Steady-state Heat Transfer Research Articles

Multiscale concurrent topology optimization of transient thermoelastic structures

Previous multiscale concurrent topology optimization methods for thermoelastic structures were primarily based on static loading and steady-state heat transfer conditions, which do not account for transient effects associated with time-dependent loads. To address this limitation, this paper establishes a novel generic multiscale concurrent topology optimization method that incorporates transient thermoelastic coupling based on transient heat conduction and structural dynamics. In this study, first, a transient multiscale thermoelastic sensitivity equation is innovatively derived through adjoint sensitivity analysis. The effectiveness of this equation is then demonstrated through comparative cases involving transient heat conduction, structural dynamics, and transient thermoelastic (including multimaterial and 3D problems) optimization. Furthermore, the research finds that the topology optimization of transient thermoelastic structures also presents transient effects at microscale. This method demonstrates good versatility and applicability across various optimization cases. The method has great potential in the integrated design of materials and structures involving coupling between time-dependent thermal loads and time-dependent mechanical loads.

Yielding onset in FGM thick-walled spherical shells under thermo-mechanical loading

Based on von Mises yield criterion, a thermoelasto-plastic analysis of a thick-walled spherical shell composed of functionally graded material (FGM) subjected to internal pressure and thermal gradient is conducted in order to accurately predict the onset radius of yielding within the vessel wall. The modulus of elasticity, thermal conductivity and thermal expansion coefficients, and yield stress of FGM are assumed to follow power-law functions in radius according to Erdogan’s model. The equilibrium differential equation of the shell under thermo-mechanical loading in steady-state conduction heat transfer are derived analytically and then solved to determine through-thickness variations of the radial and circumferential stresses and radial displacement in elastic and perfectly plastic zones in the vessel wall. The presented approach leads to the definition of new formulation to predict the onset radius of yielding. Moreover, a neural network (NN) solution to reliable quantify the influence of all uncertain input parameters with respect to uncertain output parameter is utilized. The numerical results showed that for various FGM parameters and specific thermal gradient, the plastic zone can commence from inside radius, outside radius, simultaneously in both radii, or may be launched in the intermediate radius of the spherical shell wall.

The effect of heterogeneous geometry on steady-state heat transfer in extrusion-based 3D printed structures

The 3D printed buildings constructed using rapid manufacturing techniques provide opportunities for structural optimization and performance design, which are beneficial in meeting the vision of digital and sustainable development of the construction industry. However, there are still many research gaps in the heat transfer of 3D printed buildings, impacting the accurate design of their thermal performance. This study quantifies the effect of heterogeneous geometry on heat transfer in extrusion-based 3D printed structures. The experiment reveals that the non-uniform surface temperature distribution primarily originates from geometrical factors, with heterogeneous physical properties caused by cold joints having little influence. Numerical simulations using equivalent geometric models indicate that the local temperature and the convective heat transfer coefficient of raised surfaces vary periodically, corresponding to surface shape. As surface bulges increase, the overall average heat transfer efficiency of the 3D printed structure decreases, while total surface heat transfer increases. These findings help to understand the effect of heterogeneous geometric properties on the heat transfer process of 3D printed structures, thus providing a reference for the accurate design of 3D printed structures with thermal functions.

Investigating intermolecular interactions of surfactant solutions using femtosecond thermal lens spectroscopy

In this study, we examined the impact of various surfactants (oleic acid, butyric acid, Span-20, and CTAB) on the thermophysical properties of methanol (MeOH) using a femtosecond laser-induced thermal lens (TL) spectroscopic technique. Methanol was chosen for its unique convective properties under intense localized heating, making it a promising candidate for studying photothermal responses. We discovered that the TL characteristics of both pure methanol and methanol-surfactant mixtures are significantly influenced by the molecular interactions and physical properties of the components. Our experimental results indicate that the addition of surfactants notably alters the heat transfer dynamics of the solvent by restricting natural molecular movement and modifying thermal properties, which in turn affect the TL signatures. Beyond the surfactant concentration, we observed that the extent of variation in steady-state TL signals, inflection points, and heat transfer mechanisms depends on the molecular properties of the surfactants, such as chain length, the number of active (hydrophilic) groups per molecule, thermal conductivity, viscosity, and intermolecular interactions. Our TL findings provide a detailed investigation into the effect of surfactants on the photothermal response and heat transfer process of a solvent for the first time.

Multi-scale modeling: Finite element analysis of the thermophysical properties of carbon/carbon composites considering manufacturing defects and porosity at high temperature

Carbon/carbon (C/C) composites have strict requirements for their thermal properties in extreme environments, especially at high temperature, where their properties are crucial for long-term life. The structure of C/C composites is exceptionally complex and exhibits multi-scale characteristics, and their thermophysical properties are closely related to temperature. Therefore, exploring their thermal response and heat transfer mechanisms through experimental method is relatively costly. This paper constructs a multi-scale finite element model to investigate the influence of structure and manufacturing defects on performance, and analyzes the thermophysical properties of the composites at High-temperature. By constructing a micro-representative volume element (Micro-RVE) that includes fibers, matrix, and pores, and using a steady-state heat transfer analysis method, the influence of material phase distribution on performance is studied. At the same time, a Meso-RVE reflecting the layering form, needle punching effect and manufacturing defects is established, and the transient heat transfer analysis method is used to investigate the influence of the structural form on performance. Finite element analysis shows that, the simulation values of the three C/C composites of unidirectional fiber bundles, short-chopped fiber felts, and needle punched C/C composites show good consistency with the experimental results in the published literature. This paper uses numerical methods to calculate the thermophysical properties of C/C composites from room temperature to 900°C and explores their variation with temperature. The constructed multi-scale model provides an accurate and effective method for predicting the thermophysical properties of C/C composites and also provides new perspectives and insights for thermal-mechanical coupling analysis and structural design.

Determination of thermal conductivity of phase pure 10H-SiC thin films by non-destructive Raman thermometry

The 10 H SiC thin films are potential candidates for devices that can be used in high temperature and high radiation environment. Measurement of thermal conductivity of thin films by a non-invasive method is very useful for such device fabrication. Micro-Raman method serves as an important tool in this aspect and is known as Raman thermometry. It utilises a steady-state heat transfer model in a semi-infinite half space and provides for an effective technique to measure thermal conductivity of films as a function of film thickness and laser spot size. This method has two limiting conditions i.e. thick film limit and thin film limit. The limiting conditions of this model was explored by simulating the model for different film thicknesses at constant laser spot size. 10H SiC films of three different thicknesses i.e. 104, 135 and 156 nm were chosen to validate the thin film limiting condition. Thermal conductivity of these thin films varied from 0.60 – 4.80 (Wm−1K−1).

Analysis of the aerothermal performance of modern commercial high-pressure turbine rotors using different levels of fidelity

In the field of design and optimization of sophisticated geometries such as film-cooled turbine blades of modern jet engines, Computational Fluid Dynamics (CFD) simulation is commonly employed. As the pursuit for higher turbine entry temperatures intensifies, it becomes crucial for computational analyses to offer accurate predictions of metal temperatures and heat transfer coefficients on these critical components. This study investigates the impact of key physical factors that characterize the operation of these components on the accuracy of the computational model. In particular, the effects of including the exchange of thermal energy between the fluid and solid domains, as well as modelling the unsteady interaction between the rotor and stator are studied. The research focuses on a fully featured one-and-a-half stage high-pressure turbine of a commercial jet engine, utilizing proprietary software for conducting 3D Reynolds-Averaged Navier-Stokes flow simulations. To model the fluid-solid thermal interaction, steady-state Conjugate Heat Transfer (CHT) simulations are performed. The CHT results are then compared with experimental data obtained from a thermal paint test, achieving good levels of agreement. Additionally, phase-lag simulations are executed under adiabatic-wall conditions to evaluate the influence of stator-rotor interaction on near-wall gas temperatures. This work shows that, by modelling the periodic unsteadiness at the stator-rotor interface with a phase-lag technique, the maximum near-wall gas temperature prediction is significantly increased, sometimes more than 100K, with respect to the steady-state model one. Findings from this work also suggest that simplified “strip” source terms used to model the presence of film cooling hole rows on the surface of a blade can be used with satisfactory accuracy only for nominal conditions. The mass flows delivered by each source strip should not be linearly scaled based on mainstream quantities for use in different conditions, but they should be recalculated from scratch for the new conditions.

Experimental analysis of transient and steady-state heat transfer from an impinging jet to a moving plate

Experimental analysis of transient and steady-state heat transfer from an impinging jet to a moving plate

Theoretical Study of the Steady Time of Thermal Transmission in Materials That Have Engineering Uses

General Background: Understanding the time required to achieve steady-state heat transfer in construction materials is crucial for various engineering applications, including construction, architecture, and electronics. Specific Background: This study investigates the steady time of thermal transmission in engineering materials using both theoretical and experimental approaches. Knowledge Gap: Despite existing research on heat transfer, there is a lack of comprehensive studies that integrate both simulation and experimental validation for a wide range of building materials.Aims: The primary aim is to evaluate the steady-state time of heat transfer in fifteen construction materials through theoretical models and simulations using MATLAB and ANSYS, and to experimentally validate these findings with four selected materials. Results: The study finds that the steady time for heat transfer varies significantly among materials, with wood packaging requiring the longest time (32.49 hours) and aluminum the shortest (0.49 hours). Theoretical results, validated by simulations, show close agreement between MATLAB and ANSYS (0.087% deviation) and between numerical and experimental results (9.5% deviation). Brick demonstrated a 61.18% longer heat transfer time compared to concrete, while thermostone showed a 17.45% and 89.31% increase over brick and concrete, respectively. Novelty: This research provides new insights into the comparative stability of heat transfer times across a broad spectrum of materials, highlighting significant performance variations and validating simulation methods against experimental data. Implications: These findings are vital for optimizing material selection in construction to enhance thermal efficiency. The study’s methodologies can aid in developing more accurate predictive models for heat transfer in construction materials, thereby contributing to improved design and energy performance in building applications.

Comparative Study on Heat Dissipation Performance of Pure Immersion and Immersion Jet Liquid Cooling System for Single Server

Heat dissipation has emerged as a critical challenge in server cooling due to the escalating number of servers within data centers. The potential of immersion jet technology to be applied in large-scale data center server operations remains unexplored. This paper introduces an innovative immersion jet liquid cooling system. The primary objective is to investigate the synergistic integration of immersion liquid cooling and jet cooling to enhance the heat dissipation capacity of server liquid cooling systems. By constructing a single-server liquid cooling test bench, this study compares the heat dissipation efficiencies of pure immersion and immersion jet liquid cooling systems and examines the impact of inlet water temperature, jet distance, and inlet water flow rate on system performance. The experimental outcomes show that the steady-state surface heat transfer coefficient of the immersion jet liquid cooling system is 2.6 times that of the pure immersion system, with increases of approximately 475.9 W/(m2·K) and 1745.0 W/(m2·K) upon adjustment of the jet distance and flow rate, respectively. Furthermore, the system model is streamlined through dimensional analysis, yielding a dimensionless relationship that encompasses parameters such as inlet water temperature, jet distance, and inlet water velocity. The correlation error is maintained below 18%, thereby enhancing the comprehension of the immersion jet cooling mechanism.

Experimental and Numerical Study of Newly Assembled Lightweight Radiant Floor Heating System

In this study, the heating capacity of a new prefabricated assembled hot water radiant modular heating system made from a recycled waste building masonry structure is investigated through experimental and numerical simulation methods. The heating capacity of the system in different working conditions (a water supply temperature of 48 °C, 51 °C, 56 °C, and 61 °C; a flow rate of 0.49 m3/h, 0.35 m3/h, and 0.21 m3/h) is analyzed and verified. A three-dimensional steady-state heat transfer numerical model of the floor heat transfer of the module is established, and the accuracy of the model is verified through the measured results to investigate the heating capacity of this system under different water supply temperatures, flow rates and coil spacings. The results show that the new prefabricated hot water radiant module heating system has a 0.9 °C higher air temperature and 2.1 °C higher average floor surface temperature than the traditional wet floor radiant heating system under the same experimental conditions, and the response time is 44% shorter. The water supply temperature can significantly change the heating capacity of the system, while the water supply flow rate has little effect on the system. The established three-dimensional steady-state numerical model can be in good agreement with the measured results. This study can provide an experimental and theoretical basis for the design and application of such systems.

Simulation Study of Thermal Performance on the Inner and Outer Surfaces of Semi-Transparent Photovoltaic (STPV) Glass with Different Transparency

This paper used the experimentally verified one-dimensional steady-state heat transfer numerical model of the semi-transparent photovoltaic (STPV) glass to simulate the influence of wind speed, ambient temperature and air gap thickness on the surface temperature of PV modules, and analyzed the thermal performance of the inner and outer surfaces of STPV glazing with different transparency. Results shows that for every 1m/s increase in wind speed, the outer surface temperatures of SL-STPV glass with transparency of 10%, DL-STPV glass with transparency of 20% and 40% decreased by 3 °C, 3.02 °C and 2.22 °C, respectively. For every 10 °C increase in ambient temperature, the outer surface temperatures of SL-STPV glass with transparency of 10%, DL-STPV glass with transparency of 20% and 40% increase by 8.45 °C, 7.6 °C, and 7.79 °C, respectively. For the DL-STPV glass with transparency of 20% and 40%, for every 2 mm increase in the thickness of the air gap, the outer surface temperature increases by 0.13 °C and 0.12 °C, respectively. The heat transfer between the inner surface of the glass and the indoor environment increases the heat gain through the glass into the room in summer, which will lead to an increase in refrigeration energy consumption. However, in winter, the heat exchange between the inner surface and the in-door air to heat the indoor air reduces the heating energy consumption to a certain extent, and achieves the effect of building energy conservation to a certain extent.

Integrated Thermal Management System Concept With Combined Jet Plate, High Porosity Aluminum Foam, and Target Plate for Enhanced Heat Transfer

Abstract An experimental investigation was carried out on high porosity metal foams subjected to array jet impingement with an objective to develop enhanced heat transfer configurations. In this study, we propose an integrated thermal management system (TMS) aimed toward leveraging the conjugate heat transfer capabilities of target plate, metal foam, and the jet plate—all made from aluminum and assembled such that a proper contact between them can be established. Steady-state heat transfer experiments were carried out for 10 and 20 pores per inch (PPI) aluminum foams of 0.93 porosity. Both metal foams were 12.7-mm thick. The normalized jet-to-jet spacing was varied from 2 to 12 times the jet diameter, while the jet diameter was fixed. The ratio of the jet plate thickness and jet diameter (nozzle aspect ratio) was 6.35, which ensured proper development of jets inside the nozzles. Experiments were conducted over a wide range of Reynolds number (based on jet diameter) varied from 100 to 5000. The obtained convective heat transfer coefficient for different configuration was evaluated in context with pressure drop. The analysis of experimental results reveal that large open area ratio jets combined with high porosity metal foams provide highly efficient and high-performance cooling for the investigated range of Reynolds numbers.

A smoothing gradient thermo-mechanical damage model for thermal shock crack propagation: Theory and FE implementation

This paper introduces a novel smoothing gradient-enhanced thermo-mechanical damage model to capture complex thermal crack patterns. To describe the adiabatic property of the damaged region, the scalar variable indicating the deterioration level of material, the damage variable, is employed for the heat conduction balance equation. In essence, the local heat flux and heat capacity are modified to present a decrease in heat flow. Formulations for steady state and transient heat transfer are given. The accuracy and efficiency of the coupled smoothing gradient damage model are illustrated through the numerical experiments for steady state and transient crack growth (e.g., quenching test), where the predicted crack patterns induced by thermo-mechanical loading are in good agreement with experimental data and other reference numerical solutions.

Heat transfer error analysis of high-temperature wall temperature measurement using thermocouple

Thermocouples are widely employed as the temperature measuring element for an aero-engine. However, due to the unique characteristics of the aero-engine test environment, there exist significant temperature measurement errors of the thermocouple. The steady-state heat transfer error of the thermocouple can be attributed to convection heat transfer error, wire heat transfer error, and radiation heat transfer error. The flow and heat transfer process of wall temperature measurements using armored K-type thermocouples were simulated numerically by Fluent software at the Mach number of 0.1–0.5 and the temperature of 700∼1200 K. The results indicate that convective error accounts for more than 55 % of the total transfer error. To reduce excessive temperature measurement errors, a novel airflow stagnation cover structure around the thermocouple was presented. When the diameter of the stagnation cover is 2 mm, the error of the thermocouple is reduced to less than 1 %.

Oscillatory instability of magneto-convection during the melting of non-Newtonian ferromagnetic nano-enhanced phase change materials at low Rayleigh number

This work complements mechanism of the oscillatory instability of magneto-convection in the process of melting heat transfer controlled by magnetic field at low Rayleigh number (Ra), aiming to provide a theoretical basis for improving the stability of energy storage system and melting manufacturing process. A latent heat storage cavity unit exposed in uniform magnetic field is designed to reveal the magnetic-controlled heat transfer in solid–liquid phase change process. The volume average method is used to describe porous media composite nano-enhanced phase change materials in latent heat unit. Special attentions are paid to the key parameters of Magnetic number (Mn) and Ra, and coupling flow heat transfer mechanism of magnetic force and natural convection effect is numerically studied. The evolution stages of different flow patterns are divided according to the Kelvin force, vorticity, velocity, flow field and isotherm distributions of characteristic points. Main results show that the magnetic field-modulated phase change process at low Ra can be divided into three stages, of which the second stage is characterized by periodic oscillations. Increasing Mn at fixed Ra accelerates the second stage of oscillatory convection heat transfer coming earlier and promotes melting. When Mn increase to 5 × 106, the full melting time is reduced to the greatest extent, resulting in 11.6 % reduction in heat storage but 17.4 % increase in heat storage efficiency. Three mechanisms of magnetic forced convection coupled with natural convection are found during the increase of Ra: synergistic (Ra < 2 × 103), antagonistic (2 × 103≤ Ra < 1 × 104), and natural convection-dominated (Ra = 1 × 104). Finally, the mode distribution map of Ra-Mn regulation is obtained, in which the unstable transformation mechanism of steady-state, periodic oscillation and chaotic oscillation heat transfer in the melting process under the control of magnetic field is described.

Insulation performance evaluation of stone-finished exterior insulation systems with insulation frames for green remodeling of concrete exterior walls

This study aimed to evaluate the thermal bridge reduction effect of insulation frames applied to a stone-finished exterior insulation system, which is commonly used in green remodeling projects. The insulation performance of the exterior walls and the energy performance of the building in a baseline case in which an existing steel pipe frame was applied were compared with those in cases alt 1 and alt 2, which included application of double- and single-wired truss-shaped insulation frames, respectively. First, a three-dimensional steady-state heat transfer simulation was conducted for the exterior wall-floor joint of the model building, and the effective U-factor was obtained. Next, mock-ups were constructed and the U-factor was tested to verify the insulation performance of cases alt 1 and alt 2. The heat loss decreased as the effective U-factors of alt 1 and alt 2 decreased by 19.0 % and 19.7 %, respectively, compared to the baseline case, according to the heat transfer simulations. In the mock-up test, the U-factors of alt 1 and alt 2 were similar to design U-factor, indicating almost no heat loss caused by the thermal bridges. Notably, the U-factor of alt 2 was 2.4 % lower than that of alt 1. Finally the energy performance of the entire building was compared through dynamic building energy simulations by reflecting the thermal bridging effect. The annual heating and cooling energy use of alt 1 and alt 2 were 2.5 % and 2.6 % lower than those of the baseline case, respectively, confirming the energy-saving effect of reducing thermal bridges.

A new set of explicit solutions for postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution and thermal loading

Thermal postbuckling analysis is presented for shear-deformable anisotropic laminated cylindrical shell with general imperfection distribution under several typical temperature fields are analyzed, including uniform temperature, tent-like linear distribution, axial and circumferential quadratic parabolic temperature fields over the shell surface and through the shell thickness. On this basis, the general temperature distribution can be obtained based on the three-dimensional steady-state heat transfer equation. At the same time, based on the high order shear deformation theory including anisotropic coupling effect, geometrically nonlinear large deflection displacement-strain relationship, the general initial geometric imperfections obtained by measurement and analytical means are introduced, and the thermal buckling equilibrium differential equation of anisotropic shear deformable laminated cylindrical shell with initial imperfections is established. A two-step perturbation-Galerkin integral method is used to obtain explicit solutions for the path development direction of post-thermal buckling equilibrium. The results of parameter analysis show that the material properties and temperature dependence, temperature distribution, lay-up and geometric parameters such as radius-to-thickness ratio have important effects on the thermal buckling load and postbuckling equilibrium path. The present method provides an effective theoretical prediction and analysis method for the design of the carrying capacity of submarine pipelines.

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.

Establishing a Multi-Vial Design Space for the Freeze-Drying Process by Means of Mathematical Modeling of the Primary Drying Stage

Primary drying is the most critical stage of the freeze-drying process. This work aimed to establish a design space for this process by means of mathematical modeling of the primary drying stage, capable of addressing the thermal characteristics of distinct vial suppliers. Modeling of primary drying was implemented on Microsoft Excel using steady-state heat and mass transfer equations at two extreme conditions as assessed by risk analysis, to predict product temperature and primary-drying time. The heat transfer coefficients (Kv) of four different vial suppliers were experimentally determined, both, at the center and edge of the freeze-dryer's shelf. Statistically significant differences (ANOVA p<0.05) were observed between suppliers throughout the assessed pressure range. Overall, the average Kve/Kvc (edge/center) ratio was higher than 1.6 for all suppliers due to the radiation effect. A design space for the drying process was established using mathematical modeling taking into account the Kv of the worst-case supplier, in the shelf edge. A primary drying cycle was carried out at a shelf temperature of -25 °C and a chamber pressure of 45 mTorr for 8 % sucrose and at -10 °C and 75 mTorr for 5 % NaCl. Freeze-dried products with good cosmetic appearance were obtained for the four vial suppliers both, in the shelf center and edge. The results show that it is possible to predict and establish the critical parameters for the primary drying stage, under a design space concept, considering the differences in the Kv of vial suppliers without adverse consequences on the quality of the finished freeze-dried product.