Time-dependent Heat Generation Research Articles

A new analytical method for transient heat conduction in composite disks applied to thermal plug and abandonment of oil wells

A new hybrid method for transient heat conduction problems is developed and applied to simulate a Plug and Abandonment (P&A) operation of oil wells. An oil well is approximated by concentric disks in a one-dimensional configuration, which allows for use of polar coordinates. The application of the Separation of Variables Method (SVM) is used as the analytical framework for the solution of the conductive heat transfer arising from a volumetric heat source located in the center of the disks. The SVM is able to solve only time-independent boundary conditions. However, using the Duhamel's theorem, the solution determined with the SVM can be used to achieve the solution when both time-dependent boundary conditions and internal heat generation are prescribed. Lastly, for verification purposes, a commercial software that solves the transient temperature field by means of numerical procedures, providing reliability to the analytical method proposed in this work.

A study on modeling of boiling heat transfer in core debris bed of SFR

In case of a hypothetical severe accident in a Sodium-cooled Fast Reactor (SFR), coolability of the debris bed in the post-accident phase plays a vital role in mitigating the accident and ensuring the structural integrity of the reactor vessel. Few numerical studies are reported in literature, in which the boiling heat transfer in debris bed is expressed as equivalent heat conduction using similarity law between heat conduction and two-phase heat transfer. However, these studies assumed steady state mass conservation for the boiling zone and neglected the gravity force. Hence, a detailed study has been carried out for various particle sizes and porosities of SFR debris to investigate the influence of above considerations. The effect of gravity on debris bed coolability is studied using steady state model of Lipinski, which showed that gravity has a non-negligible effect, for particle size of 0.3 mm and porosity of 0.5. However, the gravitation force was found to have a negligible effect in dryout heat flux estimation for the bottom cooled configuration. A transient numerical model is developed for simulating the boiling phenomena in debris beds and validated with the published experimental results. The assumption of steady state mass conservation is verified by carrying out transient analysis, which indicated early prediction of the dryout inception. For time dependent heat generation case, the unsteady mass conservation predicted higher DHF compared to constant heat generation.

Mathematical Study of unsteady micropolar fluid flow due to non-linear stretched sheet in the presence of magnetic field

The goal of this research is to check irregularity in heat generation, chemical reaction and thermal radiation effect an unsteady micropolar fluid flow. With the help of suitable similarity variables, the group of governing system of PDE and their associative boundary conditions are converted into the family of ODE and then solved using the HAM. The effect of various and important dimensionless parameters on the momentum, micro-rotation, energy and concentration equations have been discussed with graphical representation as well as tabular forms. It is observed that buoyancy force parameter, mixed convection parameter and permeability parameter enhance the velocity distribution while micropolar reduces the velocity profile. The temperature profiles are boosted for time and space dependent heat generation and absorption parameter respectively but reverse trend is observed for Prandtl number and unsteadiness parameter. Skin-friction factor, mass transfer rate and heat transfer rate have been listed and displayed in tables.

A hybrid model for simulation of lithium-ion batteries using artificial neural networks and computational fluid dynamics

Chemical reactions inside lithium-ion batteries generate heat and cause temperature rise. Hence, it is necessary to monitor battery time dependent heat generation. In this work, a hybrid model for simulating heat generation inside a pack of lithium batteries has been developed. An artificial neural network (ANN) has been employed to simulate electrochemical and thermal behaviors of a Panasonic NCR 18650 lithium-ion battery. In order to develop the hybrid model, the designed ANN has been inserted into ANSYS Fluent software through a C source code. A 3-D computation fluid dynamics (CFD) has been developed to simulate temperature distribution in the battery pack. Experimental data has been obtained using a NEWARE battery test system at different C-rates. The outputs of the proposed ANN consist of heat generation inside the battery as well as the electrochemical parameters. The combination of the ANN and CFD modeling, which led to a hybrid model, can be mentioned as the major contribution of this work. The results show an excellent consistency between the proposed model and test data. The simulation estimates the range of the manufacturer’s working temperatures (-20 to 60 oC), regarding the considered batteries.

FRACTAL MODEL OF POROUS FIN WITH TEMPERATURE-DEPENDENT HEAT GENERATION AND ITS NOVEL SOLUTION

Porous fins with temperature-dependent internal heat generation are frequently used to improve performance in a wide range of heat transfer and porous media applications. Thermal analysis of the porous fin fractal model with temperature-dependent heat generation is generated using fractal derivatives and investigated analytically using a novel Maclaurin series method (MSM). Nonlinear temperature distribution in a porous longitudinal fin is produced by the MSM. The porous fin solution is demonstrated using the Sierpinski fractal, which is based on time-dependent heat generation. The effects of the convection parameter, porosity, internal heat production, and generation number parameter on the dimensionless temperature distribution are discussed. MSM results are graphically and tabularly compared to existing solution methods such as HPM, CM, CSCM, LWCM, and GWRM. A comparison study reveals that MSM is a very reliable, accurate, and effective addition in the field of differential equations.

Численный анализ естественной конвекции кориума в условиях внутрикорпусной локализации с учетом переменного тепловыделения

Численный анализ естественной конвекции кориума в условиях внутрикорпусной локализации с учетом переменного тепловыделения

Thermal convection and radiation in a rotating cabinet with time-dependent heat-generated solid element and heat-conducting solid walls

Purpose This paper aims to study numerically the simulation of convective–radiative heat transfer under an effect of variable thermally generating source in a rotating square chamber. The performed analysis deals with a development of passive cooling system for the electronic devices. Design/methodology/approach The domain of interest of size H rotating at a fixed angular velocity has heat-conducting solid walls with a constant cooling temperature for the outer boundaries of the vertical walls and with thermal insulation for the outer borders of the horizontal walls. The chamber has a heater on the bottom wall with a time-dependent volumetric heat generation. The internal surfaces of the walls and the energy element are both grey diffusive emitters and reflectors. The fluid is transparent to radiation. Computational model has been written using non-dimensional parameters and worked out by the finite difference technique. The effect of the angular velocity, volumetric heat generation frequency and surface emissivity has been studied and described in detail. Findings The results show that growth of the surface emissivity leads to a diminution of the mean heater temperature, while a weak rotation can improve the energy transport for low volumetric thermal generation frequency. Originality/value An efficient computational approach has been used to work out this problem. The originality of this work is to analyze complex (conductive–convective–radiative) energy transport in a rotating system with a local element of time-dependent volumetric heat generation. To the best of the authors’ knowledge, an interaction of major heat transfer mechanisms in a rotating system with a heat-generating element is scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of complex heat transfer in rotating enclosures with internal heat-generating units, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Cooling of heat generating core debris using multiple passive jets in a liquid metal pool of LMFBR

A 3D numerical study on coolability of heat generating core debris by multiple passive jets in a liquid metal pool has been carried out. The computational domain considered is a cylindrical enclosure, which resembles the lower plenum of a typical 500 MW LMFBR. The plenum has provisions to ensure the coolability of the core debris resulting from the hypothetical core disruptive accident. The arrangement avoids settlement of core debris on the main vessel and ensures safe retention of destroyed core on core catcher within the main vessel. The enclosure is filled with liquid sodium and is considered as an incompressible fluid. The transient form of governing equations for flow and heat transfer are solved numerically. The k−ε model is used for closing RANS equations while the pressure velocity coupling is done by PISO algorithm to obtain smooth convergence. The developed model is validated against benchmark results on natural convection in low Prandtl fluid available in the literature and also using in-house experimental data. The Rayleigh number based on heat generation rates is varied from 1012 to 1015. Different orientations and angles of passive cooling pipes with time dependent heat generation rate are analyzed. Three different bend angles viz 90°, 135° and 180° with bend orientations of inward, outward and opposite are considered. Also, the influence of central chimney on heat removal is brought out clearly. The fluid flow and heat transfer characteristics are described using isotherms, velocity vectors and in terms of Nusselt number. It is found that cooling pipes with 1800 bend having inward orientation provides favorable cooling capability over all other configurations. The central chimney is found to have profound influence in the heat removal from heat source. A useful correlation for Nusselt number is also proposed for thermal design purposes.

Heat generation in all-solid-state supercapacitors with graphene electrodes and gel electrolytes

This study aims to investigate time-dependent heat generation in all-solid-state supercapacitors. Supercapacitors were fabricated by assembling two identical electrodes made of graphene petal arrays grown on buckypaper by microwave plasma chemical vapor deposition. The electrodes were separated by either (i) a conventional phosphoric acid in polyvinyl alcohol (PVA) gel electrolyte or (ii) a redox-active potassium ferricyanide/ferrocyanide in PVA gel electrolyte. The devices with redox-active gel electrolyte exhibited about three times larger capacitance due to additional charge storage by reversible redox reactions. However, their internal resistance was about six times greater than devices with conventional gel electrolyte due to the lower electrolyte ionic conductivity. The heat generation rate measured under constant-current cycling was the sum of irreversible and reversible contributions. The irreversible heat generation rate in all supercapacitors was caused by resistive losses, i.e., Joule heating. The reversible heat generation rate was different at the positive and negative electrodes and was affected by electric double layer (EDL) formation, reversible redox reactions, and/or the presence of negatively charged functional groups at the electrode surface. The results of this study can be used to gain insight into the charging mechanism and also to develop thermal management solution for all-solid-state supercapacitors.

Thermal wellbore strengthening through managed temperature drilling – Part I: Thermal model and simulation

This paper is the first part of a two-part series introducing a new and innovative managed temperature drilling technique for strengthening the wellbores of challenging oil and gas wells. This technique relies on heat generation within the borehole to increase the effective fracture gradient of near-wellbore zones in oil and gas wells. By releasing heat at exactly the right time and at the right location, the temperature in a near-wellbore zone can be raised, which in turn raises thermal stresses in this zone. This results in “thermal wellbore strengthening”, i.e. an increase in near-wellbore fracture initiation and propagation pressure that can be exploited to prevent or minimize induced mud losses during drilling, cementing and completion operations. As shown in Part II of this series, the heat-release is preferably achieved in a delayed fashion through the use of exothermic “heat-releasing” particles that are circulated to the zone(s) of interest in a dedicated carrier fluid.Part I describes a new computational thermal model for the proposed technique. Using finite volume techniques for an axisymmetric cylindrical geometry including a drillstring/workstring with internal and external fluid spaces, a casing string and a cementing layer (if present), and the rock formation, the model calculates the near-wellbore formation temperature as well as annulus and drill string temperature when a time-dependent and location-dependent heat generation source is acting. Model validation was conducted by comparing the simulation results from the model to analytical solutions as well as results obtained with a commercial software package for simplified cases (1D along the wellbore) with no heat source. Subsequently, near-wellbore temperature distributions were calculated for varying heat generation rates and fluid circulation times, and passed on to a geomechanical model to estimate the magnitude of the thermal strengthening effects on the fracture gradient. Results show that meaningful increases in near-wellbore stress can be obtained by the technique.The thermal wellbore strengthening technique, supported by the new thermal model described here, can be used to minimize lost circulation events and associated well trouble time and cost during drilling, cementing and completion operations, and may be particularly suited for wells with low drilling margins such as (ultra-)deepwater wells.

Characterization of the radiative heating stage in the end-forming process of PVC pipes

The end-forming of polyvinyl chloride (PVC) pipes is a manufacturing process aimed at deforming one end of a tube to allow connections between pipes. The deformation is preceded by a heating stage which leads to softening of the material and which, if not properly carried out, may cause unacceptable defects in the final product. The heating stage in the end-forming process often occurs within ovens equipped with infrared short-wave (SW) lamps, favoring the penetration of thermal radiation into the material. The lamps are placed at certain angular positions, making it necessary to impose a rotary motion to the pipe, to allow a circumferentially uniform heating. In this work a transient analysis of the end-forming heating stage has been conducted by means of two finite-element models, creating a design tool for the complete characterization of the process. The first model makes use of a time-dependent heat generation term which takes into account the actual heat flux distribution incident at the outer surface of the pipe, leading to the identification of suitable angular velocities to achieve uniform heating. In the second model, a local temperature control has been introduced in order to characterize the process in terms of heating time. To the best authors’ knowledge, this is the first numerical instrument able to completely characterize the heating stage of the end-forming process of PVC pipes.

Isothermal calorimeter for measurements of time-dependent heat generation rate in individual supercapacitor electrodes

Heat generation in electric double layer capacitors (EDLCs) may lead to temperature rise and reduce their lifetime and performance. This study aims to measure the time-dependent heat generation rate in individual carbon electrode of EDLCs under various charging conditions. First, the design, fabrication, and validation of an isothermal calorimeter are presented. The calorimeter consisted of two thermoelectric heat flux sensors connected to a data acquisition system, two identical and cold plates fed with a circulating coolant, and an electrochemical test section connected to a potentiostat/galvanostat system. The EDLC cells consisted of two identical activated carbon electrodes and a separator immersed in an electrolyte. Measurements were performed on three cells with different electrolytes under galvanostatic cycling for different current density and polarity. The measured time-averaged irreversible heat generation rate was in excellent agreement with predictions for Joule heating. The reversible heat generation rate in the positive electrode was exothermic during charging and endothermic during discharging. By contrast, the negative electrode featured both exothermic and endothermic heat generation during both charging and discharging. The results of this study can be used to validate existing thermal models, to develop thermal management strategies, and to gain insight into physicochemical phenomena taking place during operation.

Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies

Finite integral transform techniques are applied to solve the one-dimensional (1D) dual-phase heat conduction problem, and a comprehensive analysis is provided for general time-dependent heat generation and arbitrary combinations of various boundary conditions (Dirichlet, Neumann, and Robin). Through the dependence on the relative differences in heat flux and temperature relaxation times, this analytical solution effectively models both parabolic and hyperbolic heat conduction. In order to demonstrate several exemplary physical phenomena, four distinct cases that illustrate the wavelike heat conduction behavior are presented. In the first model, following an initial temperature spike in a slab, the thermal evolution portrays immediate dissipation in parabolic systems, whereas the dual-phase solution depicts wavelike temperature propagation—the intensity of which depends on the relaxation times. Next, the analysis of periodic surface heat flux at the slab boundaries provides evidence of interference patterns formed by temperature waves. In following, the study of Joule heating driven periodic generation inside the slab demonstrates that the steady-periodic parabolic temperature response depends on the ratio of pulsatile electrical excitation and the electrical resistivity of the slab. As for the dual-phase model, thermal resonance conditions are observed at distinct excitation frequencies. Building on findings of the other models, the case of moving constant-amplitude heat generation is considered, and the occurrences of thermal shock and thermal expansion waves are demonstrated at particular conditions.

Function estimation of laser-induced heat generation in a gas-saturated powder layer heated by a short-pulsed laser

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse heat conduction problem with a dual-phase-lag equation for estimating the unknown space- and time-dependent laser-induced heat generation in a gas-saturated porous medium exposed to short-pulse laser heating from the temperature measurements taken within the medium. Subsequently, the powder particle temperature distributions in the porous medium can be determined as well. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The effect of measurement errors on the estimation accuracy is also investigated. The inverse solutions are justified based on the numerical experiments in which two different forms of heat generation are estimated. Results show that the unknown laser-induced heat generation can be predicted precisely by using the present approach for the test cases considered in this study.

Time-dependent and energy dissipation effects on the electro-mechanical response of PZTs

In this study, we formulate a constitutive model for coupled thermo-electro-mechanical behavior of piezoelectric ceramics, i.e. lead zirconate titanate (PZT) that takes into account time-dependent behavior and heat generation due to energy dissipation from the electro-mechanical response. Experimental studies show that PZTs dissipate energy when subjected to cyclic electric fields. The dissipated energy is, in some part, converted into heat and raises the temperature of the PZTs. The hysteretic dielectric and strain responses are also dependent on the amplitude and frequency of the applied electric field. The aim of this study is to investigate the energy dissipation and time-dependent effects on the electro-mechanical responses of polarized PZTs. The thermodynamics of irreversible processes for modeling dissipative material responses is adopted to incorporate the time-dependent electromechanical coupling effect. A Gibbs free energy is defined in order to account for the different time-dependent and dissipation behaviors in piezoelectric materials under combined electro-mechanical stimuli. Experimental data on polarized PZTs and PZT based composites at applied electric field magnitudes lower than the coercive electric field, are used to examine the model. The constitutive equations along with the energy equations are solved numerically and used to predict the creep, hysteretic and heat generation responses of PZTs and composites at different frequencies and cyclic electric fields.

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation, Part I: Methodology

ABSTRACTThis work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation, Part II: Applications

ABSTRACTThis work investigates the analytical solution for transient temperature and thermal stresses within three circular geometries. First, the transient temperature and thermal stresses within a composite disk are addressed. Then, two examples regarding transient temperature and thermal stresses throughout circular heaters are analyzed. Pulsed and sinusoidal internal heat generations are incorporated into the second and third examples, respectively. For the composite hollow-disk example, merely the separation of variables method (SVM) is used to overcome the energy partial differential equation. For the other two examples, the combination of the SVM and Duhamel's theorem are adopted to solve the partial differential equations. Accordingly, assuming plane stress formulation, the transient thermal stresses within structures are obtained.

An analytical solution for the hyperbolic unsteady thermal behaviour of micro-thermoelectric coolers with a suddenly time-dependent heat generation

The ultrafast thermal behaviour of a micro thermoelectric cooler under the hyperbolic heat conduction model is analysed. An important step forward is taken in that the instantaneous application of the electric current is modelled by means of the Heaviside function. Two terms of internal heat generation derive from this model: the former is time-independent, whereas the latter is time-dependent through Dirac’s delta function. A modified Separation of Variables method is used to solve analytically the governing equations. Also, the initial linear problem is split up into three sub-problems through the principle of superposition. In order to eliminate the numerical oscillations in the temperature profiles at early times in correspondence of the wave fronts, the semi-infinite hyperbolic body model is considered. The performance (COP) of the device is evaluated and then compared with that derived from the parabolic case. An increase of about 27% is observed at early times.

The BFGS method for estimating the interface temperature and convection coefficient in ultrasonic welding

An inverse heat transfer problem is investigated in the present study by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method to predict the unknown time-dependent heat generation at the weld interface and convection heat transfer coefficient during an ultrasonic metal welding process based on the knowledge of temperature measurements taken on the horn. With known temperature data at some locations on the horn, the inverse solution was rapidly obtained by solving nonlinear direct problem, Central Finite Difference and Simple Step Method. The proposed method which did not need solving adjoint and sensitivity problem revealed the characteristics of high efficiency, lower iterations for a computational algorithm and high accuracy for estimating values even when measurement error was considered. Besides, a comparison of the BFGS method with some previous methods (i.e. CGM, SCGM) was established. These results show that an excellent estimation on interfacial heat generation (or temperature), as well as a convection heat transfer coefficient, can be simultaneously obtained in this study. The current methodology will provide a useful tool to optimize welding conditions in ultrasonic welding.

A Nonlinear Inverse Problem in Estimating the Heat Generation in Rotary Friction Welding

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat generation at the interface of cylindrical bars during rotary friction welding process from the knowledge of temperature measurements taken within the stationary bar. In the direct problem, the heat capacity and thermal conductivity are functions of temperature; hence, this is a nonlinear inverse problem. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat generation can be obtained for the test cases considered in this study. The current methodology can be applied to the prediction of heat generation in rotary friction welding.