Inverse Heat Conduction Method Research Articles

Effects of temperature gradients on thermomechanical fatigue of nickel-based superalloy

Temperature-gradient-mechanical fatigue (TGMF) is a significant concern in internal cooling turbine blades. In the present study, the through-thickness temperature gradient was determined by the inverse heat conduction method and investigated in TGMF. Using the continuum damage mechanics, the environmental impact was identified as the primary contributor to the in-phase TGMF damage. A damage accumulation model encompassing fatigue, creep and environmental impact was established and provided satisfactory accuracy in TGMF life assessments. The main conclusion is that temperature gradients do not change the fracture mode but significantly increase stress levels by at least 20%, accelerating oxidation damage and resulting in a TGMF life ca. 10 times shorter than that of TMF.

Real-Time Data-Driven Inverse Heat Conduction Method for a Reentry Flight Vehicle Based on the Random Forest Algorithm

Real-Time Data-Driven Inverse Heat Conduction Method for a Reentry Flight Vehicle Based on the Random Forest Algorithm

Electrowetting assisted shedding of droplets by a shearing airflow in dropwise condensation

Condensation is a necessary part of most industrial processes dealing with phase change. Efficient condensate removal (shedding) increases the systems’ performance. This study investigated the influence of electrowetting on droplet shedding and heat transfer enhancement during humid air condensation on a horizontal substrate. A mini closed-looped wind tunnel was used to simulate the condensation environment and control condensation parameters. AC electric field with the frequencies of 1 and 10 kHz was applied and compared with the control case (no voltage). The transient inverse heat conduction method was used to determine the heat transfer coefficient, and heat transfer measurements were synchronized to a high-resolution camera to monitor the condensation dynamics. The results show that the area-weighted average droplet radius was increased by 61 % and 84 % for 1 kHz and 10 kHz, respectively, compared to the control case for 1 m/s airflow. At 10 kHz, the shedding time was reduced, particularly at higher airflow velocities. Additionally, the heat transfer coefficient (HTC) exhibited a significant increase at 10 kHz when shedding was present. Notably, the difference in HTC became pronounced at an airflow velocity of 15 m/s, where shedding was prominent. In this scenario, the HTC rose by an impressive 35 % compared to the control case. These findings provide a promising foundation for utilizing EW to enhance heat transfer and improve condensate shedding under shear flow conditions.

Study of flow boiling in a vertical mini-channel with surface structuring: Heat transfer analysis using inverse method

Using a boiling fluid to cool components is a very efficient process, which is often used in micro/mini channel flows. A proposed application is the direct contact liquid cooling of lithium-ion battery cells, where a dielectric fluid is required and where the effects a cell thermal runaway could be mitigated by a convective boiling flow between the cells. For such applications, better designs require both to understand confined convective boiling with coupled flow phenomena and to quantify the local heat transfer accurately. The present paper introduces new experimental results of flow boiling heat transfer of a dielectric fluid, the HFE-7100, in a vertical rectangular 1 mm deep, 30 mm wide and 120 mm long mini-channel. The test section is an aluminum block instrumented with three lines of five K-type thermocouples located all along the flow. The experiment mainly aims at determining the heat transfer coefficient and CHF and at characterizing both the flow regimes and the dry-out phenomenon. Measurements are carried out from start of boiling to dry-out, at different mass fluxes (140, 390 and 648 kg/(m2.s)) and at a pressure of 1.1 bar. These tests were performed on a reference unmodified surface and compared to two biphilic surfaces including coating techniques. The visualization of the flow is achieved through a glass pane with a high-speed camera to identify different flow patterns. The local heat transfer coefficient is calculated by a resolution of a 2D inverse heat conduction method. This approach uses a numerical Finite Difference Method (FDM) for the spatial discretization and a Tikhonov's method for regularization. The inverse 2D method permits to follow the evolution of the heat transfer coefficient along the channel with the visualized flow pattern. The experimental results show a small sensitivity of the mass flux on the heat transfer coefficient and a predominance of nucleate boiling. On the other hand, there is a significant sensitivity of the mass flux on the dry-out occurrence. Finally, the sensitivity of two techniques of biphilic surface coating on boiling and on the dry-out occurrence is quantified and discussed.

Solutions of one-dimensional inverse heat conduction problems: a review

Estimations using the inverse conduction approach to predict temperature and heat flux at the exposed surface lead to indirect measurements away from the exposed surface within the solid. The approach is extremely useful when access to direct measurements is not possible due to various working conditions, and thereby provides estimates without disturbing the flow under the real flow condition over the surface. The approach is useful not only for heat transfer applications but also for numerous engineering applications, including fluid mechanics and furnace applications. The approach requires the time history of effective parameters at the strategic locations away from the exposed surface to be known. In the present paper, a review of sequential development of various inverse heat conduction methods is presented to get solutions in different geometries.

Experimental investigation of heat transfer characteristics of polyethylene glycol (PEG) based quench media for industrial heat treatment

Aqueous polymer quenchants are now increasingly used in the quench hardening of steels. The inverse solubility property of polymer media leads to polymer film encapsulation of the quenched component, followed by an instantaneous rupture of the polymer film. The film boiling stage is absent, thus improving heat transfer uniformity. In the present investigation, the effect of molecular weight of Polyethylene glycol (PEG) on heat transfer characteristics of PEG/water quenchants with concentrations of 5, 10, and 20 vol% was studied. The cooling curve analysis is performed to assess the cooling characteristics. Spatially dependent surface heat flux transients are estimated using the inverse heat conduction method. The rewetting kinematics is analyzed by videography and acoustic analysis of polymer film rupture during quenching. The results indicated that an increase in the molecular weight of PEG from 200 to 6000 changed the rewetting kinematics from a local wetting front movement to an instantaneous rupture of the polymer film. The change in the rewetting kinematics is reflected in the surface heat flux, indicating an increased uniformity of heat transfer. The film rupture acoustics showed that the polymer film's instantaneous breakup had a higher sound intensity than the one showing wetting front motion.

Investigation of reacting fuel jets in hot vitiated crossflow

Near-wall reacting jets can occur in different engineering applications, such as rocket combustion chambers and in gas turbine combustors and turbines. This work presents results of experimental investigations of reacting gaseous fuel jets (hydrogen, methane, propane) injected normally into a hot oxygen-rich cross-flow using OH laser-induced fluorescence and OH* chemiluminescence diagnostics. RANS CFD simulations with EDC combustion model are performed for comparison. To determine the surface heat fluxes, the inverse heat conduction method was applied using measured wall temperature data as input. It was observed, that hydrogen jets ignite directly at the injection location and caused a higher surface heat flux than the hydrocarbon jets, where jet-like diffusion flames emerged. With the latter fuels, a significant ignition delay length was observed. Operation with methane fuel showed the least stability, least reactivity and the lowest surface heat flux. Increasing the jet momentum ratio led to a reduced ignition delay length due to enhanced jet-crossflow interaction, and to a reduction of surface heat flux as the reacting jet detached more from the surface. CFD results using the Eddy-Dissipation Concept (EDC) combustion model predicted ignition delay lengths and reaction zone shapes in qualitative agreement with the experiment but with a trend of overestimating combustion temperatures.

Heat Transfer Characteristics of Fullerene and Titania Nanotube Nanofluids under Agitated Quench Conditions.

Distilled water and aqueous fullerene nanofluids having concentrations of 0.02, 0.2, and 0.4 vol % and titania (titanium dioxide, TiO2) nanofluids of 0.0002, 0.002, and 0.02 vol % were analyzed for heat transfer characteristics. Quenching mediums were stirred at impeller speeds of 0, 500, 1,000, and 1,500 RPMs in a typical Tensi agitation system. During the quenching process, a metal probe made of ISO 9950 Inconel was used to record the temperature history. The inverse heat conduction method was used to calculate the spatial and temporal heat flux. The nanofluid rewetting properties were measured and matched to those of distilled water. The maximum mean heat flux was 3.26 MW/m2, and the quickest heat extraction was 0.2 vol % fullerene nanofluid, according to the results of the heat transfer investigation.

Determination of Secondary Cooling Zone Heat Transfer Coefficient with Different Alloy Types and Roughness in DC Casting by Inverse Heat Conduction Method

The cooling characteristic curves in a heated ingot with a diameter of 100 mm quenched by a water jet were measured under different conditions. A two-dimensional calculation model was established to calculate the HTC of magnesium alloy ingot with water spray cooling. Data from cast-in thermocouples trail were input into the model and the HTCs were back-calculated for the water quench region. The HTCs were calculated under different alloy types and roughness conditions, and the relationship between the ingot surface temperature, roughness, and the HTC was established accordingly. The results show that the greater the thermal conductivity of the alloy, the greater the heat transfer coefficient (HTC). The HTCs of AZ80, AZ31, and ZK60 alloys increase successively. With the decrease in the surface temperature, the HTC in both the impingement zone and the free−falling zone shows a trend of a rapid increase at first, then slowly increasing to the maximum value, and finally, a rapid decrease, with the peak value appearing at about 400 K. Considering the influence of the ingot surface temperature and the surface roughness on the HTC, the mathematical relationships between them are established.

Analysis of temperature gradients in thin-walled structures under thermomechanical fatigue loading conditions

In recent thermal gradient mechanical fatigue (TGMF) investigations, it is verified that the material fatigue lives are significantly affected by the temperature gradients. Determination of temperature gradients of thin-walled structures is always a difficult task. In the present work, tubular specimens were experimentally and computationally investigated under different conditions. The inverse heat conduction (IHCP) method was improved to predict the inner boundary from external measurements. Two models were finally developed, based on direct IHCP or modified Nusselt number estimation. The models are qualified to acquire temperature gradients in TGMF experiments with reasonable accuracy and versatility.

Estimation and analysis of surface heat flux during gas quenching through IHC method

Gas Quenching is a process of quenching steel components with a gas quenchant. This process, due to its several advantages is being extensively used now a days. This work studies the effect of the variation of gas jet pressure and the standoff distance (SOD), which is the distance between the quench probe and the tip of the nozzle on the quenching heat transfer during gas quenching. A gas quenching chamber of octagonal cross-section of side 100 mm was used for quenching experiments, in which an array of nozzles was fixed. The cylindrical workpieces of 20 mm diameter and 50 mm length were machined from stainless steel 304L and K-type thermocouples were fixed at the selected locations inside the workpiece to read the temperature during quenching. Compressed air as the quenchant at different pressures of 4 bar, 6 bar and 8 bar and different SOD of 9 cm, 10 cm and 11 cm were used to study the effect of these two parameters on the quenching heat transfer rates. Surface heat flux computations were made using Inverse Heat Conduction (IHC) method using the measured time–temperature data as input. It was found out that as the pressure increased, the cooling rate and the peak surface heat flux increased and as the nozzle standoff distance was increased, the cooling rate and the peak surface heat flux dropped. The effect of increasing the nozzle SOD by 1 cm was more than the reduction of gas jet pressure by 2 bar.

Identification of the thermal contact resistance in transient regime to detect the phenomenon of delamination in multilayer electronic devices

The present study is based on the numerical analysis of the thermal behavior around multilayers electronic component’s interfaces. These components are increasingly miniaturized and receive constantly growing powers. These operating conditions cause serious thermal problems, which can lead to a progressive degradation of their performances and decrease their duration life. In multilayer electronic structures, this alteration is translated by delamination phenomenon in the interface contact regions. In order to detect damages on multilayers electronic components, we propose to follow the evolution of the thermal contact resistance between layers in the transient phase. To do this, we identify the thermal contact resistance by inverse heat conduction method from temperature measurements.

Effect of process temperatures on material flow and weld quality in the friction stir welding of high density polyethylene

The material flow in the weld zone of friction stir welded bi-modal high density polyethylene (HDPE) was investigated under different in-process temperatures. The in-process temperatures were controlled by changing the tool rotation speed, welding speed and the material initial temperature. Boundary temperature measurements were recorded on the top and bottom surfaces of the welded plates and the temperature distribution in the workpiece was determined numerically using an iterative inverse heat conduction method. Material flow patterns were observed by welding two different colors of the polymer blanks, white on the advancing side and black on the retreating side. Joint quality was assessed using optical microscopy, and joint strength and elongation were measured by tensile testing. It was found that process temperatures greatly affect the extent of material flow in the weld zone, which in turn affects the tendency to form defects and the overall joint mechanical properties. It was also found that proper fusion across the interfaces occurs when the material in the welding zone was maintained at temperatures in excess of 100 °C across the thickness. The high temperature conditions instigated proper fusion of the material, which in turn resulted in large weld efficiencies and elongations in excess of 100%.

Research on the heat transfer characteristics of air-atomized water spray cooling by experiment and inverse heat conduction method

Research on the heat transfer characteristics of air-atomized water spray cooling by experiment and inverse heat conduction method

Inverse Heat Conduction Method to Estimate the Heat Flux During Quenching Process of Hot Metals with Infrared Thermography Measurements

Inverse Heat Conduction Method to Estimate the Heat Flux During Quenching Process of Hot Metals with Infrared Thermography Measurements

Using the Inverse Method to Investigate Flow Models for Mixed Convection of Annular Finned Tube Heat Exchanger

The inverse heat conduction method (IHCM) and three-dimensional (3D) computational fluid dynamic (CFD) in combination with are used to select the appropriate flow model and near-wall treatment for the mixed convection of the annular finned tube heat exchanger. Thus, the numerical results obtained by all k-ε models and near-wall treatments are yielded for 4 m/s ≤ Va ≤ 5 m/s. First, IHCM combined with is applied to estimate and Q values. The obtained estimates of and Q are used as reference values for CFD. The results show that the Tk and results obtained by the standard (STD) k-ε model with the standard wall function (SWF) are closer to and the estimates of than those by the realizable (REAL) and RNG k-ε models with various wall functions for Va of 4-5 m/s. The value obtained from the STD k-ε model with SWF, Va =5 m/s and S=15 mm may be 1.14 times that of the RNG k-ε model and 0.48 times that of the REAL k-ε model. The value of the RNG k-ε model with SWF is about 1.6-1.7 times that with EWT for S = 5 mm and Va = 4 m/s and 5 m/s. These differences mean that the appropriate flow model needs to be varied with Va to obtain more accurate numerical results. The y+ of RNG and STD k-ε models does not exceed 3. However, the y+ of the REAL k-ε model exceeds 6. To our best knowledge, no studies have explored this issue and the present investigation tries to bridge this gap.

Sensitivity Coefficient-Based Inverse Heat Conduction Method for Identifying Hot Spots in Electronics Packages: A Comparison of Grid-Refinement Methods

Abstract Estimating the distribution and magnitude of heat generation within electronics packages is pivotal for thermal packaging design and active thermal management systems. Inverse heat conduction methods can provide estimates using measured temperature profiles acquired using infrared imaging or discrete temperature sensors. However, if the heater locations are unknown, applying a fine grid of potential heater locations across the surface where heat generation is expected can result in prohibitively large computation times. In contrast, using a more computationally efficient coarse grid can reduce the accuracy of heat flux estimations. This paper evaluates two methods for reducing computation time using a sensitivity-coefficient method for solving the inverse heat conduction problem (IHCP). One strategy uses a coarse grid that is refined near the hot spots, while the other uses a fine grid but only considers heater locations near the hot spots. These methods are compared using input temperature maps acquired from a “numerical experiment,” where the outputs of a three-dimensional (3D) steady-state thermal model in FloTHERM are used for input temperatures, and temperature maps procured using infrared microscopy on a real electronics package, using sensitivity coefficients calculated with the FloTHERM model. Compared to the coarse-grid method, the fine-grid method is found to reduce computation time without significantly reducing accuracy, making it more convenient for designing and testing electronics packages. It also avoids the problem of “false hot spots” that occurs with the coarse-grid method. Overall, this approach provides a mechanism to predict hot spot locations during design and testing and a tool for active thermal management.

Online estimation of the heat flux during turning using long short-term memory based encoder-decoder

Heat flux during machining has received extensive attention due to its importance for understanding the cutting mechanism and promising prospects on intelligent manufacturing. Research on heat flux estimation by inverse heat conduction methods faces many challenges, including measurement error amplification, stability of the methods, and limitations for applications. In this paper, we introduce a long short-term memory (LSTM) based encoder-decoder (ED) scheme in online estimation of the heat flux imposed at the tool-chip region during turning. The math-physical model and finite element model are established to generate training datasets. Numerical tests using simulated heat flux and temperature data representing different machining conditions are carried out to evaluate the method performance. Compared with other artificial intelligence methods such as multilayer perceptron, convolutional neural networks and LSTM, the LSTM-ED model performs better at all tested noise levels (1≤σ≤20K) with acceptable time cost for online process. Effects of the location and number of sensors on the accuracy of heat flux estimations are also investigated. Experimental validations based on cutting temperature measurements by five thermocouples located in the insert are conducted. Both numerical and experimental tests indicate the potential of the LSTM-ED method for online heat flux monitoring in scientific research and industrial production.

Determining transient heat transfer coefficient for dropwise condensation in the presence of an air flow

It is necessary to understand humid air condensation because of its various applications, such as water harvesting. In this study, the influence of airflow on the condensation heat transfer coefficient of humid air on a horizontal surface was investigated experimentally. Airflow velocities from 1 to 15 m/s were investigated, because the condensate's shedding usually happens in this range. A relative humidity of 10–80% and subcooling temperature (Tsc) of 0–10 °C were used to achieve both single-phase and condensation regimes. To study the relationship between condensate morphology and heat transfer coefficient (HTC), transient and instantaneous heat flux measurements were required. To facilitate this, a transient inverse heat conduction method was developed to characterize the time-varying surface heat flux and associated heat transfer coefficient. A 5-fold decrease in response time was found for the transient method compared to the steady-state method. The effect of condensation parameters on the heat transfer coefficient, as well as the relationship between condensate morphology and heat transfer coefficient, is discussed. The results show that HTC for the subcooling of T = 0 °C is smaller than for other temperatures. Also, the effect of RH on condensation was investigated and higher HTC was found for higher RHs. The results clearly show that the shedding of condensate kept the average droplet size low and doubled heat transfer performance improvement.

Experimental investigation of heat transfer characteristics during water jet impingement cooling of a high-temperature steel surface

ABSTRACT The microstructure and mechanical properties of the hot rolled steel depend on the laminar jet cooling control on the runout table. An experimental and numerical study of the heat transfer during water jet impingement cooling of a hot steel plate (600 to 900°C) is presented. The effects of plate temperature upon the heat transfer were analyzed by the inverse heat conduction method that provided the heat fluxes on top surface from measured temperatures into the plate. Rewetting (liquid-solid contact) occurs on surface above 880°C. Higher initial temperatures enlarge the heat flux, but delay the onset of the rewetting and the advance of rewetting front radius (Rwet). Heat transfer coefficient (HTC) increases as surface temperature decreases. The size of the non-symmetric effective jet cooling zone depends on strip speed. Correlations to predict HTC and Rwet have been proposed. Results will contribute for enhancement of fast cooling system in hot strip mill.