Two-dimensional Transient Heat Transfer Research Articles

Transient thermal management of laser systems using Plate-Fin phase change heat Exchangers: Experimental and computational study

To mitigate transient thermal shocks in lasers and reduce thermal stresses caused by temperature fluctuations, the use of phase change materials (PCMs) in thermal management systems is a viable solution. This study proposes an innovative two-dimensional transient heat transfer model specifically designed for plate-fin phase change heat exchangers (PFPCHEs). The model meticulously simulates the complex heat transfer phenomena within the heat exchanger, including fluid convection, solid thermal conduction, and the phase change processes of PCM. The convective heat transfer coefficient between fluid and plate is calculated using the Wieting correlation. An advanced pulse-mode experimental test platform was constructed to validate the model, dynamically monitoring and recording outlet temperatures and heat exchange performance for stringent experimental comparison. The research explores the impact of key operating parameters such as initial temperature, flow rate, and inlet temperature of the cooling cycle on the performance of the heat exchanger, providing valuable design and control strategies for transient thermal management of laser systems. The experimental results confirm that the model accurately predicts the dynamic response characteristics and temperature distribution of PFPCHEs under multi-cycle pulse loads, with 96% of the predictions within a 10% error margin. A significant finding is that the initial temperature has negligible influence on the heat transfer characteristics when it is below the solid phase temperature of the PCM. Moreover, by meticulously adjusting the flow rate and inlet temperature of cooling cycle, it is possible to effectively maintain the stability of the outlet temperature throughout the entire pulse cycle. This is crucial for minimizing temperature fluctuations within the thermal management system and extending the service life of electronic components.

Comprehensive numerical modeling of intermittent flow cooling with enhanced photovoltaic efficiency in PVT/NPCM systems

The photoelectric conversion efficiency of photovoltaic thermal (PVT) systems is a key concern in solar energy research. The widespread use of continuous nanofluid cooling in PVT/NPCM (Nano-Enhanced Phase Change Material) systems leads to heightened energy consumption. In order to improve efficiency of the PVT/NPCM systems, a two-dimensional transient heat transfer numerical model is established to analyze the PVT/NPCM system with intermittent flow cooling. Corresponding govern equations with boundary conditions are proposed, and numerically solved by using the finite element method. Simulation results are compared with experimental data, showing a deviation of less than 7 %. The findings indicate that the intermittent cooling reduces the flow energy consumption required to drive 2220 L of nanofluid compared to continuous cooling over a 7-h period. Furthermore, under intermittent cooling conditions, the average electrical efficiency stands at approximately 19.7 %. Notably, the electrical efficiency of PVT/NPCM systems employing intermittent flow cooling closely aligns with those employing continuous flow cooling, exhibiting a maximum deviation of merely 0.0348 %. Additionally, intermittent flow cooling emerges as a favorable choice under solar radiation intensities surpasses 1000W/m2, enabling a significant reduction in overall energy consumption while maintaining commendable cooling performance.

Numerical investigation and optimisation of solid–solid phase change material composite-based plate-fin heat sink for thermal management of electronic package

Phase Change Material based Thermal Management Systems show promise in electronic packaging systems for safe operation, acting as a thermal storage element to prevent sudden temperature surges, enhancing operational time and mitigating electronic system failures. Therefore, the meticulous design of a solid–solid phase change material (SSPCM) based heat sink with fins is imperative for effective electronic thermal management by improving its safe operational time. This study performs a numerical analysis of two-dimensional transient heat transfer for the SSPCM-based plate-fin heat sink using the modified enthalpy porosity method, where the plate fins serve as Thermal Conductivity Enhancers (TCEs). Neopentyl glycol with 6% (w/w) Copper oxide nanoparticle is used as the SSPCM composite. Enhancement ratio based on safe operational time at different power levels (2–6 W) with different percentages of TCE and fin count recorded variation from 1.32 to 13.7. The TCE integration is more effective at higher power levels. The optimisation of SSPCM-based heat sink design for maximum safe operational time is accomplished through Response Surface Methodology. The significance of the TCE fraction, number of fins, heat generation rate, and interaction effects over the safe operational time are observed. The correlation for safe operational time as a function of TCE volume fraction, fin count and heat generation rate is developed. TCE volume fraction possesses the highest influencing factor over safe operational time at lower and higher power levels compared to fin count. At 2 W and 6 W, a maximum change in safe operational time is observed from 72.7% at 2 W to 83.45% at 6 W. The heat sink with 0.262 volume fraction of TCE and 11 fins is the optimised design that can provide the desirable safe operational time for the tested range of power levels.

Quench cooling of steel plates by reciprocating moving water jet impingement

Owing to the short time duration and violent nature of boiling regimes, the steel quench cooling on the Run Out Table is extremely complex, this challenges the prediction of the heat transfer coefficient. In this study, we first established a novel reciprocally moving nozzles platform to experimentally investigate the moving quenching process. Then the two-dimensional transient heat flux, wetting behaviors, and heat transfer mechanism that was influenced by the surface temperature, and moving speed were explored. These results revealed the heat flux reduced with the moving speed but elevated with the surface temperature. The wetted area also expanded linearly with the decrease in temperature. With the aid of the developed two-dimensional transient heat flux, the heat quantity was revealed to decrease with the surface temperature at different speeds, but the decline proportion was much lower than that of MHF (maximum heat flux). Notably, the transient heat flux and heat transfer capacity in two-dimensional favored predicting the temperature field of the steel quenching process under industrial conditions. The findings in this work provided the envision to understand the heat transfer mechanism in the moving quenching cooling and provided a flexible method to investigate cooling in a moving state.

Investigation and optimization of solidification performance of concentration tube type latent heat storage unit with herringbone wavy fin designs

The solidification rate of the latent heat storage units is relatively low and can be significantly improved using fins. The current study investigates the solidification performance of concentric tube-type latent heat storage unit with different designs of herringbone wavy fins. A validated two-dimensional transient solidification heat transfer model for latent heat storage unit with different herringbone wavy fin designs has been utilized and solved in a commercially available CFD solver. For all the studied cases, the fin's volumetric fraction is 5.5 % of the LHSU volume in the numerical solution. Initially, the solidification performance of different herringbone wavy fins and conventional longitudinal fins have comparatively analyzed. The fin-D design has been found to be the most effective, with a 22 % reduction in the solidification time compared to conventional longitudinal fins. Additionally, the effects of geometrical parameters, viz. relative fin height, relative divergence angle, and wave number for fin-D have also been investigated. The optimum values of relative fin height, relative divergence angle and wavenumber have been found at 1, 0.667 and 0.12 mm−1, respectively. The solidification time has been found to be 29 % less for the optimum herringbone wavy fin design than the conventional longitudinal fins.

Dynamic Heat Transfer Calculation for Ground-Coupled Floor in Emergency Temporary Housing

Generally, ground-coupled floor heat transfer is supposed as annual periodic, which is reasonable for conventional buildings. However, for emergency housing with a short life cycle, the influence of initial soil temperature needs to be considered. In a previous study, the Wiener–Hopf technique was introduced to solve the two-dimensional transient heat transfer equation with mixed Dirichlet and Robin boundary conditions. Based on that, an analytical solution of the dynamic heat transfer equation with initial soil temperature conditions was obtained. Since the solution was in the form of a double integral, its numerical evaluation method was also analyzed to improve computational efficiency. The accuracy and efficiency of the solution were validated by the finite volume method. Then, the effects of initial soil temperatures in different seasons, soil heat conductivities, and floor insulation on ground-coupled heat transfer were discussed. Results showed significant temperature differences between the current solution and the annual periodic solutions (long-time solutions), especially in hot and cold climates. Moreover, the larger the thermal capacity of the soil, the bigger temperature differences occurred. Therefore, this study is expected to provide a theoretical foundation for the indoor environment prediction and optimization design of emergency temporary housing.

Two-dimensional transient heat transfer model of moving quenching jet based on machine learning

The heat transfer model plays a significant role in improving the steel quality during quench cooling by water jet impingement. However, the available models are still incapable of accurately modeling the heat transfer process. In this work, we perform the multiple impingements of jet on high-temperature steel plate surface experimentally and reveal the effects of surface temperatures, jet velocity, moving speed, and equalization time on the heat transfer behaviors. Then, we propose a time-constrained surface heat flux calculation method to measure the transient heat flux more accurately. Even in the case of lower temperature measurement frequency and larger heat conduction delay, precise calculation results can also be predicted. Importantly, a machine learning method is employed to fit and analyze a large number of experimental data, the machine learning model can predict two-dimensional (2D) transient heat flux in the moving cooling process and the accuracy can be continuously reinforced with the increase of experimental data. Based on the well-trained machine learning model, a heat flux prediction software is developed and open access at GitHub. This work provides an accurate heat transfer model for numerical analysis and shows great application potential in the steel industry, and the results will help deepen the understanding of the heat transfer mechanism.

An improved sequential function specification coupled with Broyden combined method for determination of transient temperature field of the steel billet

Accurate knowledge of the steel billet temperature field in the reheating furnace is of crucial importance to improvement of product quality and energy conservation. For this purpose, the determination of the transient temperature field of the steel billet during reheating is investigated based on the inverse heat conduction problem. The transient two-dimensional heat transfer model of the billet in the furnace is established and used as the direct problem. The sequential function specification coupled with the Broyden combined method (BC-SFSM) is developed to obtain the temperature field of steel billet. A real measurement experiment is conducted for validation of the inverse model, which indicates that the BC-SFSM can accurately determine the billet temperature field from the temperatures measured at three points inside the billet. A series of numerical experiments are implemented to analyze the performance of the BC-SFSM and study the effects of the measurement point locations and of the number of future time steps on inverse results. The results illustrate that the BC-SFSM can take only 49.0% of the computing time of the sequential function specification method to estimate the billet temperatures, and the relative root-mean-square error of estimated temperatures is generally less than 1.5% when the reasonable number of future time steps and suitable measurement point locations are adopted. Therefore, the BC-SFSM in this work is a promising algorithm to determine the billet temperature field in the reheating furnace with high accuracy and efficiency.

Study of two-dimensional transient heat transfer through a multi-layers wall: Application to the buildings thermal insulation

The two-dimensional transient heat conduction through a multilayers wall made of different materials and thicknesses was numerically resolved. The equations system resolution was carried out by Alternating direction implicit method (ADI). The outdoor and indoor temperatures and the convective coefficients used as boundary conditions in the developed Fortran program were from the Algerian regulatory technical document. After validation of the Fortran program with literature, it was used to studying the influence of different boundary conditions (bottom and top sides), on the thermal insulation in the building, for many configurations of external walls, usually used in building construction at Batna city (Algeria). Results showed that for the configurations that give bad thermal insulation, the conditions imposed on the top and bottom of the wall have practically no influence on the internal temperature of the multilayers wall, however, the opposite is observed for the configurations that ensure good thermal insulation.

Thermal performance of phase change material–based heat sink with hybrid fin‐metal foam structure under hypergravity conditions

The thermal management systems or heat sinks are an integral part of electronic devices for aerospace applications. The heat transfer characteristics of the widely used phase change material (PCM)-based heat sinks under hypergravity conditions are essential in the designation of the heat sink. The current study conducts a systematic evaluation on the thermal characteristics of PCM coupled with hybrid fin-metal foam (FMF) structure under variable hypergravity conditions. A validated two-dimensional transient melting heat transfer model of the designed system is proposed, and the influences of enclosure orientation, fin height, PCM slab thickness, and the distribution of fin and metal foam under different hypergravity conditions are investigated. Results show that with the decrease in inclination angle, the melting time and the heating wall temperature become lower, and the optimal inclination angle is 0°. As the PCM slab thickness gets larger, natural convection is enhanced, while the heating wall temperature and melting time become larger. With the rise of hypergravity value, the effect of inclination angle strengthens, while the influence of PCM slab thickness weakens. Furthermore, with the rise of the copper foam fraction in the hybrid FMF structure, the melting time and the heating wall temperature firstly decrease and increase afterward. The optimal copper foam fraction is 58.62%. This study guides the optimal design of the PCM-based heat sink in aerospace applications.

Optimization of thermal model and prediction of crystallinity during the laser-assisted tape winding process

Laser-assisted tape placement and tape winding represent the most advanced automated manufacturing technologies for thermoplastic composites. It is important to accurately predict the complete thermal history of the manufacturing process, on which many properties of the product are strongly dependent, such as interlaminar bonding strength and crystallization. In this article, a nonlinear two-dimensional transient heat transfer model was established in ANSYS APDL, and a new temperature closed-loop controlled near-infrared laser heat source was described. Most importantly, the thermal contact pairs were introduced following the activation of elements, and the value of interlaminar thermal contact resistance was obtained by fitting an independent experiment and finite element analysis, which greatly optimized the heat transfer process in the direction of thickness. The thermal model was verified by infrared cameras and an online temperature measuring system based on thermocouples. The results of thermal history are in good agreement with the experiment, which were input into the crystallization kinetics model to predict the evolution and distribution of crystallinity in the laser-assisted tape winding process. The calculated results are coincident with the differential scanning calorimeter test very well, and the crystallinity was about 17% higher than that before manufacturing.

Design of sensible and latent heat thermal energy storage systems for concentrated solar power plants: Thermal performance analysis

A shell-and-tube design with different thermal energy storage (TES) media was investigated as a promising TES system for a next generation concentrated solar power (CSP) plant. Sensible TES using graphite, latent TES using phase change materials (PCMs) and a hybrid of both were investigated. A two-dimensional transient heat transfer model was applied to simulate the thermal performance of multiple shell-and-tube TES modules connected in series. Considering the realistic operation of the CSP plant, an intensive numerical investigation was conducted to design and size the storage system. The TES systems studied were categorized as 3-PCM cascade, 5-PCM cascade, PCM-graphite-PCM hybrid and single graphite. All the PCMs considered in this paper have been experimentally proven as potential candidate storage media. It was found that all the TES systems studied, if well designed, can meet the CSP operational requirements. In comparison, single graphite storage is less problematic, but it has the lowest storage density (47.3 kWhr/tonne). By forming a PCM-graphite-PCM sandwich configuration, the energy density was increased to 60.9 kWhr/tonne and the storage effectiveness of this hybrid system is 70.7%, the highest among all the TES systems studied.

Effective thermal conductivity of a bed packed with granular iron–manganese oxide for thermochemical energy storage

Heat transfer is studied in a lab-scale tubular reactor packed with spherical 0.5–1 mm iron–manganese oxide particles with an Fe/Mn molar ratio of 2:1. A two-dimensional transient heat transfer model considering conduction, convection and radiation heat transfer is developed to simulate the temperature profile in the reactor. The effective thermal conductivity of the packed bed as well as the wall heat transfer coefficient are determined based on the experimental data and a steady-state model. The validity of calculated effective parameters is checked by employing the parameters in a transient model and comparing the predicted temperature profile with transient experimental data and by comparison with existing correlations found in the literature.

Unsteady Natural Convection in a Differentially Heated Rectangular Enclosure Possessing Sinusoidal Corrugated Side Walls Loaded with Power Law Non-Newtonian Fluid

This research is a numerical analysis exhaustively investigating two-dimensional (2D) transient convective heat transfer in a differentially heated rectangle, possessing sinusoidal corrugated side walls at constant temperatures. The quadrilateral space is filled with a power-law non-Newtonian fluid, plus the right and left walls are uniformly cooled and heated, respectively. The top and bottom walls are retained as adiabatic and the side walls are recast exploiting sinusoidal corrugated shape. The governing equations of the problem are solved using the finite volume method. The evaluation of fluid flow and heat transfer is conducted in such a manner that the power law index n varies from 0.6 to 1.4, the Rayleigh number Ra from 103 to 107, the corrugation amplitude CA from 0.1 to 0.5, and the corrugation frequency CF of the sinusoidal side walls is in the range of 1 to 5. The results are studied at different values of Ra, n, CA, and CF; they are presented in the form of streamlines, isotherms, and average Nusselt numbers ( $$\overline{\rm{Nu}}$$ ) of the hot side wall. Further, the heat transfer characteristics are presented and the effect of sudden differential heating, as well as its consequential transient behavior, on the fluid flow, velocity, and temperature plots are demonstrated in accordance with the scope of the governing parameters.

Numerical investigation of phase change material thermal storage for space cooling

Space cooling is the main contributor to high electrical power demand in summer. This research investigates the effect of adding a phase change thermal energy storage unit (PCTSU) to an air source heat pump (HP) cooling system. The HP model improves on an existing model in the simulation software library to simulate the HP performance. The PCTSU performance is simulated using a newly developed two-dimensional transient heat transfer model, which is experimentally validated against available experimental results. The cooling system is operated in three modes to satisfy the space cooling demand of a 7.6 stars house in the City of Adelaide, Australia. The PCTSU is charged by the HP when outdoor temperature is relatively low and discharged either whenever space cooling is required during the day (mode M2) or during the peak period only (mode M3). The simulation is conducted for the whole cooling season, and the cooling energy and electricity usage performances of the system with a PCTSU (modes M2 and M3) are compared with those of the system without a PCTSU (mode M1). A sensitivity analysis reveals that the PCTSU performance is slightly sensitive to the uncertainties of melting temperature of the phase change material and to the inlet temperature of the heat transfer fluid. The PCTSU provides 25% and 13% of the cooling energy and requires 11% and 6% of the electrical energy usage for charging by the HP in modes M2 and M3 respectively. Both electricity usage and demand tariffs are considered, and the cost savings are 14% and 7% in the former and 14% and 13% in the latter, in modes M2 and M3 respectively. The cost analysis indicates that techno-economic benefits of using PCTSUs should be carefully analysed. Appropriate economic incentives are needed to accelerate the uptake of thermal storage for space cooling applications to reduce high electrical power demand and help to avoid the need to further increase the grid capacity.

Characterization and modeling of deposition geometry in directed energy deposition over inclined surfaces

Abstract Directed Energy Deposition (DED) is setting a relatively new trend for the repair and restoration of high value components. Repair of these components necessitates contoured depositions due to the complexity in the geometry. This further demands depositions at various inclination angles. The influence of inclination angle needs to be studied so as to predict the final deposition geometry which will be a function of the powder loss and the melt-flow. Therefore, this study is aimed at exploring the effect of inclination angle on the powder catchment efficiency and shape evolution of the deposited track. Asymmetry is observed in the cross-section of the deposited track while carrying out the DED at an inclination. A two-dimensional transient heat transfer model with fluid flow has been developed to predict the temperature distribution, track melt pool boundary during the deposition process. The solidification and the arrest of the melt pool flow is accounted by employing the enthalpy porosity model. The model is used to predict the deposition geometry. Predicted deposition geometry values agree reasonably well with the experimental results. This model is used to recognize the factors contributing towards this asymmetry during the deposition at inclination. The study reveals that there is a substantial drop in the powder catchment efficiency from 66% to 19% as the inclination angle is increased from 0o to 75o. In order to have uniform clad, increasing mass flow rate is a viable option as the catchment efficiency is almost unchanged with increasing mass flow rate.

Transient temperature fields and thermal stress fields in glazing of different thicknesses exposed to heat radiation

Thermal performance analysis and cracking prediction of glazing elements are essential for fire safety evaluation of a building. This work investigated the transient temperature fields and the corresponding stress fields in glazing of different thicknesses with one side exposed to heat radiation. Based on the results of investigation, the criterion of critical temperature difference in cracking prediction was formulated. Glass samples of different thicknesses were tested under the same radiation exposure. Besides, a transient two-dimensional heat transfer model was presented to obtain the transient temperature fields in the glass samples. In addition, the temperature fields were loaded to ANSYS to obtain the thermal stress fields. It is found that in the initial heating period, the maximum stress was mainly caused by the temperature gradient component across thickness and the stress value was larger for thicker glazing; as time evolved, the maximum stress was gradually dominated by the temperature gradient component along the planar direction. Thus, for thick glazing under strong heat, thermal bending stress caused by temperature gradient across thickness should be calculated first to evaluate the cracking time, and the criterion of critical temperature difference is appropriate only if the thermal bending stress cannot reach the breaking value. For other conditions, cracks will result from the stress caused by the temperature gradient along the planar direction, and the criterion of critical temperature difference is applicable for cracking prediction of glazing in any thickness.

Numerical and experimental investigation of heat transfer in a solar receiver with a variable aperture

Variable aperture can assist in maintaining semi-constant temperatures within a receiver’s cavity under transient solar loading. An in-house code has been developed to model a receiver and effectively control its components to achieve semi-constant temperatures under transients. The code consists of a full optical analysis performed via the Monte Carlo ray tracing method in addition to a transient two-dimensional heat transfer analysis. The system studied consists of a cavity type solar receiver with 60 mm radius fixed aperture on the cavity body, a variable aperture mechanism mounted on the receiver’s flange, and a 7 kW Xenon arc solar simulator. A composite shape consisting of a hemisphere attached to a cylinder is proposed to model the Xenon arc. The in-house code has been experimentally validated through experimental tests for different input currents to the solar simulator, volumetric flow rates, and aperture’s radii. The optical analysis was validated based on heat flux measurements, where it had percentage errors of 0.8, 0.5, 1.1, and 3.2% for the peak power, total power, half width, and half power. For the heat transfer model, percentage errors of 3.2, 2.9, and 5.3% at the inlet, center, and outlet sections of the receiver were determined for different flow rates using maximum input current and opening radius. The aperture mechanism was capable of maintaining an exhaust temperature of 250 °C based on actual Direct Normal Irradiance data. Results showed that the variable aperture is a promising apparatus even in applications where the maximum temperatures are desired based on an observed optimum radius of 57.5 mm.

An alternative sensitivity method for a two-dimensional inverse heat conduction-radiation problem based on transient hot-wire measurements

ABSTRACTAn inverse approach based on hot-wire measurements has been proposed to simultaneously estimate radiative and conductive properties of metallic/ceramic foam samples, from a unique experiment. A theoretical model of two-dimensional transient conduction-radiation heat transfer in a cylindrical medium allowed to accurately simulate real temperature measurements in a hot-wire cell. Based on this model, the Levenberg–Marquardt method (LMM) has been adopted as the inverse technique. According to a sensitivity and correlation analysis, measuring points were suitably chosen and a proposed two-stage estimation technique was successfully performed. Due to the dimension of the model and to the number of identified parameters, a large computational time was required to calculate the sensitivity matrix. The Broyden’s combined update method has been adopted as an alternative sensitivity method, whose combination with the LMM reduced considerably the amount of computation. This reduction reached 69% for each of the studied samples.

Optimization design of built-up thermal protection system based on validation of corrugated core homogenization

An optimization procedure aiming to design a built-up thermal protection system is presented in this paper. The built-up thermal protection system comprises of classical Integrated Thermal Protection System (ITPS) and additional layer of insulation material which is attached to the cold surface of ITPS. In this paper, corrugated core sandwich panel which is fabricated using C/SiC composite material is considered as an ITPS when the core void is filled with insulation material. It is found in this paper that for the built-up TPS the temperature calculated based on corrugated core homogenization shows significant deviation from the exact solution. The significant advantage of the built-up TPS in insulation ability compared to the traditional ITPS is validated. An interesting phenomenon is also found that with the increasing insulation ability of the attached insulation, the temperature on the cold surface of the sandwich panel would converge to a stable value. Based on this finding, a two-step design procedure with high accuracy and high efficiency is exploited for the built-up thermal protection system. At the first step, the stable value of temperature on the cold surface of the sandwich panel is obtained utilizing the finite element technique, and is used as the boundary condition needed in the second step. At the second step, the two-dimensional transient heat transfer problem is transformed into a one-dimensional problem based on which the optimal thicknesses of the multiple insulation layers are obtained utilizing the finite difference formulation. Numerical results show that the thickness and the areal density of the built-up TPS can be significantly reduced by considering multilayer design.