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During drilling, different kick locations significantly impact the formation-wellbore temperature (FWT) profile under the co-existence of kick and leakage condition (CKL). To ensure safety and efficiency during drilling, we study the effect of different kick locations on the FWT under the CKL. In this paper, a full transient heat transfer model based on the first law of thermodynamics is established to obtain four distinct WFT profiles under CKL conditions, incorporating both convective heat transfer and variable mass flow effects. Compared with the actual temperature measurement data, the reliability of the developed model is verified. The case studies show that the annular temperature (AT) is lower under the single-point leakage (SL), continuous leakage (CL), and CKL conditions than that in the normal drilling condition. Wellhead temperature in CKL differs significantly from that in normal drilling (ND). As the kick location gets closer to the bottom hole, the AT gets higher, and the temperature difference between the formation and annular gets smaller. Compared with the wellbore temperature profile under ND, the kick location can be detected by real-time monitoring of the FWT profile under the CKL.

In the production process, the printed circuit board with all kinds of electronic components is placed in the rewelding furnace and the electronic components are automatically welded to the circuit board by heating. In this production process, the temperature control of the resolder furnace is very important to ensure the product quality. In this paper, by analyzing the heat transfer characteristics of rewelding furnace, the three-dimensional problem is transformed into one-dimensional problem, and the transient heat transfer process is studied and analyzed. Considering the two heat transfer modes of heat conduction and heat convection, the partial differential equation model of one-dimensional double-layer heat conduction is constructed, and the classical mathematical and physical method is used to model and simulate the heat conduction in the welding process of printed circuit board. the variation diagram of the furnace temperature curve and the temperature in the center of the welding zone at different positions in the small temperature zone are obtained.

Purpose The paper aims to present an advanced 2 D transient heat transfer analysis capable of accounting for the effect of spalling in terms of amount, location and time. The model accounts for moving thermal boundary conditions to comply with the changing member cross section. The discussed numerical model provides a tool to quantify the effect of spalling on the flexural capacity of reinforced concrete beams. Design/methodology/approach The implementation of the presented numerical model in an in-house code and its validation has been discussed. The thermal subroutine has been sequentially coupled with the mechanical subroutine (sectional-analysis) to compute the variation of sectional moment carrying capacity with exposure time. Findings The temperatures predicted while considering spalling were in good agreement with experiments available in literature. The presented results also emphasise the importance of considering the time of spalling. The results also show that the fire rating of simply supported beams is also affected by spalling in the compression zone. Research limitations/implications It should be acknowledged that the model does not predict spalling, rather is developed as a tool to study the effect of spalling. The model takes the information related to spalling in terms of the location, amount and time, as user input. Originality/value The paper quantitatively presents the effect of spalling on the predicted temperature variation across the beam cross section and the moment carrying capacity.

In deep water drilling, the existence of boost line makes the wellbore temperature change violently, and the thermal stress caused by it has a great influence on the strength of the riser. The paper considers the variable mass flow caused by the boost line fluid entering the wellbore during deepwater drilling. Based on the principle of conservation of mass and energy, the paper establishes a mathematical model for transient heat transfer in different regions of the wellbore and formation, analyzes the effect of the displacement of boost line on the temperature field of the wellbore, and calculates the transient stress of the casing under thermal effect. The results show that with the increase of cycle time, the temperature of the inner wall of the riser above the critical well depth first decreases and then increases. The thermal stress of the inner wall of the riser first increases and then decreases to zero, and then gradually increases, and the final thermal stress remains unchanged. With the increase of cycle time, the thermal stress of the inner wall of the riser increases with the increase of the circulating temperature of the inner wall of the riser below the critical well depth, and the rate of increase decreases gradually, and the final thermal stress remains unchanged. As the displacement of the riser increases, the circulating temperature of the inner wall of the riser increases, and the thermal stress on the inner wall of the riser increases. The research results can provide reference for the analysis of the factors affecting the riser stress in deep water drilling.

Annular pressure buildup (APB) is induced by high‐temperature tubing fluid heating the trapped annular fluid, which leads to liquid thermal expansion at the production stage in deepwater wells. Casing would be burst or collapsed without APB mitigation. A novel recovery relief method was adopted to mitigate APB through the principle of differential pressure. To assess the application effect of the method, APB prediction model and pressure relief threshold determination method were proposed, where the transient heat transfer and volume and pressure coupling were involved. The laboratory test of the principle prototype was conducted so that the feasibility of the recovery relief method was validated. The numerical APB mitigation effect was simulated by the field example. The production simulation results indicated that the high‐temperature‐induced APB caused casing failure. The simulation of APB mitigation with both inward and outward directions demonstrated that the casings using outward mitigation method were safer with lower safe factor. Besides, comparing the mitigating effect to the rupture disk, the recovery relief method had more maximum allowable APB of annulus A. Additionally, compared to other 11 ordinary mitigation methods with the qualities of engineering reliability, technology feasibility, and economy, the recovery relief method had best mitigation performance. Therefore, the recovery relief method was recommended for APB mitigating practice. The paper proposed a recovery relief method for annular pressure buildup (APB) mitigation in deepwater wells. The tool is worked by the pressure difference between the adjacent annulus. Both the simulation results and tests validate the feasibility of the method. Also, the tool is compared with other mitigation method, which is found the best overall performance for reliability, feasibility, and economy. Therefore, the recovery relief method is recommended for APB mitigation practice.

We conducted a transient experimental investigation of steam–water direct contact condensation in the absence of non-condensible gas in a laboratory-scale column with the inner diameter of 325 mm and the height of 1045 mm. We applied a new analysis method for the steam state equation to analyze the molar quantity change in steam over the course of the experiment and determined the transient steam variation. We also investigated the influence of flow rates and temperatures of cooling water on the efficiency of steam condensation. Our experimental results show that appropriate increasing of the cooling water flow rate can significantly accelerate the steam condensation. We achieved a rapid increase in the total volumetric heat transfer coefficient by increasing the flow rate of cooling water, which indicated a higher thermal convection between the steam and the cooling water with higher flow rates. We found that the temperature of cooling water did not play an important role on steam condensation. This method was confirmed to be effective for rapid recovering of steam.

The efficiency of horizontal ground heat exchangers (GHEs) is strongly influenced by soil saturation, which directly affects heat transfer rates and system stability. This study presents a numerical analysis of how soil moisture content impacts the thermal response of a horizontal GHE operating in heating mode over a one-month period. A finite element-based transient heat transfer model was developed to simulate dynamic interactions between the heat exchanger and surrounding soil, incorporating saturation-dependent soil properties and variable thermal conductivity to replicate realistic field conditions. The results show that higher soil saturation enhances heat exchange efficiency by increasing effective thermal conductivity, reducing thermal resistance, and stabilizing temperature distribution around the pipes. Conversely, low saturation levels lead to greater temperature fluctuations and reduced heat transfer rates, negatively impacting system performance over time. The study further highlights the cyclic thermal behaviour of the heat exchanger, demonstrating how soil moisture content influences both daily and long-term thermal variations. These findings emphasize the critical role of soil moisture in optimizing geothermal heat exchanger design and operation.

This article represents the result of experimental research on transient heat transfer in a multilayered (heterogeneous) wall. Our non-steady thermal transmission simulation is based on a finite-difference calculation method. The value of a Fourier number shows the similarity of thermal variation in conditional layers of an enclosure. Most scientists recommend using no more than a value of 0.5 for the Fourier number when performing calculations on dynamic (transient) heat transfer. The value of the Fourier number is determined in order to acquire reliable calculation results with optimal accuracy. To compare the results of simulation with experimental research, a transient heat transfer calculation spreadsheet was created. Our research has shown that a Fourier number of around 0.5 or even 0.32 is not sufficient ( ≈17% of oscillation amplitude) for calculations of transient heat transfer in a multilayered wall. The least distorted calculation results were obtained when the multilayered enclosure was divided into conditional layers with almost equal Fourier number values and when the value of the Fourier number was around 1/6, i.e., approximately 0.17. Statistical deviation analysis using the Statistical Analysis System was applied to assess the accuracy of the spreadsheet calculation and was developed on the basis of our established methodology. The mean and median absolute error as well as their confidence intervals has been estimated by the two methods with optimal accuracy ( FoMDF=0.177 and FoEPS=0.1633 values).

We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.

Abstract An advanced evaluation method for transient heat transfer experiments using thermochromic liquid crystals (TLCs) combining the advantages of standard hue and maximum intensity methods is presented. In order to obtain a global evaluation of locally correct heat transfer coefficients by using the one-dimensional solution of Fourier's equation, assuming heat conduction in a semi-infinite medium with a convective boundary condition, local input values have to be identified from measurements of the fluid and surface temperatures. For that reason, two different approaches have emerged. First, a two-dimensional numerical method has been adapted to evaluate the transient fluid temperature distributions in multi-pass systems from a few local measurements. Additionally, on the basis of latest calibration and indication experience of TLCs, especially in complex passages, an innovative temporal indication analysis method using a neural network has been implemented in the process of heat transfer evaluation.