package for the considered geometrical cases varies between 2.2 and 10.6 W/(m·K), which is an order of magnitude lower than the thermal conductivity of the individual sections. This parameter increased dynamically with the temperature. Moreover, the heat transfer intensity within the package of sections was nearly an order of magnitude lower than the heat conduction observed in a solid steel charge. Additionally, it was shown that the primary heat transfer mechanisms governing the heating process were thermal conduction (in the lower temperature range—up to approximately 350 °C) and thermal radiation (in the higher temperature range—above 350 °C). The gas convection inside the sections had a minimal impact on the heating process of the package. The primary parameters influencing the quality of the results were the joint resistance between the adjacent sections and the emissivity of the sections. The presented model can be used for the optimization of heat treatment processes for the considered charge.

Analytical Model for Heat Transfer Around Energy Piles in Layered Soil With Interfacial Thermal Resistance by Integral Transform Method

ABSTRACTEnergy piles are commonly deployed in vertically layered geological conditions due to the geological structure and pile foundation backfill. The imperfect contact between adjacent soil layers results in resistance to heat transfer at the interface, known as the interfacial thermal resistance effect. In this paper, the energy pile was simplified as a finite‐length solid cylindrical heat source, and an analytical model was established for layered heat transfer of energy piles considering the interfacial thermal resistance effect. The Laplace‐domain solutions to the temperatures in the layered ground were derived by using the finite Hankel and Laplace transforms. The Crump method was subsequently employed to numerically invert Laplace‐domain solutions to the time‐domain solutions. The proposed model was validated by comparing with an analytical solution of a homogeneous model and COMSOL numerical solution. These solutions were used to analyze the temperature response around energy piles considering interfacial thermal resistance. Finally, a parametric study was performed to explore the effects of interfacial thermal resistance and other thermal properties of the soil layer on the layered heat transfer of energy piles.

Analytical Modeling of Mass and Heat Transfer on Unsteady Squeezing Viscous Nanofluid Flow under the Influence of Slip Velocity

In this article, two-dimensional unsteady incompressible viscous nanofluids magneto-hydrodynamic (MHD) flow among two parallel plates extended infinitely is investigated. The equations that results from the use of similarity transformations for non-linear partial differential system are solved by the new algorithm. The important key to this construct is the derivatives that appear as coefficients in the power series. The effects of apparent physical parameters on velocity concentration and temperature distributions are described using a schematic diagram and interpreted physically. The effects of apparent physical parameters on concentration, temperature, and velocity distributions are described by graphs. For the flow of nanofluids, the results indicate that it is inversely proportional between the rate of mass and heat transfer with nanoparticle size fraction and magnetic parameter. Over time, squeeze number and schmidt number lead to increase the rate of mass transfer. This problem is dissolved numerically by using the Runge-Kutta scheme of fourth-order (RK4S) .

Temperature-Dependent Thermal Conductivity Identification by Bayesian Inference

The identification of temperature-dependent thermal conductivity in aerogel material, which is commonly used as insulation in thermal protection structures of high-speed aircraft, faces the challenge of selecting the appropriate model in engineering practice. Considering the uncertainties in the selection process of an appropriate functional model, a novel Bayesian probability method computational framework based on response data is established to improve the accuracy of thermal conductivity identification. Three implementation steps are presented: 1) the database of candidate models is established; 2) the reconstructed signals can be calculated by a heat transfer analysis model; and 3) the posterior probability of each candidate model is estimated to obtain the optimal thermal conductivity model and determine the characteristic coefficients. Numerical simulations of a theoretical one-dimensional heat transfer model and a curved thermal protection structure are performed to verify the proposed method. Then, a heating experimental investigation of the curved thermal protection structure is conducted to identify the temperature-dependent thermal conductivity of aerogel material. The results indicate that the temperature-varying thermal conductivity can be accurately identified by the proposed method, which can be applied to the heat transfer analysis and design of aerogel materials in high-speed aircraft.

An analytical heat transfer model for transient Raman thermometry analysis.

Transient Raman thermometry improves on its steady-state counterpart by eliminating the error-prone steps of temperature calibration and laser absorption measurement. However, the accompanying complex heat transfer process often requires numerical analysis, such as the finite element method, to decipher the measured data. This step can be time-consuming, inconvenient, and difficult to derive a physical understanding of the heat transfer process involved. In this work, the finite element method is replaced by fitting the measured data to an analytical three-dimensional heat transfer model. This process can be completed in a few seconds. Using this approach, the in-plane thermal conductivity of two bulk layered materials and the interfacial thermal conductance between two-dimensional materials and quartz have been successfully measured. Based on our model, we performed an analytical quantitative sensitivity analysis for transient Raman thermometry to discover new physical insights. The sensitivity of the in-plane thermal conductivity of bulk layered materials is dictated by the ratio between the spot radius and heat spreading distance. The sensitivity of the interfacial thermal conductance between two-dimensional materials and quartz is determined by its conductance value. In addition, the uncertainty of the measured value contributed by the uncertainty of the input parameters can be efficiently estimated using our model. Our model provides an efficient data and sensitivity analysis method for the transient Raman thermometry technique to enable high throughput measurements, facilitate designing experiments, and derive physical interpretations of the heat transfer process.

Liquid Piston Compression Heat Transfer Prediction via Thermal‐Resistance Network: Simulation, Experimental Validation, and Liquid Carryover Evaluation

Liquid piston compressors gain attention due to their potential for more efficient and isothermal compression compared to traditional solid piston compressors. Liquid piston compressors use a liquid column instead of a solid piston, allowing for innovative mechanisms to enhance heat transfer and achieve near‐isothermal compression. However, a validated analytical model for heat transfer in liquid piston compressors is still needed to understand the exhaust phase within a liquid piston. In this work, a thermal network model, able to predict the polytropic index to within 8% of the experimental results, is proposed. Moreover, thorough experimentation is conducted to measure the amount of liquid carried over to better understand the exhaust phase. In the results, it is revealed that the piston carries over 13–21 mL of liquid within the exhaust gas for 10–23 s of stroke. Notably, the difference in liquid carried over for the three‐stroke times is not statistically significant, indicating that the liquid carried over is a function of liquid piston design and not stroke time. Finally, most liquid piston applications consider only water; hence, for the first time, this research assesses the stability of a cycle using a nonflammable hydraulic fluid (Fuchs 46 M red) to enhance compressor longevity and material compatibility.

Influence of surface structure and tube material on the condensation heat transfer coefficient of n-butane on horizontal single tubes and in tube bundles

The present study examines the condensation heat transfer coefficient αcond of n-butane on the outside of different horizontal tubes and in corresponding tube bundles. Experiments were conducted with a smooth tube, finned tubes with various fin densities, fin heights and tube materials, and a high-performance condensation tube (HPT) at vapor temperatures of (40 and 78) °C and varying heat flux densities q̇. The influence of inundation on αcond was systematically investigated by varying the mass flow of liquid condensate at q̇ of (20 and 60) kW·m−2. Differences between the experimental results from this work and previous ones for propane on the same condensation tubes could be explained with the help of the thermophysical properties and, thus, the retention angle of the condensate in the channels between the fins and the condensate layer thickness. For single copper tubes, αcond increased with increasing fin densities from (19 to 48) fins per inch and was between 9 and 17 times larger than for the smooth tube. This enhancement factor even reached a value of about 24 for the HPT. These increases can be attributed in part to the increased surface area, but the strongest effect appears to be related to surface tension-driven drainage of the condensate. In addition to the experimental investigations, αcond of the finned condensation tubes was predicted using an analytical model for the condensation heat transfer on finned tubes. Here, excellent agreement with an average deviation from the experimental results of 6.6 % could be found. Studies of the inundation effect have shown that the expected decrease in αcond due to the additional condensate impinging on the tubes inside bundles and increasing the film thickness often holds, but is partially counteracted by other effects and depends on the tube geometry.

A novel microgroove-based absorber for sorption heat transformation systems: Analytical modeling and experimental investigation

This study proposes a novel sorber bed design, a stationary thin film microgroove-based absorber, that can address the low specific power and oversized sorber bed issues in existing oscillatory solid sorption heat transformation systems. An analytical heat and mass transfer model is developed for the proposed stationary thin film microgroove-based absorber. A highly-wettable microgrooved aluminum substrate is fabricated by the deposition of a hybrid Al2O3/TiO2 layer, and experimental water uptake measurements are obtained using a custom-built gravimetric large pressure jump setup to validate the analytical model. The model examines how key design parameters affect specific cooling power, cooling power density, and energy storage density. Findings indicate that cycle time and groove depth significantly impact system performance. Also, it is found that there is an optimum groove depth, or film thickness, to achieve maximum power. Trapezoidal grooves achieve higher specific cooling power and cooling power density, while rectangular grooves yield a higher maximum energy storage density. It is experimentally shown that a specific cooling power enhancement of up to 600 % can be obtained compared to the experimental data available for oscillatory sorber beds. Also, the absorption rate of the present sorber bed is up to three times higher than that of falling film absorbers.

Digital twinning of temperature fields for modular multilayer multiphase pipeline structures

The temperature field of oil and gas wells in the field of petroleum engineering presents a core problem and challenge in the digital twin framework due to its ultra-long-distance and highly variable structural characteristics. The varying wellbore cross-sectional structures with depth make it difficult to establish an effective and generalized analytical model for heat transfer. In this study, we propose, for the first time, a method to automate the construction of multi-layered and multi-component heat transfer models by using a general computational model based on non-steady-state single-phase structural modules. This method enables the automated generation of complex multi-layered and multi-component heat transfer models, thereby achieving the construction of a generalized model for temperature field characterization with varying wellbore cross-sectional structures over ultra-long distances. Utilizing this modeling approach, we validate the proposed method through case studies using actual wellbore temperature field data. The results demonstrate the lightweight and efficient computational analysis of temperature field information under non-steady-state conditions.

Analytical solution model of heat transfer for energy soldier piles during excavation to backfilling

This paper presents a two-dimensional heat transfer model for energy soldier piles during excavation and after backfilling. Based on Green's function and separation of variables method, this model considers the heat transfer process from various angles during excavation and after backfilling, deriving a series of analytical solutions for the heat transfer processes. It is more suitable for solving the heat transfer problem of energy soldier piles. The accuracy of the analytical solution was verified by numerical simulation and classical analytical solutions. Then, the effects of air convection coefficient and backfill materials' thermal diffusivity on heat transfer are analyzed. The results show that the temperature rise of both the soil and the pile in the non-excavated case (ordinary energy pile) is lower than that of the various convective coefficient cases, and the convective heat transfer contributes to the heat transfer capacity of energy soldier piles. After backfilling, materials with higher thermal diffusivity have smaller temperature rise. Conversely, materials with lower thermal diffusivity have higher temperature rise. Under the long-term operation strategy, the heat flux within the soil and backfill is higher and favorable for heat transfer by selecting the backfill with lower thermal diffusivity.

Enhancing ground source heat pump system design optimization: A stochastic model incorporating transient geological factors and decision variables

In this study, a cost minimization model of a ground source heat pump (GSHP) was performed to obtain its best design configurations based on system reliability. To implement a high-fidelity optimization, the uncertainties of decision parameters and geological parameters' distributions were considered. The GSHP's lifespan costs were functionalized based on an analytical borehole heat transfer model. Multiple constraints were established to serve as reliability goals to ensure a turbulent ground pipe flow without extreme temperature variations. The ground thermal conductivity, groundwater velocity, and unit price of electricity were considered as three random variables. Their dynamic characteristics were incorporated by assigning different increasing rates to the average magnitudes of them. Additionally, their transient fluctuations were accommodated by integrating probabilistic uncertainties into the optimization process, all of which followed normal distributions. The results demonstrated that the time-dependent characteristics of these uncertain variables could significantly affect the system investment of GSHP by reducing the total costs by 20.7% and 21.1% when the increasing rates of groundwater velocity and ground thermal conductivity reach 5% and 4% respectively. The study also provided optimized design variables under an 85% confidence level in various predicted scenarios, considering a wide range of dynamic geological parameters and energy costs.

Ground Heat Flux Reconstruction Using Bayesian Uncertainty Quantification Machinery and Surrogate Modeling

AbstractGround heat flux (G0) is a key component of the land‐surface energy balance of high‐latitude regions. Despite its crucial role in controlling permafrost degradation due to global warming, G0 is sparsely measured and not well represented in the outputs of global scale model simulation. In this study, an analytical heat transfer model is tested to reconstruct G0 across seasons using soil temperature series from field measurements, Global Climate Model, and climate reanalysis outputs. The probability density functions of ground heat flux and of model parameters are inferred using available G0 data (measured or modeled) for snow‐free period as a reference. When observed G0 is not available, a numerical model is applied using estimates of surface heat flux (dependent on parameters) as the top boundary condition. These estimates (and thus the corresponding parameters) are verified by comparing the distributions of simulated and measured soil temperature at several depths. Aided by state‐of‐the‐art uncertainty quantification methods, the developed G0 reconstruction approach provides novel means for assessing the probabilistic structure of the ground heat flux for regional permafrost change studies.

Thermal and structural analysis of TCABR vacuum vessel during baking process

TCABR is a small-sized tokamak located at the University of São Paulo, in Brazil. It is planned to undergo an extensive upgrade, which includes a baking system. However, this tokamak wasn't designed considering baking as a possible wall conditioning technique. This paper analyzes whether a baking system with ohmic heating could in principle be installed on TCABR, considering the thermal stresses that it might produce on the vacuum vessel. An analytical steady-state heat transfer model was used to estimate the heat fluxes required to reach a target temperature of 200 °C. Thermal and structural transient finite element method models were developed using ANSYS Workbench®. The temperature distribution was used to calculate the thermal stresses, also considering the effects of gravity and vacuum pressure. The stresses produced in the vacuum vessel by baking were below the limit defined by the ASME stress code, but the graphite tiles’ support rails reached stress values above their material's yield strength. The resulting temperature distribution was not uniform, with some regions far from the 200 °C target. A redesign of the baking system will be required to reach a more uniform temperature field and avoid stresses above yield strength for some components.

An overview of the Transient Hot Wire and preliminary studies for its implementation

The opportunity to design a new portable system for measuring thermal conductivity in fluids arose from the need to measure the phase state (liquid and/or vapour). As is well known, thermal conductivity varies in relation to the phase state of the fluid. The Transient Hot Wire Method was used to measure thermal conductivity. First, the work includes innovations in the analytical model of heat transfer, progressing over time to contemporary numerical models used in standards. The applications in the bibliography span a wide range, including gases, liquids, and the latest advances in the field of nanofluids. Secondly, the study delves into the transient model of heat exchange, focusing on conduction. The authors used standardized correction equations for the prototype, ensuring accuracy and relevance. Finally, the work includes the design and construction of the transducer. This process begins with a Monte Carlo simulation, predicting the expected results. This simulation helps to define measurement system components based on their performance characteristics and in-depth analysis.

Heat Transfer Analysis Methodology for Compression Hydrogen Storage Tank during Charge–Discharge Cycle

Heat transfer analysis for the compression hydrogen storage tank (CHST) during the charge–discharge cycle is necessary to ensure quick and safe refueling for fuel cell vehicles. In this paper, a dual‐zone dual‐temperature (DZDT) model for a CHST during the charge–discharge cycle process is established. The constant/variable mass flow rates and heat transfer coefficients (HTCs) are combined to form three methods. Method 1 uses constant mass flow rate and constant HTC. Method 2 uses variable mass flow rate and variable HTC calculated through the energy conservation equation. Method 3 uses variable mass flow rate and variable HTC calculated through the empirical equation. Then, these methods are applied to the DZDT model for heat transfer analysis in three cases. Research shows that for the charging process, the simulated hydrogen temperatures by Method 2 agree well with experiment data for three CHSTs. Method 1 has a maximum error of about 20°C for 19 L CHST, 15°C for 29 L CHST, and 25°C for 40 L CHST. The error of Method 3 is between Methods 1 and 2. The simulated hydrogen pressures by Methods 2 and 3 agree well with the experimental data, while Method 1 has a maximum error of about 5 MPa for 19 L CHST, 10 MPa for 29 L CHST, and 3 MPa for 40 L CHST. For the discharge process, the simulated hydrogen temperatures by Methods 2 and 3 have a relatively slight difference with the experimental data, while Method 1 has relatively significant differences for three CHSTs. Only slight differences exist between the simulated hydrogen pressures by Methods 1, 2, and 3 with the experimental data for three CHSTs. In short, Method 2 can simulate the hydrogen temperature and pressure well during the charge–discharge process. Method 3 can simulate the approximate hydrogen temperature and precise hydrogen pressure during the charge–discharge process. Method 1 can only simulate the hydrogen pressure during the discharging process. The conclusions of this article can inform researchers which analysis methods are more reasonable to choose in future hydrogen‐filling studies.

A mechanistic explanation of shrinkage porosity in laser powder bed fusion additive manufacturing

This work focuses on the occurrence of shrinkage porosity and its manifestation in Alloy 718 during laser-powder bed fusion (PBF-LB) processing. Shrinkage porosity is a common defect in metal castings that degrades part performance. In traditional metal castings, the Niyama criterion is a reliable heuristic for predicting the formation of shrinkage porosity. However, the Niyama criterion’s applicability in the PBF-LB process remains unexplored, and there is no known and evaluated heuristic to predict shrinkage porosity in the PBF-LB manufactured parts. This work employs microstructure characterization and an analytical heat transfer model to develop a mechanistic explanation for the formation of shrinkage porosity in the PBF-LB process. The results show that the Niyama criterion could not effectively predict the occurrence of shrinkage porosity. Further, the formation of shrinkage porosity is primarily driven by secondary dendrite arm growth in the solidifying microstructure, where the transition to cellular growth at high cooling rates during solidification mitigates porosity by removing locations for pore formation. This means a heuristic based on solidification cooling rate could reliably predict the occurrence of shrinkage porosity. For practical use, shrinkage porosity process maps are presented for use in process design and control to directly aid shrinkage porosity mitigation in process planning. The process-shrinkage porosity relationship results also indicate that trends in PBF-LB manufacturing toward higher deposition temperatures and higher throughput are likely to aggravate the conditions for shrinkage porosity formation and further elevate the importance of the mitigation strategies presented in this work.

Preliminary analysis of maximum hypothetical accident for a solid core space nuclear reactor power system

In order to study the safety characteristics of the solid core space nuclear reactor power (SNRP) system under the maximum hypothetical accident, a two-dimensional entire core transient heat transfer analysis model was established, and the key parameters response characteristics of the ultra-small lithium-cooled SNRP under two maximum hypothetical accidents, namely, loss of heat sink (LOHS) and loss of coolant accident (LOCA), were calculated and analyzed. In the maximum hypothetical accidents, the coolant cooling capacity is lost, thus the core decay power is discharged into space only through the radiation of the residual heat removal system and the side surface of the reactor vessel. During the accidents, the heat transfer of the core deteriorated, and the fuel temperature may rise to the melting point, resulting in radioactive leakage. The results show that: (1) In the LOHS accident, the maximum fuel temperature reaches 2150 K at 550 s, and the pressure of the primary system volume accumulator continues to increase to the set system pressure safety limit of 2 MPa, resulting the primary loop overpressure failure. And the fuel matrix temperature is close to the set cladding limit temperature of 2200 K; (2) In the LOCA, the deterioration of heat transfer in the core makes the temperature increase rapidly, reaching a maximum of 3016 K at about 630 s, which is very close to the melting temperature of UN fuel 3123 K. As the decay power decreases, the maximum core temperature decreases to less than 1600 K after 24 h of the accident. The auxiliary cooling system of the solid core SNRP system under the maximum hypothetical accident is optimized, and the design parameters of the auxiliary cooling system meeting the safety requirements are obtained.

Post-fire performance of circular steel tube confined steel-reinforced concrete slender columns: Testing, simulation and design

Steel tube confined steel-reinforced concrete (STCSRC) stub columns offer good residual bearing capacity, great ductility, and large stiffness after fire exposure because inner steel profiles are unaffected by exterior temperature. Nonetheless, instability issues exist in STCSRC slender columns, and study into the mechanical characteristics of post-fire slender specimens is critical. At present, no relevant study on the axial performance of STCSRC slender columns after fire exposure has been reported. In this paper, nine circular STCSRC slender columns that had been exposed to fire were tested under axial load. The failure modes, axial load–displacement relationship, and lateral deflections of STCSRC columns were discussed. Furthermore, heat transfer analysis models and mechanical analysis models were established, and the effects of crucial variables on the buckling responses of STCSRC slender columns were explored. Among the parameters studied, sectional diameters and steel profile to concrete area ratio have a significant impact on buckling capacity. To calculate the buckling capacity of the post-fire STCSRC slender column, a simplified calculation method according to JGJ/T 471–2019 was proposed.

Modeling of heat conduction processes in porous absorber of open type of solar tower stations

An analysis of existing methods for calculating heat and mass transfer processes in porous absorbers of receivers of tower solar power plants is carried out. It is shown that the resulting thermophysical properties of the material are influenced not only by the porosity but also by the location of the pores in the material volume. The criterion of the dislocation vector is proposed as a mathematical indicator of various porous structures. The shortcomings of the existing dependences of the effective thermal conductivity of a material on the type of porosity are shown. The most reliable dependences for determining the thermophysical parameters of a porous medium are also determined and independent factors are proposed on which the mathematical model of heat and mass transfer in open-type solar receivers should be based.The current state of research on the effective thermal conductivity of the porous structure of solar receivers is described in detail. A new formula for calculating the effective thermal conductivity of a porous structure with regard to the dislocation vector and a method for calculating the processes of heat transfer in open solar receivers based on the proposed formula are proposed. The proposed equation has been tested. It is determined that for simple channel structures it is sufficient to use the existing equations to calculate the thermal conductivity coefficient, while for more complex porous structures, such as the StepRec absorber, it is better to use the proposed equation.Among the strengths of this study is a new calculation formula that allows us to build an analytical model of heat transfer in a porous medium. The use of the analytical model can significantly reduce the complexity of modern calculations of heat transfer processes in a porous absorber and will help improve the quality of optimization models of solar receivers.