Line Heat Source Research Articles

On the interfacial deformations and thermal characteristics exhibiting self-similar behavior under the action of a line heat source

Interfacial dynamics resulting from a heating source located near the interface play a crucial role in dictating the heat and momentum transport in the near-interface region. This paper aims toward simultaneous characterization of interfacial deformation and thermal behavior under the action of a line heating source placed below the interface. Experiments have been conducted on aqueous glycerol with a heating wire at different power inputs and depths from the interface. The interfacial deformations are mapped and quantified by employing moon-glade background oriented schlieren, which offers real-time, non-intrusive whole field measurements based on the deflection of light rays from liquid interface. Infrared thermography is used to measure transient interfacial temperature variations. Results show that the interface exhibits a convex-shaped deformation under the influence of the heating wire for all cases of heating power and depth. The maximum interface temperature coincides with the peak interfacial deformation. However, the region of thermal influence is smaller compared to the deformed region. Non-dimensionalization of transient interface deformation and temperature profiles establishes the underlying similarity of the phenomenon as non-dimensional interface perturbation profiles overlap for all cases of height and heating power. These characteristics are also observed for normalized temperature profiles at different wire depths.

Numerical simulation of the thermal wave induced by a moving interfacial heat source with respect to Christov–Cattaneo's equation

AbstractThe hyperbolic wave equation of heat conduction with respect to Christov's formulation is utilized with the Streamline‐ Upwind‐Petrov‐Galerkin method in space and the Θ, Houbolt, linear acceleration, Wilson‐Θ and Newmark methods in time. The derivation of this equation and its matrix formulation are shown. A 2D transient finite element simulation of a generic asperity with an infinite line heat source in an interface, either as a heat flux density q̇ or temperature distribution T, is performed for Math = [0.5; 1.0]. A sensitivity study is presented for the mentioned numerical schemes. The temperature jump in the solution is interpreted as an indicator for a thermal shock.

Transient multilayer analytical model of a line heat source probe for in-pile thermal conductivity measurements

In-pile measurements of nuclear fuel properties is of critical importance for the design, performance, and safety considerations of next generation nuclear reactors and can be difficult due to the high temperature and high neutron flux environment. Real-time data for thermal conductivity is currently lacking due to the difficulty in deploying advanced instrumentation for thermal properties measurements in situ during nuclear operations. This limitation hinders our understanding of the mechanisms responsible for these changes. In this study, we have developed analytical models, utilizing the quadrupoles method, for in-pile thermal conductivity measurements using a novel line heat source. This probe uses Joule heating of a single wire to induce a temperature gradient and heat flow in surrogate fuel samples, while simultaneously leveraging the temperature dependent resistance of the wire as a thermometer to monitor the temperature rise of the sample for thermal conductivity extraction. The analytical models have been verified against more computationally intensive finite element models and experimental results were obtained from Teflon (PTFE) and aluminum samples. Coefficient of determination (R2) values for the measurements were 0.995, 0.987, and 0.992 for 10, 20, and 30 mm PTFE respectively and 0.983, 0.992, and 0.960 for 10, 20, and 30 mm aluminum respectively. Further complimenting the fits, sensitivity parameter studies were conducted on the 10 and 30 mm PTFE and aluminum highlighting the potential of our approach for rapid in-pile thermal conductivity measurements.

Analysis of a borehole ground heat exchanger with shape-stabilized phase change material backfill

GSHP (ground source heat pump) is a popular green building technology that utilizes renewable energy sources, but its efficiency can decrease significantly due to heat accumulation in soil. The borehole ground heat exchanger (BGHE) with shape-stabilized phase change material (SSPCM) backfill is a novel method to alleviate temperature fluctuation owing to better thermophysical properties. However, relevant experimental studies are still in scarcity and the impacts of backfill material on the soil temperature remain to be explored. This study conducted an experimental measurement on the soil temperature of a BGHE with SSPCM (expand graphite adsorbed paraffin) and sand backfill. A numerical model is established accordingly to be validated by the experimental results, in order to provide additional simulations on the sand-SSPCM mixture to identify the system performance and cost-effectiveness under different mass ratios of SSPCM. The experimental results show that SSPCM can effectively mitigate temperature fluctuations, especially closer to the heat source. The excess temperature difference is up to 10 °C near the heater wall. Compared to sand backfill, the sand-SSPCM backfill area's outside also maintains a steady temperature for a longer time during the cooling process. The numerical model couples the line heat source model of the BGHE with the validated phase change process. The simulation results found that the heat influence radius under the novel backfill was reduced by 16.5% after one operating cycle. Furthermore, after a 14 h shutdown, the novel backfill temperature is higher than the traditional backfill in the backfill area. The impact of various SSPCM mass mixing ratios indicates that a higher mass ratio can help reduce temperature variations, but the larger the mass ratio the less cost-effective it becomes. The optimum mass ratios are dependent on different parameters used as objectives.

Characterization of a Thermal Insulating Material Based on a Wheat Straw and Recycled Paper Cellulose to Be Applied in Buildings by Blowing Method

The thermal envelope is a key component of a building’s energy efficiency. Therefore, considerable efforts have been made to develop thermal insulating materials with a better performance than the existing products. However, in the current climate change scenario, these materials must be sustainable, principally during their production stage. In this context, the use of recycled raw materials and agro-industrial waste can be the basis of a material with a low environmental impact and a good thermal performance. In this study, cellulose and wheat straw were characterized. Then, they were mixed in different proportions and densities and the best thermal behavior was selected. The materials were chemically analyzed by TAPPI 2007, thermogravimetric and infrared spectroscopy, together with the measurement of their thermal conductivity with a thermal property analyzer based on the transient line heat source method. The results show that both raw materials are chemically similar to each other. When mixed, they have a thermal conductivity ranging from 0.031 to 0.036 (W/mK), being comparable with several conventional thermal insulators. On the other hand, to achieve the commercial use of this material, an installation through a blowing process has been proposed and proves to be highly promising, achieving a proper density and efficiency in its application.

Fully analytical solution in time and space domains on temperature in multi-barrier nuclear waste repository

Temperature evolution is one of the crucial factors in safe operation and geometric design of high-level radioactive waste disposal repositories. A three-dimensional two-layer axisymmetric heat transfer model was established to study the temperature evolution of the repository in the case of single canister. Applying a series of mathematical tools such as the finite Fourier sine transform, separation of variables and Duhamel's theorem, a fully analytical solution was obtained, which can visually and quickly represent the temperature evolution in both time and space. The validity of the model and solution was confirmed by comparing it with the existing line heat source solution, semi-analytical solution and finite element simulation results. The canister surface temperature was obtained by superimposing the temperature difference between the internal and external surfaces of buffer layer on the rock wall temperature. A single-panel calculation model was established, and dimensional and parameter analysis were carried out using the obtained fully analytical solution. According to the quantitative analysis using the obtained solution, increasing the canister spacing has a better effect on reducing the peak temperature than increasing the tunnel spacing. The effect of the two ways in reducing the peak temperature weakens with increasing the spacings.

Analysis of thermoelectric viscoelastic wave characteristics in the presence of a continuous line heat source with memory dependent derivatives

Analysis of thermoelectric viscoelastic wave characteristics in the presence of a continuous line heat source with memory dependent derivatives

General solution and Green’s function for fluid-saturated infinite and semi-infinite orthotropic poro-thermoelastic materials

In this study, two-dimensional (2D) steady-state general solution and Green’s function for orthotropic materials under the influence of poro-thermoelasticity (PTE) are investigated. Using the superposition principle and operator theory, the complete general solution of corresponding governing equations is calculated and stated in terms of harmonic functions. Based on these compact general solutions, the 2D Green’s function for a steady line fluid source and line heat source in the interior of an infinite orthotropic PTE plane and on the surface of a semi-infinite orthotropic PTE plane is presented. Consequently, eight newly implemented harmonic functions with undetermined constants are obtained. The equilibrium, boundary, and continuous conditions are used to obtain undetermined constants, and the corresponding coupled field is obtained by inserting these harmonic functions into the general solution. All coupled field’s components are described in terms of elementary functions, which can be used as the benchmarks for various numerical codes and approximate solutions.

Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source

Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source

On the memory-dependent derivative electric-thermoelastic wave characteristics in the presence of a continuous line heat source

In the present work, the definition of memory-dependent derivative (MDD) heat transfer in a solid body was used to investigate the problem of wave characteristics in an unbounded electric-thermoelastic solid due to a continuous line heat source in the presence of a uniform magnetic field. Both Laplace and Hankel's transform strategies are used to acquire the widespread answer in a closed-form. Analytical findings were obtained for the distribution within the medium of various fields such as temperature, displacement, and stresses. For the inversion of the Laplace transformations, a computational approach is used. The distributions of the numerical consequences of the non-dimensional considered bodily variables are represented graphically. Detailed comparative evaluation is represented thru the numerical outcomes to estimate the results of the kernels, time-delay, figure-of-merit, and magnetic number on the behavior of all variables. The effect offers a concept to research main electric-thermoelastic materials as any other type of pertinent materials.

Gradient models of moving heat sources for powder bed fusion applications

In this paper, we derive closed form solutions for the quasi-stationary problems of moving heat sources within the gradient theory of heat transfer. This theory can be formally deduced from the two-temperature model and it can be treated as a generalized variant of the Guyer–Krumhansl model with the fourth order governing equation. We show that considered variant of the gradient theory allows to obtain useful singularity-free solutions for the moving point and line heat sources that can be used for the refined analysis of the melt pool shape in the laser powder bed fusion processes. Derived solutions contain single additional length scale parameter that can be related to the mean size of the powder particles . Namely, we show that developed gradient models allow to describe the decrease of the melt pool depth with the increase of the powder’s particles size that was observed previously in the experiments. We also derived the dimensionless relations that can be used for the experimental identification of the model’s length scale parameter for different materials. Semi-analytical solution for the Gaussian laser beam is also derived and studied based on the Green function method within the considered theory.

Horizontal convective flow from a line heat source located at the liquid–gas interface in presence of surface film

Development of the convective flow from a line heat source located at the liquid surface is studied for the case when thermocapillary convection is inhibited by the surface film. Surface film is formed by small amounts of surfactants present in non-deionized (distilled or natural) water. It imposes a no-slip boundary condition for velocity at the surface and determines the fluid dynamics of the surface layer. For the heat source located at the surface, the vertical stratification is stable and the flow is driven by a horizontal pressure gradient, formed by non-uniform heating of the liquid along the surface. Experimental studies include measurements of velocity fields using particle image velocimetry, surface relief measurements using moon-glade background oriented Schlieren and surface temperature measurements using infrared thermography. Also, numerical simulations of the flow development are performed and a new similarity solution for the steady state in a laterally unbounded domain is constructed, which takes into account the pressure gradient. The results are shown to be in good agreement with experimental data. The obtained dependencies of the maximal velocity, boundary layer thickness, local and total Nusselt numbers on the Rayleigh number are consistent with literature data obtained for the non-uniformly heated bottom case, which demonstrates universal properties of horizontal convection.

Numerical simulation of natural convection MHD flow in a wavy L‐shaped cavity with line heat source using hybrid EFGM/FEM

AbstractIn the current paper, the natural convection of power‐law nanofluid within a wavy l‐shaped cavity under the magnetic field has been simulated by a hybrid (EFGM/FEM) technique with parallel implementation. A line heat source with length Lhs and height Hhs is applied on the right vertical wall of the cavity. The cavity is filled with power‐law non‐Newtonian nanofluid. Parallel implementation with hybrid EFGM/FEM is used to solve the governing partial differential equations. Effect of Rayleigh number, Hartmann number, power‐law index, aspect ratio, nanoparticle volume fraction, location, and length of the heat source has been studied on the fluid flow, isotherms, and heat transfer. It is observed that the power‐law index, Hartmann number, and height of heat source have a decreasing effect on heat transfer rate while the Rayleigh number, length of heat source, and volume fraction of nanoparticle increases the heat transfer rate. Heat transfer rate improves by 51% and 73% with increasing the volume fraction of nanoparticles and Rayleigh number while heat transfer rate reduces by 28% with increasing the Hartmann number. The main application of such problems is found in the building corners, lubricating machines, and medical and electronic equipment (thermometer device and PCB). The hybrid method is one of the novel contributions of the author. Parallel implementation of the meshfree method (EFGM) is one of the novel features of this paper.

Determining the Thermal Properties of the Pangasius Using a Dual Needle Heat-Pulse Sensor

In the field of food cooling and freezing computation, the accurate determination of thermo-physical properties such as specific heat, thermal conductivity and density is necessary and specially important to optimize the energy consumption of equipment. These parameters depend on the food composition and temperature usually determined by theoretical or experimental method or the combination of both. Experimental method using differential scanning calorimetry (DSC) is the best approach to yield correct results. However, DSC method requires expensive equipment and it might be not suitable for limited funding in some Vietnamese research centers. Therefore, the line heat source was chosen in this study.This paper introduces a new approach to determine thermal properties of the Vietnamese Pangasius in the temperature range from-40 °C to +40 °C using the line heat source. The results indicated that there is good correllation between the obtained measured data and the results calculated using theoretical models as well as other published experimental results.

Development of a Small-Sized Line Heat Source Apparatus for the Thermal Conductivity Measurement of Extraterrestrial Soils

The thermal conductivity of planetary soils, or regolith, is essential for understanding the present global thermal state of bodies. The thermal conductivity of lunar soils is important with respect to lunar crustal heat flow. Although in situ measurements were performed by the Apollo 15 and 17 missions, laboratory measurements of the returned lunar samples have not reproduced the estimated subsurface values. Since the amount of extraterrestrial soil samples is limited, a small apparatus is needed to measure their thermal conductivity. In this study, we developed an apparatus enabling the measurement of the thermal conductivity of a small amount of soil (< 10 g) via the line heat source method as a function of compressional pressure under vacuum conditions. The thermal conductivity of glass beads and lunar regolith simulant derived by the new apparatus is higher than that obtained from the larger line heat source, and then, reliable apparatus. To evaluate the experimental results, we performed numerical simulation of the temperature evolution during the line heat source measurement, and found that the thermal conductivity derived from the simulation data is higher than the input thermal conductivity. This is consistent with the experimental results and is caused by the heat loss through a line heat source with a limited length. The difference depends on the contact conductance between the sample and the line heat source, and the calibration factors for each sample are determined.

Thermal properties of lentil and chickpea in relation to radio frequency heat treatment

ABSTRACT Thermal properties of lentil (Lens culinaris) and chickpea (Cicer arietinum L.) were determined experimentally and with predictive mechanistic models as functions of temperature and moisture content (four levels). Thermal conductivity (k), specific heat (Cp ), and density (ρ) of the samples were evaluated using a line heat source probe, differential scanning calorimeter (DSC), and pycnometer, respectively. Except for Cp which was measured at a temperature range of 30 to 90°C, other properties were measured at room temperature. Specific heat of the samples increased linearly with moisture content (MC) and temperature, ranging from 0.824 to 2.433 kJ/kg K and 0.444 to 2.067 kJ/kg K for lentil and chickpea, respectively. Thermal conductivity increased with MC in all samples with its values ranging from 0.161 to 0.191 W/m K for lentil and 0.160 to 0.227 W/m K for chickpea. However, thermal conductivity values of flours were higher at lower MC levels when compared to seeds at higher MC levels. Thermal diffusivity, (0.159 × 10−6 to 0.221 × 10−6 m2/s and 0.163 × 10−6 to 1.175 × 10−6 m2/s for lentil and chickpea flours, respectively) was calculated from known values of k, Cp , and density (ρ), with its values decreasing as the MC levels increased. Thermal properties data from our experiments did not fit into the components-based mechanistic models. Models generated in this study have good significance (p< .05 and R2 ≈ 1), meaning they can be used for prediction of these properties, as well as modeling and simulation of thermal behavior of pulses during conventional or radio frequency (RF) heating.

Silicon Thermal Flow-Sensor Semi-ideal Model

A so-called semi-ideal model has been derived for a pulse-operated MEMS thermal flow sensor by reciprocal numerical mapping of the ideal model of an instantaneous line heat source to the experimental data of the sensor. The novel model not only applies as a precise potential working equation for the sensor but also provides insight into the complete thermal signal transmission chain from the heater to the thermometers of the sensor. It gives answers to prominent peculiarities of the actual heat path of the sensor, prepares ways to improve its design, and offers guidance for a better control of the measuring process. The semi-ideal model was derived in order to replace the so far utilized empirical relations that require multiple calibration measurements. It was found out that the transient temperature profile of the sensor in response to an electrical pulse to the heater is substantially shaped by series thermal conduction of heat. Moreover, it is demonstrated that the impact of the thermal mass of a (practical) line heat source on its transient temperature and released enthalpy can be modeled by considering a virtual cylinder surrounding the source. The same analytical technique also applies for (practical) temperature stations. The findings of the study primarily concern the MEMS sensor. Nevertheless, the presented simple method of numerical mapping can be an effective analytical tool for mathematical modeling by means of numerical data analysis and function evaluation. The concept of a virtual cylinder can help in modeling the dynamics of practical pulsed heating.

Characteristics of a buoyant plume in a channel with cross-flow

We present data from direct numerical simulation (DNS) of a buoyant plume in a channel with cross-flow. The plume originates from a line heat source at the bottom channel wall, impinging the top wall and propagates downstream and/or upstream based on the strength of the cross-flow. We study the critical velocity, defined as the minimum cross-flow velocity which prevents negative backlayering length from occurring. For cross-flow velocities higher than the critical velocities, all the plume generated from the source would be forced downstream and the location of the backlayering front would move downstream. We also visualise the structure of the plume for different source Reynolds number, which indicates that the backlayering is thicker at lower source Reynolds numbers. The thicker backlayering acts like as a blockage, which influences the cross-flow. In addition, an investigation into the relationship between critical velocity, source Reynolds number and the heat release rate has been carried out. A one-third power between the heat release rate critical is found, which is in good agreement with previous studies. For a fixed heat release rate, the critical velocity increases with increasing source Reynolds number. However, the critical velocity approaches an asymptotic value when the source Reynolds number is sufficiently high.

Correction to: Thermoelastic response of non-simple solid cylinder with variable properties under a continuous line heat source

Correction to: Thermoelastic response of non-simple solid cylinder with variable properties under a continuous line heat source

Study of wave propagation in an infinite solid due to a line heat source under Moore–Gibson–Thompson thermoelasticity

Study of wave propagation in an infinite solid due to a line heat source under Moore–Gibson–Thompson thermoelasticity