Steady-state Heat Transfer Analysis Research Articles

Introducing a microstructure-embedded autoencoder approach for reconstructing high-resolution solution field data from a reduced parametric space

Abstract In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into an autoencoder architecture. This method’s integration of parametric space information significantly reduces the amount of training data needed to effectively predict high-fidelity solutions from low-fidelity ones. In this study, we examine a two-dimensional steady-state heat transfer analysis within a heterogeneous materials microstructure. The heat conductivity coefficients for two different materials are condensed from a 101 $$\times $$ × 101 grid to smaller grids. We then solve the boundary value problem on the coarsest grid using a pre-trained physics-informed neural operator network known as Finite Operator Learning (FOL). The resulting low-fidelity solution is subsequently upscaled back to a 101 $$\times $$ × 101 grid using a newly designed enhanced autoencoder. The novelty of the developed enhanced autoencoder lies in the concatenation of heat conductivity maps of different resolutions to the decoder segment in distinct steps. Hence the developed algorithm is named microstructure-embedded autoencoder (MEA). We compare the MEA outcomes with those from finite element methods, the standard U-Net, and an interpolation approach as an upscaling technique. Our analysis shows that MEA outperforms these methods in terms of computational efficiency and error on representative test cases. As a result, the MEA serves as a potential supplement to neural operator networks, effectively upscaling low-fidelity solutions to high-fidelity while preserving critical details often lost in traditional upscaling methods, such as sharp interfaces features lost in the context of interpolation approaches.

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.

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

The techno-economics of transmitting heat at high temperatures in insulated pipes over large distances

This study reports a systematic techno-economic assessment of the cost-optimal transmission for air as the heat transfer fluid at temperatures of up to 1200 °C, at scales of 1 to 1000 MW and at distances of up to 10 km. It employs a steady state heat transfer analysis, with energy balances, to assess the effect of scale, temperature and insulation on the heat losses and efficiency of the thermal transmission system, following by a techno-economic assessment. The sensitivity of the Levelised Cost of Heat, LCOHtr, to variations in thermal scale, operating temperature, distance, refractory and insulation thickness, ratio of the thickness of refractory and insulation, cost of any supplementary heat and lifetime is reported. The results show that LCOHtr decreases with an increase in thermal scale, as expected. The role of insulation is much more complex, since increasing the thickness of thermal barrier increases both cost and efficiency of the transmission, requiring an economic optimum to be determined for each of the various conditions assessed. Parameters are also coupled because a higher cost of supplied energy/ heat justifies the use of more insulation material. For a large GW scale thermal system, we estimate that it is possible to achieve a minimum overall LCOHtr,min of 0.16–0.36 USD/GJ/km of the length of the thermal transmission system, excluding additional location-specific costs such as land-access and local construction costs. These estimated costs are sufficiently attractive to justify ongoing development of systems to transport renewable heat to industry from sources such as concentrated solar thermal energy.

Analysis of variable inductor employing vegetable-based transformer oil with magnetic nanoparticles

Variable inductors using magnetorheological fluids have recently been successfully applied to power-conversion devices; however, the thermal properties of Vegetable oil-based Magnetic Nanofluids (VMNFs) have not been investigated. In this study, the temperature characteristics of a variable inductor embedded with a VMNF were analyzed by developing a multiphysics analysis method and verified experimentally. To analyze the temperature distribution efficiently, a coupled analysis of the Magnetoquasistatic (MQS) field and steady-state heat transfer field based on the finite-element method was performed. The B-H curves of the VMNF and ferrite core were obtained via magnetic property measurement experiments, and the input waveforms were measured from the current and high-frequency pulse voltages applied to the variable inductor of the DC–DC converter. To predict the temperature rise of the VMNF-gap variable inductor, the power dissipation was determined using the Steinmetz experimental equation modified by the Bertotti model in the electronic system solver and input as a heat source in the steady-state heat-transfer analysis. The temperature increase predicted by the multiphysics analysis method agreed well with the experimental data, and an increasing the concentration of magnetic nanoparticles had a cooling effect. The developed MQS–thermal field coupled analytical method and the cooling properties of VMNFs can be applied to the design of power-conversion devices operating with high-frequency power sources.

Comparative analysis of insulation strategies for improving thermal performance of wall to parkade suspended slab

This article focuses on the thermal bridging issues associated with interface of parkade concrete suspended slab to base of wall. The study aims to determine the optimal length and thickness of insulation at the top and underside of the suspended slab to minimize heat loss. The thermal performance of wall to parkade suspended slab is investigated, for both wood frame and steel stud constructions. Various insulation configurations are proposed and evaluated, including different lengths and thicknesses of extruded polystyrene foam (XPS) and Fiberglass spray insulations. The thermal performance calculations are conducted using steady-state heat transfer analysis. A finite-element based software is utilized for the simulations. The study provides a detailed methodology for analyzing the thermal performance of building envelope details, considering different insulation configurations. The results of the simulations are presented as Thermal Resistance Values (R-Values) and Linear Thermal Resistance Values (PSI-Values), allowing for a comparison of the thermal efficiency of different insulation configurations. The results show that utilizing the optimal insulation configuration can lead to up to 80 % enhancement in the thermal efficiency of the assembly. The findings serve as a guideline and aim to assist building designers in improving the thermal performance of concrete suspended slabs.

Cryogenic flow boiling in microgravity: Effects of reduced gravity on two-phase fluid physics and heat transfer

With the growing interest in space exploration, cryogenic technologies involving two-phase flow and heat transfer are in high demand to successfully procure advanced space applications such as fuel depots and nuclear thermal propulsion (NTP) systems for deep space missions. However, the unique and extreme thermal properties of cryogenic fluids introduce distinct flow boiling fluid physics and energy transport phenomena, which differ significantly from those observed with conventional fluids. Understanding the unique two-phase physics in cryogenic flow boiling remains an ongoing challenge. Furthermore, the lack of readily available microgravity cryogenic steady-state heat transfer data hinders the assessment of gravitational effects on cryogenic flow boiling. This study aims to elucidate the gravitational effects on two-phase fluid physics and heat transfer by conducting the first-ever experimental measurement of cryogenic flow boiling performance using a steady-state heated method in a reduced gravity environment. Parabolic flight experiments were performed to acquire both heat transfer measurements and high-speed video of interfacial behaviors, under varying gravity levels (microgravity, hypergravity, Lunar gravity, and Martian gravity). The experiments involved flow boiling of liquid nitrogen (LN2) with a near-saturated inlet along a circular heated tube of dimensions 8.5-mm inner diameter and 680-mm heated length. The operating parameters varied are mass velocity of 398.3 – 1342.8 kg/m2s, inlet quality of -0.08 to -0.01, and inlet pressure of 413.68 – 689.48 kPa. Captured microgravity flow patterns range from bubbly to annular, all having vapor structures that are larger than those under higher gravity levels. Under microgravity, absence of buoyancy yields symmetrical vapor structures without flow stratification, laying a physical foundation for the distinct two-phase heat transfer trends during LN2 flow boiling in microgravity. Transient data collected during the flight parabolas exhibited decreasing heated wall temperature as the aircraft transitioned from hypergravity to microgravity phases. The temperature variation indicated an enhancement in flow boiling heat transfer with decreasing gravity levels and a reduction with increasing gravity levels. The effect of reduced gravity on cryogenic flow boiling heat transfer coefficient (HTC) is discussed based on steady state heat transfer analysis. Seminal HTC correlations are evaluated against the measured microgravity HTC data, of which one is identified for superior accuracy in predicting microgravity data. Finally, a new HTC correlation is proposed to improve accuracy of microgravity predictions, yet there still exists room for further improvement with future terrestrial flow boiling experiments at different flow orientations relative to Earth gravity.

Numerical investigation and optimisation of flat plate solar collectors using two swarm-based metaheuristic algorithms

In the present work, four flat-plate solar collectors of similar dimensions have been simulated using the CFD approach. Model 1 has been considered as circular with a U-shaped zigzag channel, while model 2 is a square-shaped plate. In the 3rd model, the number of turns in the channel has been increased by keeping the geometry of the pipe constant, while in the 4th model, multiple straight channels have been incorporated instead of a single U-shaped zigzag channel. Three-dimensional simulations have been primarily done to understand the effect of channel geometry area and turnings on the collector's performance. A steady-state incompressible forced convective heat transfer analysis has been performed here. Water is used as a fluid in the channel to carry heat. The results of the numerical analysis led to the conclusion that model 3 is the best flat plate solar collector where turnings are maximum. With a maximum collector performance of 41.57, model 3 performs 36.7% better than model 1. Additionally, when water flows at a rate of 8 m/s inside the collector's channel, the rate of heat transfer in model 3 is 2.5% faster than in model 1. Moreover, a global optimization study has been performed using two swarm-based metaheuristic algorithms, Gravitational Search Algorithm (GSA) and Firefly Algorithm (FA), with the aim of determining good optimum values of the design variables that will maximize collector efficiency for model 3 at different flow velocities. For model 3, the percentage variation in collector efficiency between CFD and optimised findings using metaheuristic algorithms is found to be (a) 41.08% for v = 2 m/s; (b) 28.41% for v = 4 m/s; (c) 21.71% for v = 6 m/s; and (d) 13.09% for v = 8 m/s. Therefore, it is possible to anticipate that as flow velocity increases, there will be a steady decrease in the variation between computed and optimized results.

Conceptual design of a compact multipurpose space simulation system

One of the biggest challenges in space systems engineering is simulating the space environment when developing and testing various components, subsystems and entire satellites prior to a mission. Therefore, a space simulation system is needed to reproduce the vacuum of space, the intense solar radiation and the extreme temperature variations. Such a facility can be extremely complex and expensive. One way to reduce costs is working with small-sized systems and implementing a compact facility capable of fulfilling multiple applications. The system must be useable as a space simulator, a thermal-vacuum chamber or a standard vacuum chamber, all the while allowing a quick and easy transition between operational modes. This requires the implementation of a removable thermal shroud capable of reaching −150 °C and +150 °C. First, the thermal shroud geometry is defined and the nitrogen flow and temperature requirements are calculated. The second step is a steady-state heat transfer and structural analysis, performed using the software Ansys in order to obtain the temperature, stress and deformation. The last step is the virtual integration of the thermal shroud and vacuum chamber using the software Catia V5.

Impact of grooved cylinder on heat transfer by natural convection in cylindrical geometry

The current study reports a numerical analysis of a two-dimensional steady-state natural convection heat transfer from grooved heated cylinder for laminar flow regime. Two groove shapes are investigated in this work: circular and triangular groove. Simulations were carried out by varying the groove location, radius ratio f from 0.1 to 1, and the Rayleigh number over the range [103–106]. The thermal and dynamic behaviors are carefully analyzed and compared to the case of non-grooved cylinder (model 0). It is found that the heat transfer rate rises up with the increase of Rayleigh number. In addition, the groove locations φ = −90, and 80° provide the lowest heat transfer rate. A decrease of 9.4% in the heat transfer rate is detected for the case of triangular groove with f = 0.7 and Ra = 105. On the other hand, the highest heat transfer rate is provided at a position φ = −45° and 45° for f > 0.65. For these last groove locations, lower f present optimal configurations to accumulate heat on the cylinder. In fact, circular grooved cylinder with f = 0.1 decreases the heat loss by 9.3% and 12.4% for the locations φ = −45° and 45°, respectively compared to model 0. These results would be useful for engineering applications that are interested in the accumulation or transfer of heat through cylindrical ducts.

Temperature response and thermal performance analysis of a super-long flexible thermosyphon for shallow geothermal utilization: Field test and numerical simulation

• Super-long flexible thermosyphon (SFTS) fabricated by metal corrugated pipe, 32m in length. • Field tests of SFTS for shallow geothermal utilization. • Start-up and steady-state thermal performance of SFTS. • CFD simulation of long-term underground temperature variation near SFTS. • A method to avoid the heat transfer problem due to super-high liquid column of working fluid in super-long thermosyphon. A super-long flexible thermosyphon (SFTS) fabricated by the corrugated pipe, with a total length up to 32m, was field-tested in a drilling, in order to evaluate its potential for use in shallow geothermal utilization. The seasonable dependence of local underground temperature and air temperature, the corresponding temperature response of SFTS, and the its heat transfer characterists were investigated. The underground temperature recovery characteristics under the operation of uni-directional heat extraction were also conducted by a combination analysis of field tests and CFD simulation. The temperature response characteristics of SFTS in start-up of field tests show that the SFTS could operate effectively as the vaporization of working fluid occurs all over the whole evaporator. This indicates that employing a corrugated pipe prevents the formation of a super-high liquid pool at evaporator, which would inhibit the boiling of working fluid at the bottom. The maximum heat transfer power of SFTS obtained in field tests of this work is approximately 305W under the conditions with the inlet temperature of cooling water controlled at 5.5°C and the flow rate at 1500mL/min. The analysis of steady-state heat transfer results reveal that the underground temperature plays the most important role in the overall thermal performance of SFTS, followed by the flow rate and the temperature of cooling water. The long-term uni-directional heat extraction of SFTS from underground for heating is feasible and however the heat extraction rate is recommended to be maintained below 30W/m at the drilling site aiming to make sure a good sustainability. This work reports field tests of a super-long flexible thermosyphon in geothermal utilization for the first time.

Studies on heat transfer characteristics of vapor chamber under periodic-pulsed heat source

In a high-power microwave device, the intense electron beam causes a high-heat-flux on the collector’s inner surface which results in an instant temperature increase which eventually causes the output power to drop. The vapor chamber is one of the passive cooling devices effective for high-heat-flux heat dissipation. To study the heat dissipation capacity and the surface temperature control effect of the vapor chamber, a numerical heat transfer model of the vapor chamber is proposed based on the effective thermal conductivity method. The accuracy of the steady-state heat transfer analysis and the applicability of the transient simulation are verified by comparing with experimental data, and the heat transfer are calculated under the condition of periodic pulsed heat sources. Lastly, the transient performance of a vapor chamber relative to a copper heat spreader of the same external dimensions is investigated as a function of the wick effective thermal conductivity, pulsed heat flux, and pulse duration. The transient behavior of the vapor chambers are examined to find a performance threshold to determine if the performance is superior to that of a copper heat spreader. The present work provides a basis to understand the advantages and limitations of metal heat spreader in pulse mode operation of vapor chamber and plays a vital role in the design of improving transient performance.

Numerical analysis of heat transfer in electric motor casing made of ceramic reinforced aluminium matrix composites

Sustainable and renewable energy is the need of the hour. Scientists and Engineers around the world are pushing for electric vehicles and electrically run machines to save the environment from pollution and global warming, to create a sustainable planet for us humans to live. The aim of the present research work is to understand the heat transfer characteristics of an electric motor casing made of Aluminium Metal Matrix Composites (AMMCs) so as to implement such casings on a larger scale. As aluminium composites are light in weight, this would improve the performance and efficiency of the electric motor in the long run, and when thought about at the global level considering the new upcoming age of electric vehicles, the slightest of improvements could produce a major impact in the upcoming years. The CAD model of the casing is designed using Solidworks software. This model is used to conduct Finite Element Steady State Heat Transfer analysis in Ansys software to study the heat transfer characteristics. Five AMMCs are chosen for analysis. A comparative study is made based on the weight of the casing and the heat transfer characteristics for each material. Al/Graphite composite is found to produce promising results in the heat transfer domain.

Temperature-based optimization of friction stir welding of AA 6061 using GRA synchronous with Taguchi method

Friction stir welding (FSW) is a recent novel joining mechanism in the solid-state welding process. It is extensively used to join similar and dissimilar materials as well. This research studied and found the optimum process parameters of FSW based on the temperature simulation results on a 5-mm 6061 Al alloy sheet with a butt joint configuration. Steady-state heat transfer analysis was performed using a transient thermal workbench to predict and identify the optimum parameters based on the simulation welding temperature result. The parameters are optimized using the hybrid Taguchi L9 orthogonal array and grey relation analysis (GRA) method with a larger is better quality characteristic. The mechanical properties of the weld joints such as hardness and tensile strength were studied at an ambient temperature. The result revealed that a higher rotational and minimum welding speed with taper threaded tool pin imparts the optimum parameter settings. Analysis of variance (ANOVA) was carried out also to determine the effects of each process parameter. At a 95% confidence interval, rotational and welding speed are significant parameters. The joint efficiency reached 92.25% of the base metal at optimum parameter settings. Additionally, the microstructure of the stir weld zone of the specimen was studied as well. Metallographic characterization carried out using a scanning electron microscope (SEM) revealed the microstructure of the samples after the weld did not show much significant change with the base metal.

Heat Transfer Effect on Micro Gas Turbine Performance for Solar Power Applications

This paper presents an experimentally validated computational study of heat transfer within a compact recuperated Brayton cycle microturbine. Compact microturbine designs are necessary for certain applications, such as solar dish concentrated power systems, to ensure a robust rotodynamic behaviour over the wide operating envelope. This study aims at studying the heat transfer within a 6 kWe micro gas turbine to provide a better understanding of the effect of heat transfer on its components’ performance. This paper also investigates the effect of thermal losses on the gas turbine performance as a part of a solar dish micro gas turbine system and its implications on increasing the size and the cost of such system. Steady-state conjugate heat transfer analyses were performed at different speeds and expansion ratios to include a wide range of operating conditions. The analyses were extended to examine the effects of insulating the microturbine on its thermodynamic cycle efficiency and rated power output. The results show that insulating the microturbine reduces the thermal losses from the turbine side by approximately 11% without affecting the compressor’s performance. Nonetheless, the heat losses still impose a significant impact on the microturbine performance, where these losses lead to an efficiency drop of 7.1% and a net output power drop of 6.6% at the design point conditions.

Simple exact analytical solution of laser-induced thermal transport in supported 2D materials

This work proposes a very simple and exact analytical method for analysis of laser-induced steady-state heat transfer in supported two-dimensional (2D) materials over an infinite domain. The present method uses Hankel transform and special Meijer's G-functions to solve the heat diffusion equation in order to avoid the use of numerical methods at any stages of the solution. Herein, a concise description on the mathematical and physical assumptions required to apply the method, is also provided. The finite element method (FEM) is used to support the validity of our new analytical approach. In two short examples, it was demonstrated that the results of this method are in complete agreement with the FEM and previously published data. Finally, the probable factors which have led to some discrepancies between our results and those in the literature were addressed.

Thermal behaviour of annular hyperbolic fin with temperature dependent thermal conductivity by differential transformation method and Pade approximant

The current paper explores the steady-state heat transfer and thermal stress analysis of a hyperbolic annular fin with temperature dependent thermal conductivity. The framed equations are articulated in terms of non-linear ordinary differential equations. The domination of non-dimensional parameters on the thermal gradient of the fin has been analysed graphically by using Runge–Kutta Fehlberg fourth-fifth order (RKF-45) process and DTM-Pade approximant. Here, differential transformation method (DTM)-Pade approximant has been implemented to find the analytical solution for the non-linear ordinary differential equations. The RKF-45 method is used to obtain numerical outcomes for different non-dimensional parameters. Further, the obtained numerical results are compared with the results achieved from DTM-Pade approximant solution. This relation demonstrates that numerical outcome obtained by DTM-Pade approximant are nearer to that of numerical results. Outcome results exposes that, the escalating values of thermal conductivity parameter upsurges the thermal distribution. The growing values of the radius ratio elevate the thermal distribution in the fin. Further, the radial stress and tangential stress distribution varies for larger values of dimensionless parameters.

Investigation of the effect of contact pattern design on the mechanical and thermal behaviors of plastic‐steel helical gear drives

This article describes an investigation that has been conducted to assess the effects of the contact pattern design on the mechanical and thermal behaviors of plastic-steel helical gear drives. The maximum contact pressure, frictional power loss, transmission error function and operating temperature are determined for different designs of the pinion tooth surfaces. Several numerical examples based on loaded tooth contact analyses and steady-state heat transfer analyses are carried out considering different types of micro-geometry modifications of the involute tooth surfaces. The obtained results show that an appropriate design of the pinion tooth surfaces can help reducing the maximum contact pressure and the maximum operating temperature, increasing the durability of the transmission. The frictional power loss and the peak-to-peak transmission error can be diminished, improving the performance of the transmission and increasing its efficiency. Also, it has been shown that the design of the pinion tooth surfaces can provide some capability to the transmission to absorb angular misalignments.

Temperature Distribution Analysis of Composite Heat Sink (Pin Fin) by Experimental and Finite Element Method

Design of machine components plays a vital role in the field of Engineering where it includes the shape of component, size, applied loads, position and materials used. Due to the applied loads namely static, thermal and combined loads etc., the component undergoes stresses and deformations which affect the life of component and also the system. The Finite Element Method (FEM) is a numerical tool used for solving problems of engineering and mathematical problems in the fields of structural analysis, heat transfer, fluid flow, mass transport etc., For problems involving complicated geometries, loadings and material properties, it is generally not possible to obtain analytical solutions. These solutions generally require the ordinary or partial differential equations. Because of the complicated geometries, loadings and material properties, the solution can’t be obtained easily. So, in FEM the complicated shape of the component is divided in to small entities called elements. Element characteristics are studied and then all the elements are combined to make a single system of component. In the present work, Experiments have been conducted to find the temperature distribution within the pin fin made of composite metals and steady state heat transfer analysis has been carried using a finite element software ANSYS to test and validate results. The temperature distribution at different regions of pin fin are evaluated by FEM and compared with the results obtained by experimental work. The results are in good agreement and thus validated.

Steady-state heat transfer analysis in a spherical domain revisited

The paper discusses the numerical solution of the one-dimensional radially axi-symmetric non-linear second-order differential equation to model the conduction and radiation transfer through a spherical domain as a result of an exothermic heat source. The equation is transformed to a non-dimensional form. The dimensionless numbers emanating from the transformation represent the effect of the reaction rate, reaction type, activation energy, radiation and the convection on the temperature. The non-dimensional differential equation for the temperature distribution was previously solved using the Runge-Kutta-Fehlberg method coupled with a Shooting technique. In this paper the solution of the non-dimensional differential equation using an iterative Galerkin finite element method approach employing the Picard method is described. The commercial finite element code Comsol is also employed to solve the non-dimensional differential equation. The current study was motivated by inconsistencies that were observed in the previous results that were presented. Although the assumed underlying physics is used to evaluate the results, the study focuses purely on the numerical solution of the non-dimensional differential equation. The results obtained by the Galerkin finite element code and Comsol were found to be in exact agreement and also exhibit no inconsistencies.