Transient Heat Research Articles

Topography optimisation using a reduced-dimensional model for transient conjugate heat transfer between fluid channels and solid plates with volumetric heat source

Consideration of transient effects is important for industrial applications of heat transfer structure optimisation studies; however, the huge computational cost associated with transient problems is a pressing concern. This paper proposes an extension of a previous reduced-dimensional model to transient conjugate heat transfer between a fluid flow and solid-heated plates in a plate heat exchanger. The extended reduced-dimensional model introduces the temperature field of the plate governed by the heat conduction equation, which is coupled to the temperature field of the fluid, governed by the convection-diffusion equation, through the heat flux balance equation at the contact surface. The model is based on assumptions of fully developed flow and constant temperature profile, reducing the three-dimensional problem to a planar problem and significantly reducing computational costs. The accuracy of the model for the simulation of transient heat transfer is verified by comparison with a three-dimensional model. In this paper, the topography of the heat exchanger plate is optimised for both steady-state and transient conditions by applying the reduced-dimensional model. The effectiveness of the optimised design was demonstrated by the cross-check of both the reduced-dimensional and full three-dimensional models. Furthermore, this work considers the effect of time-independent boundary conditions and time-dependent boundary conditions on transient optimisation. The transient and steady-state optimised designs are analysed and compared for both conditions, and the necessity of transient optimisation is discussed.

Fast explicit time integration schemes for parabolic problems in mechanics

AbstractWe present a family of fast explicit time integration schemes of first, second and third order accuracy for parabolic problems in mechanics solved via standard numerical methods that have considerable higher computational efficiency versus existing explicit methods of the same order. The derivation of the new explicit schemes is inspired on the finite increment calculus (FIC) procedure used for obtaining stabilized numerical schemes in fluid and solid mechanics. The new (so‐called) explicit FIC‐Time (EFT) schemes allow considerable larger time steps than the standard first order forward Euler (FE) scheme and the second and third order Adams–Bashforth schemes. The comparison with Runge–Kutta schemes also favors the FIC‐Time schemes in terms of the limit time step size (for second order schemes) and the total number of matrix‐vector multiplications per time step (for second and third order schemes). The new first order explicit schemes have a faster convergence to steady‐state than the FE scheme. The accuracy and efficiency of the new EFT schemes are verified in examples of application to the transient heat conduction equation using the finite element method.

Nonlinear dynamic response of a temperature-dependent FGM spherical shell under various boundary conditions and thermal shocks: Examination of dynamic snap-through

In this study, a comprehensive exploration of the nonlinear dynamic snap-through phenomenon observed in shallow spherical shells composed of functionally graded materials (FGMs) is examined. The analysis encompasses the interplay of thermomechanical characteristics within metal and ceramic phases, taking into account their temperature-dependent behaviors. To address this problem, the transient heat conduction equation in a nonlinear form, accounting for the temperature dependence factor is derived. To solve this complexity, the Generalized Differential Quadrature (GDQ) method is employed, coupled with the Crank-Nicolson time integrating scheme, leveraging an iterative approach for precision. The formulation of nonlinear dynamic motion equations is based on Hamilton's principle and incorporates the utilization of nonlinear strain-displacement equations and uncoupled thermoelasticity. In the spatial domain, GDQ proves invaluable in solving these nonlinear, coupled equations. In the temporal domain, the Newmark procedure in conjunction with the Newton-Raphson iterative method are utilized to navigate through dynamic equations, yielding insights into shell's behavior over time. In the initial stages of the investigation, we validate our spherical shell formulation and methodologies by comparing shell's response with existing, simpler works. This step ensures the reliability and accuracy of our model. The primary objective is to assess the presence and characteristics of the thermal snap-through phenomenon within the shell under these diverse conditions.

Assessment of Axisymmetric Dynamic Snap-Through and Thermally Induced Vibrations in FGM Cylindrical Shells Under Instantaneous Heating

This paper addresses the investigation of axisymmetric thermally induced vibrations in Functionally Graded Material (FGM) cylindrical shells. It considers temperature-dependent (TD) properties and geometric non-linearity (the von Karman effect). The study systematically solves a transient heat conduction equation using finite differences method and the Crank–Nicolson method. During the heating stages, the evaluation of thermal forces and moments takes place. Equations of motion are derived through the application of Hamilton’s principle. Spatial dependencies are discretized using the generalized Ritz method, while temporal dependencies are approximated using the [Formula: see text]-Newmark method with Newton–Raphson linearization. A comparative analysis validates the procedure’s efficiency and precision. Parametric studies explore the influence of parameters, including the temperature-dependency material properties, geometric nonlinearity, and shell’s power-law index, providing valuable insights into FGM shell behavior under thermal shock.

Experimental and numerical assessments of thermal transport in phase change material embedding additively manufactured triply periodic minimal surfaces: A comparative evaluation

Phase change materials (PCMs), due to their inherent low conductivity, are presently restricted in their potential applications for thermal energy storage (TES) systems. Extensive effort has been made over the past few years to investigate the potential of porous materials, such as metal foams, as effective thermal conductivity enhancers (TCEs) for PCMs. Porous materials have superior specific surface area over conventional honeycomb structures and fins, providing great potential in thermal storage systems. In this study, taking advantage of the implicit function of triply periodic minimal surface (TPMS), new varieties of lattices with continuous surface structures were developed and then manufactured by using AlSi10Mg powder via selective laser melting (SLM). A three-dimensional transient phase-change heat storage model of TPMS (Primitive and I-WP) structure-paraffin composite PCMs was adopted to study both the phase-change heat transfer performance and heat storage capability of TPMS-PCMs during the phase transition. Meanwhile, the evolution of the solid–liquid interface and temperature–time history were investigated by utilizing the visualized thermal storage experiments. The findings revealed that embedding TPMS lattice decreased the natural convection effect, resulting in a maximum flow velocity of liquid paraffin wax (PX) within TPMS-PCMs that was only 0.1 times that of pure PX. The melting onset time of TPMS-PCMs was advanced by 82.2 %-91.1 %, and the duration of phase change was shortened by 68.3 %-75.9 %, respectively. In addition, the total heat storage of TPMS-PCMs fell from 4464.0 J to 4217.2 J compared to pure PX, but their average heat storage rate rose from 1.04 to 4.58 J/s. Primitive rod (PS)-type TPMS-PCM was the most potential among the three types of TPMS lattices as the TCE for PCM because it achieved the highest heat storage rate with the most negligible overall heat storage loss.

Exploring flow boiling characteristics on surfaces with various micro-pillars using the lattice Boltzmann method

In this study, the lattice Boltzmann method is utilized to simulate flow boiling within a microchannel featuring a micro-pillar surface. This investigation aims to explore the impacts of micro-pillar shape and quantity on the flow boiling characteristics across various superheats and Reynolds numbers (Re). A systematic examination is conducted on three types of micro-pillars, five quantities of micro-pillars, four Re values, and 18 superheat levels. The mechanisms contributing to enhanced heat transfer in flow boiling are elucidated through a comprehensive analysis of bubble dynamics, temperature and velocity fields, local and transient heat fluxes, and boiling curves. Moreover, the critical heat fluxes (CHF) of all surfaces are evaluated to identify the superior micro-pillar configurations. The findings revealed that microchannels with micro-pillar surfaces induce more vortices compared to those with smooth surfaces, attributable to the combined effects of bubble dynamics and micro-pillars. Bubble patterns and boiling curves demonstrated the significant impact of micro-pillar geometrical shapes on the boiling regime and heat transfer performance. As flow boiling progressed, an increase in micro-pillar quantity and Re can mitigate the fluctuation and decline rate in transient heat flux, respectively. Among the three types of micro-pillar surfaces, the circular shape exhibited the highest flow boiling performance, followed by the triangular and rectangular shapes. For all surfaces, the CHF increased with Re, and each micro-pillar type displayed an optimal quantity for achieving maximum CHF, with the highest increase reaching 45.2%. These findings are crucial for optimizing microchannel designs to enhance flow boiling heat transfer efficiency.

Sublethal thermal stress promotes migration and invasion of thyroid cancer cells.

Radiofrequency ablation is a viable option in the treatment of benign thyroid nodules. Some reports suggest that thermal ablation may also be safe for the management of low-risk thyroid cancer. In this study, we applied transient heat treatment to thyroid cancer cells to mimic clinical scenarios in which insufficient ablation leads to incomplete eradication of thyroid cancer. Differentiated thyroid cancer cell lines B-CPAP, TPC-1, and FTC-133 were subjected to heat treatment at different temperatures for 10 min. Effects on cell growth, clonogenicity, wound healing assay, and Transwell invasion were determined. Heat treatment at 45°C or higher reduced cell growth, whereas viability of thyroid cancer cells was not changed after heat treatment at 37, 40, or 42°C. Heat treatment at 40°C increased the number of colony formations by 16% to 39%. Additionally, transient heat treatment at 40°C resulted in a 1.75-fold to 2.56-fold higher migratory activity than treatment at 37°C. Invasive capacity was increased after heat treatment, ranging from 115% to 126%. Expression of several epithelial-mesenchymal transition markers, including ZEB1, N-cadherin, and MMP2, was upregulated following heat treatment at 40°C. We for the first time demonstrate that sublethal thermal stress may increase clonogenicity, migration, and invasion of thyroid cancer cells.

Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models

This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given.

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Functionally graded materials (FGM) have attracted much attention due to their superior thermal shock resistance in extreme thermal environment. In addition, the memory-dependent feature of transient heat transfer progress can’t be reflected in the frame of integer-order heat conduction model due to the inability of depicting the effect of the past states on the current state. It is noticed that the size-dependent effect of elastic deformation has become significant due to the development of micro-devices. To describe the memory-dependent effect and the size-dependent effect in the functionally graded microstructures, the work aims a thermoelastic model by incorporating the fractional dual-phase-lag heat conduction model and the Eringen’s nonlocal model. To illustrate its application values, the modified model is used to investigate the dynamic performance of an functionally graded spherical microshell subjected to a thermal-mechanical loading. Governing equations including the modified parameters are derived and solved by Laplace transformation. The achieved results show that considering the influences of nonlocal effect and ceramic composition will reduce the thermal deformation under ultrafast heating condition.

Thermoelastic transient memory response analysis of non-localized nano-piezoelectric plates based on Moore-Gibson-Thompson thermoelasticity theory

With their abilities to induce electric charge, stress or deformation in response to external forces as well as the ease of fabrication, design flexibility and excellent electromechanical properties, piezoelectric materials have been widely used in actuators, sensors and even in nano/micro-electro-mechanical systems. With the rapid advancement of nano/micro-technology, from the perspective of theoretical analysis, the priority is to develop applicable models to describe the piezoelectric-thermoelastic responses of piezoelectric nano/micro-structures suffering transient heat conduction by taking the size-dependent effect and the memory-dependent effect into consideration. In this work, a new model based on the existing piezoelectric-thermoelastic model is established by introducing the nonlocality into the constitutive equations and the memory-dependent derivative into Moore-Gibson-Thompson (MGT) heat conduction equation respectively. Then, this new model is applied to investigating the dynamic responses of a piezoelectric nanoplate subjected to thermal shock. The corresponding governing equations are formulated and then solved by Laplace transform and its numerical inversion. In calculation, the influences of the time delay factor and the kernel function of MDD and the non-local parameter on the thermal, electric and elastic fields in the piezoelectric nanoplate are examined. Meanwhile, the predictions of transient response among different thermoelastic models are compared. The numerical results are illustrated graphically and discussed in detail. The obtained results show that MDD has a significant effect on the transient response, where the effect of the kernel function is more pronounced. This work may provide a theoretical reference for strength design, thermal protection and thermal processing strategies for piezoelectric nanodevices.

A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

Experimental Thermal Conductivity Studies of Agar-Based Aqueous Suspensions with Lignin Magnetic Nanocomposites

Nanoparticle additives increase the thermal conductivity of conventional heat transfer fluids at low concentrations, which leads to improved heat transfer fluids and processes. This study investigates lignin-coated magnetic nanocomposites (lignin@Fe3O4) as a novel bio-based magnetic nanoparticle additive to enhance the thermal conductivity of aqueous-based fluids. Kraft lignin was used to encapsulate the Fe3O4 nanoparticles to prevent agglomeration and oxidation of the magnetic nanoparticles. Lignin@Fe3O4 nanoparticles were prepared using a pH-driven co-precipitation method with a 3:1 lignin to magnetite ratio and characterized by X-ray diffraction, FT-IR, thermogravimetric analysis, and transmission electron microscopy. The magnetic properties were characterized using a vibrating sample magnetometer. Once fully characterized, lignin@Fe3O4 nanoparticles were dispersed in aqueous 0.1% w/v agar–water solutions at five different concentrations, from 0.001% w/v to 0.005% w/v. Thermal conductivity measurements were performed using the transient line heat source method at various temperatures. A maximum enhancement of 10% in thermal conductivity was achieved after adding 0.005% w/v lignin@Fe3O4 to the agar-based aqueous suspension at 45 °C. At room temperature (25 °C), the thermal conductivity of lignin@Fe3O4 and uncoated Fe3O4 agar-based suspensions was characterized at varying magnetic fields from 0 to 0.04 T, which were generated using a permanent magnet. For this analysis, the thermal conductivity of lignin magnetic nanosuspensions initially increased, showing a 5% maximum peak increase after applying a 0.02 T magnetic field, followed by a decreasing thermal conductivity at higher magnetic fields up to 0.04 T. This result is attributed to induced magnetic nanoparticle aggregation under external applied magnetic fields. Overall, this work demonstrates that lignin-coated Fe3O4 nanosuspension at low concentrations slightly increases the thermal conductivity of agar aqueous-based solutions, using a simple permanent magnet at room temperature or by adjusting temperature without any externally applied magnetic field.

Computational Analysis and Regression Laws for Nozzle Erosion Prediction in Hybrid Rockets

The erosion of the nozzle throat can represent one of the major limitations against the future widespread use of hybrid rocket engines (HREs) in the space industry. In fact, nozzle erosion in HREs can be more severe and harder to predict than in solid rockets due to the higher concentration of oxidizing species in the combustion products and to mixture ratio shifts and/or throttling. Therefore, an accurate understanding of the erosion phenomenon is of fundamental importance for the technological advancement of HREs. This work is focused on the investigation of graphite nozzle erosion in HREs burning high-density polyethylene with two different oxidizers, oxygen and nitrous oxide. First, the results of a computational fluid dynamics parametric analysis are used to derive closed-form regression laws for the rapid estimation of nozzle throat erosion and wall temperature depending on chamber pressure and mixture ratio. Then, a one-dimensional transient heat conduction solver is loosely coupled with the aforementioned regression laws, allowing to reconstruct the transient heating process within the solid. The obtained numerical results are validated against experimental data. Finally, the effect of gas-phase reactions on the heterogeneous reactions occurring at the nozzle surface is highlighted when moving from fuel-rich to oxidizer-rich conditions.

Numerical Modeling and Analysis of Transient and Three-Dimensional Heat Transfer in 3D Printing via Fused-Deposition Modeling (FDM)

Fused-Deposition Modeling (FDM) is a commonly used 3D printing method for rapid prototyping and the fabrication of plastic components. The history of temperature variation during the FDM process plays a crucial role in the degree of bonding between layers. This study presents research on the thermal analysis of the 3D printing process using a developed simulation code. The code employs numerical discretization methods with an implicit scheme and an effective heat transfer coefficient for cooling. The computational model is validated by comparing the results with analytical solutions, demonstrating an agreement of more than 99%. The code is then utilized to perform thermal analyses for the 3D printing process. Interlayer and intralayer reheating effects, sensitivity to printing parameters, and realistic printing patterns are investigated. It is shown that concentric and zigzag paths yield similar peaks at different time intervals. Nodal temperatures can fall below the glass transition temperature (Tg) during the printing process, especially at the outer nodes of the domain and under conditions where the cooling period is longer and the printed volume per unit time is smaller. The article suggests future work to calculate welding time at different conditions and locations for the estimation of the degree of bonding.

Fabrication and evaluating thermophysical properties of microencapsulated organic and eutectic phase change material

This study explores the synthesis and characterization of microencapsulation of organic and eutectic phase change materials with a melting point ranging from 5 to 30 ℃ for low-temperature applications. Emulsion polymerization utilizing methyl methacrylate monomer as the shell material is employed for effective encapsulation. Comprehensive characterization of microcapsules is undertaken, including chemical composition (using Fourier transform infrared (FT-IR) spectroscopy), morphology (employing scanning electronic microscopy (SEM) and metallurgical microscope), particle size distribution (measured by ImageJ software), enthalpy (evaluated through differential scanning calorimetry (DSC)) and thermal degradation (explored via thermogravimetric analysis (TGA)). The successful production of microencapsulated phase change materials (MPCM) is confirmed by their two-phase decomposition process, the presence of specific chemical bonds, and the spherical morphology of particles with an average diameter between 25.63 and 49.62 μm. However, in the case of eutectic core material, irregular microcapsules are shaped with a larger mean diameter. It has also affected the encapsulation efficiency in which around 29.43% and 30.1% efficiencies are reached for eutectic cores compared to 45.11% and 47% in organic ones. Simultaneously, thermophysical properties of MPCMs, such as density, thermal conductivity, and specific heat, are determined using the displacement method, transient line heat source, transient hot wire, and DSC. These properties are expressed through regression equations based on the determined effective factors. The derived equations enhance the capability to implement MPCMs in practical applications and numerical simulations.

Experimental study of the evaporation characteristics of unsymmetrical dimethylhydrazine in a sub-supercritical environment

In this study, the temperature–pressure separation technique was used to successfully obtain the process of the unsymmetrical dimethylhydrazine droplet diameter variation with time during evaporation in subcritical, supercritical, and far-supercritical environments at temperatures and pressures of 473–773 K and 1–9 MPa, respectively. The results show that unsymmetrical dimethylhydrazine droplet evaporation has two characteristic stages, transient heating and steady-state evaporation, under low-pressure and low-temperature environments; the steady-state evaporation stage influences droplet evaporation life more than the transient heating stage. Under high-pressure and high-temperature environments, droplet evaporation shows only a single feature of steady-state evaporation, and the droplet expansion process in the transient heating stage disappears. The normalized droplet lifetime decreased exponentially with temperature and decreased linearly and monotonically with pressure. The evaporation rate constant increases linearly and monotonically with temperature and exponentially with pressure.

Numerical analysis of the powder mixed electrical discharge machining (PMEDM) process for TZM-molybdenum superalloy using finite element method

The powder mixed electrical discharge machining (PMEDM) process was simulated via finite element analysis in the current study to assess heat behavior and material removal rate. The goal of this paper is to conduct a thorough experimental and thermal examination of electrical discharge machining (EDM) in order to forecast its cutting characteristics and subsequently optimize the output variables using a response surface methodology for simulations and choosing the most suitable set of process variables related to the PMEDM process. This study’s objective is to design a 2D axisymmetrical transient thermal model that might also describe the physics of material removal in a single spark PMEDM operation on a Titanium Zirconium Molybdenum (TZM) superalloy. ANSYS (version 9.1) software is used to perform transient heat transfer simulations to determine the temperature profile with the amount of material removal at different current, pulse on and off times, gap voltages, and fraction of heat that enters the specimen. The PMEDM process produced craters with a lower diameter and depth, which increased the material removal rate and enhanced the surfacing quality. Compared to the conventional EDM process, the inclusion of powder raised the heat flux given to the work material by 10%–12%. It has been determined that with the single spark modeling technique, the temperature significantly dropped in both the radial and depth directions. The computational results are compared with experimental observations for similar machining conditions, and both results agree satisfactorily.

Computational Fluid Dynamics Modeling and Analysis of Axial and Radial Temperature of Wellbore during Injection and Production Process

Summary To solve problems such as additional tubing/casing load, casing deformation, and packer failure caused by changes in annular temperature during oil and gas reservoir fracturing and production, based on the well structure of oil and gas reservoirs and transition transient heat transfer mechanism, a four-field coupling simulation model of the temperature field in the main fluid domain of the tubing, the temperature field in the solid domain of the tubing, the temperature field in the annular fluid domain, and the temperature field in the solid domain of the casing is proposed. Considering the coupling of fluid temperature, pressure, and physical parameters, boundary conditions are established based on reservoir characteristics, wellbore heat transfer characteristics, and fracturing and production conditions, and are compiled into Fluent software for simulation through the user-defined function (UDF) method. The effects of the temperature and flow rate of injected fracturing fluid and produced oil and gas on the distribution of the wellbore temperature field and temperature gradient are studied. The research results show that by applying D14-1 and D5-5 gas wells to the model, the simulated temperature is in good agreement with the measured wellbore temperature, and the maximum errors of the simulated values of the two different wells are 6.4% and 4.3%, respectively. As the injection and production operation time increase, the heat transfer between the wellbore and the formation gradually stabilizes. At this time, the injection and production flow rate have little impact on the wellbore temperature field, while the injection and production temperature have a greater impact on the wellbore temperature field. The injection and production temperature will cause changes in annular temperature and temperature gradient, leading to an increase or decrease in pressure within a limited annular volume, resulting in local stress on the tubing and casing. The research results can provide a theoretical basis for the analysis of the temperature field and pressure field of the wellbore during fracturing and oil and gas production, ensuring the safety and stability of fracturing and production.

Noninvasive neuromodulation of subregions of the human insula differentially affect pain processing and heart-rate variability: a within-subjects pseudo-randomized trial.

The insula is an intriguing target for pain modulation. Unfortunately, it lies deep to the cortex making spatially specific noninvasive access difficult. Here, we leverage the high spatial resolution and deep penetration depth of low-intensity focused ultrasound (LIFU) to nonsurgically modulate the anterior insula (AI) or posterior insula (PI) in humans for effect on subjective pain ratings, electroencephalographic (EEG) contact heat-evoked potentials, as well as autonomic measures including heart-rate variability (HRV). In a within-subjects, repeated-measures, pseudo-randomized trial design, 23 healthy volunteers received brief noxious heat pain stimuli to the dorsum of their right hand during continuous heart-rate, electrodermal, electrocardiography and EEG recording. Low-intensity focused ultrasound was delivered to the AI (anterior short gyrus), PI (posterior longus gyrus), or under an inert Sham condition. The primary outcome measure was pain rating. Low-intensity focused ultrasound to both AI and PI similarly reduced pain ratings but had differential effects on EEG activity. Low-intensity focused ultrasound to PI affected earlier EEG amplitudes, whereas LIFU to AI affected later EEG amplitudes. Only LIFU to the AI affected HRV as indexed by an increase in SD of N-N intervals and mean HRV low-frequency power. Taken together, LIFU is an effective noninvasive method to individually target subregions of the insula in humans for site-specific effects on brain biomarkers of pain processing and autonomic reactivity that translates to reduced perceived pain to a transient heat stimulus.

Hybrid stress and heat‐flux formulation of thermodynamics for long‐term simulations in thermo‐viscoplasticity

AbstractIn this article, we present a variational formulation for coupled problems in thermodynamics the most suitable for long‐term simulations of plastic behavior. We start with three‐field Hu–Washize variational formulation and perform regularization to include non‐symmetric stress, we thus recover the formulation that can accommodate any choice of discrete approximation. Such a regularized variational formulation allows us to eliminate the rotation field (as typically less important) and recover the corresponding hybrid stress format for equations of motion and transient heat conduction. The regularized variational formulation is further combined with discrete approximation based upon the Raviart–Thomas vector space for both mechanical and thermal fields, which enforces continuity across element boundaries for stress vector and normal component of heat‐flux. The conservation properties are validated with energy‐conserving scheme for thermoelastic behavior. The time integration of thermo‐viscoplastic behavior is carried out by energy‐decaying scheme to provide superior accuracy for computed stress in a long‐term simulation. The proposed approach offers higher computational robustness and results accuracy than the classical finite elements and time‐integration schemes. Such a performance is illustrated on several numerical simulations in non‐stationary problems for thermo‐viscoplastic behavior.