Circular Heat Source Research Articles

Hybrid Nanoparticle-Enhanced Fluid Flow and Heat Transfer Behaviors in a Parabolic Cavity with a Heat Source

AbstractNatural convection of nanofluids holds considerable importance in both scientific research and engineering applications due to their exceptional heat transfer capabilities, which occur spontaneously without the need for additional energy input. In this paper, the natural convection of nanofluid inside a parabolic cavity containing a hot obstacle is studied numerically. The shape of the hot obstacle is selected as either circular or elliptical. Additionally, the effects of the Rayleigh number, nanoparticle volume fraction, and the position of the heat source are investigated. The computational fluid dynamics model was computed using COMSOL Multiphysics. It is observed that the average Nusselt number tends to increase with both the Rayleigh number and the volume fraction of nanoparticles in the fluid. When the heat source moves from the bottom region to the top area, the heat transfer performance of the heat source increases. When Ra ≤ 105, the cases with circular heat sources exhibit better heat transfer performance than those with elliptical heat sources. However, at Ra = 106, the average Nusselt number of the elliptical heat source is higher than that of the circular one.

Numerical study on a new manifold ring-shaped microchannel structure for circular heat source with excellent temperature uniformity

The manifold microchannel heat sink shows great potential for cooling high-heat-flux electronic equipment owing to its exceptional thermal and flow performance. A new manifold ring-shaped channel design is introduced to improve the temperature uniformity for circular heat sources. A comparative analysis of the manifold straight channel, radial expansion channel and manifold ring-shaped channel designs is conducted based on the same heating area under equal mass flow conditions by numerical investigation using single-phase de-ionized water. The findings indicate that the newly proposed manifold ring-shaped channel design exhibits a lower maximum temperature, a lower average temperature, a better temperature uniformity and a smaller pressure drop in comparison to the straight channel and radial channel designs. Specifically, at a mass flow rate of 2.5 g/s, the ring-shaped channel design demonstrates a 71.4 % and 45.4 % reduction in the temperature difference between the maximum temperature and the minimum temperature of the heating surface, and the coefficient of performance is enhanced by 458.2 % and 169.7 % when compared to the straight channel and radial channel designs, respectively. Additionally, three improved designs based on the original manifold ring-shaped channel design are proposed to further enhance fluid flow distribution in the ring-shaped channel design. The results reveal that all three manifold ring-shaped channel optimizations further lower the maximum temperature, the average temperature and the temperature difference. Notably, the improved case3 exhibits the best thermal and hydraulic performances among all structures. When compared to straight channel and radial channel designs, the improved case3 demonstrates an 86.9 % and 75.0 % reduction in the temperature difference, and an increase of 201.2 % and 523.4 % in coefficient of performance under the equal mass flow comparison basis. A heat flux of 1200 W/cm2 can be dissipated at 6 g/s when the maximum temperature rise is kept below 60 K, with a pressure drop of 38 kPa.

Sizing horizontal metallic inclusions in insulators using lock-in inductive infrared thermography

We present a methodology to size the area and depth of horizontal metallic inclusions of unknown geometry, embedded in insulators, using lock-in inductive thermography. The method is based on averaging the amplitude and phase thermograms along circles concentric with the center of the heated region. We present an analytical calculation of the surface temperature distribution produced by a horizontal circular heat source, taking into account conductive coupling with the air, and we propose to fit the averaged data to this model. We present lock-in thermography data on resin samples containing embedded calibrated circular and rectangular Cu slabs that we excite inductively. The results indicate that it is possible to determine the area and depth of rectangular heat sources with aspect ratio below 1.5 with accuracy better than 10 %.

Transient Thermal Spreading From a Circular Heat Source in Polygonal Flux Tubes

Abstract This study develops a numerical simulation to assess transient constriction resistance in various semi-infinite flux channel geometries, including circle on circle, triangle, square, pentagon, and hexagon, which are derived from various heat source arrangements in a large domain. Using both isothermal and isoflux circular heat sources in polygonal flux channels, and employing a finite volume method, the study evaluates transient constriction resistance. The research confirms that for different geometries, similar nondimensionalized constriction resistance results are obtained, particularly when using the square root of the source area as the characteristic length and the square root of the constriction area ratio. The study reveals that flux tube shape has a minimal impact on thermal spreading resistance, with the circle-on-triangle configuration displaying the largest deviation from a simple circle-on-circle model. These insights advance our understanding of thermal spreading resistance in polygonal flux channels and their applications in thermal engineering, especially in contact heat transfer problems.

Thermal constriction resistance of a functionally graded material plate heated by a circular disc heat source on one face and isothermal on the opposite face

This article presents a study of the thermal constriction phenomenon for the Functionally Graded Materials (FGM). The studied configuration is that of a plate subjected to a circular disc heat source. The study is carried out under steady-state conditions, considering axisymmetric heat conduction. An analytical solution is developed to calculate the temperature and thermal constriction resistance. Thermal conductivity, which varies as a function of position in the depth direction of the plate, is modeled by a law that allows to consider several possible evolutions (slow, rapid or linear). The thermal constriction resistance resulting from these thermal conductivity evolutions is studied and analyzed as a function of the geometric and physics parameters of the problem. As a verification, we compared the proposed solution with the same configuration but in the asymptotic case of homogeneous conductivity. Both solutions lead to the same result. In a second step, a homogeneous apparent thermal conductivity, which would be that measured by conventional methods, is introduced. It is shown that the calculation of thermal constriction resistance using a homogeneous apparent thermal conductivity differs from that of a calculation using the full developed analytical solution. This difference is small in the case of very thin plates but becomes very significant with increasing plate thickness.

Analysis of mixed convection and surface radiation in a horizontal channel containing different finned heat-generating blocks

In this work, mixed convection coupled with surface radiation in a ventilated horizontal channel is studied numerically. The channel containing three circular heat sources is ventilated by three openings; an inlet and two outlets. All the walls of the channel are adiabatic, and the flow enters the inlet at a cold temperature. To improve the performance of the cooling system, straight or curved fins are mounted on the surface of the hottest cylinder. The governing equations are discretized and solved using the Galerkin finite element method. The key parameters are the Reynolds number, the surface emissivity, the heat ratio and the geometric parameters of fins (size, number, and form). The numerical results show that the system's thermal performance improves by increasing the Reynolds number and the emissivity. In the absence of surface radiation (ε=0), the results indicate that adding fins leads to a decrease in the maximum temperature of the cylinder by about 6.6 °C for both straight and curved fins. However, the outcomes revealed that for ε=1, straight fins should be chosen instead of curved ones. Finally, for engineering purposes and based on the numerical data, correlations between the maximum temperature and the key parameters have been developed.

Thermographic Estimation of the Area and Depth of Buried Heat Sources for Nondestructive Characterization of Horizontal Defects

We present a methodology to estimate quantitatively the area and depth of horizontal defects that generate heat in non-destructive tests such as burst vibrothermography or inductive thermography, without previous knowledge of the shape of the heat source. The method is based on extracting the temporal evolution of the temperature at the centre of the heated region, together with the thermogram obtained at the end of the excitation. The temperature displayed in this thermogram is averaged in circumferences concentric with the centre of the heated region to obtain an averaged radial profile which is fitted, together with the temporal evolution of the temperature, to a circular heat source model. By fitting synthetic data corresponding to rectangular heat sources with added noise, we analyse the accuracy of the method to retrieve the area and depth of the heat source for different depths and aspect ratios. Experimental results show that the method is able to estimate the area and depth of heat sources with aspect ratios below 1/1.5 with accuracy of about 10%.

Finite element analysis of deformation behaviour of circular sheet during laser forming process

Laser forming of sheet metal involves inducing a bending process through the application of thermal stress using a defocused laser source. In laser forming the formation of bowl-shaped shapes requires the input of various laser process parameters. In this study, we investigate the thermo-mechanical deformation behaviour of a circular plate subjected to laser irradiation scanning. To analyse this phenomenon, we employ the Finite Element Method (FEM) with the aid of the software ABAQUS 6.10. The moving laser heat source is modelled as Gaussian heat flux, and DFLUX subroutine is written in FORTRAN. The work piece material AH36 is considered. The Finite Element Method (FEM) proposed model is verified against experimental results. Additionally, a parametric study has been conducted to assess the impact of laser process parameters on the temperature distribution of AH 36 material. The temperature distribution is noted to rise with an increase in laser power. However, as the scanning speed and laser beam diameter of the circular laser heat source increase, both temperature and bend angle exhibit a continuous decrease. Further, it is found the plastic strain is measured along the laser irradiation path, therefore the averaged material properties are not altered of the dome shaped obtained by laser forming. Based on the parametric studies, the optimum laser process parameters are also determined to get the dome shaped of the circular sheet.

"THERMOELASTIC DISPLACEMENT AND TEMPERATURE RISE IN A HALF-SPACE DUE TO A STEADY-STATE HEAT FLUX "

Due to model complexity, classical contact mechanics theory assumes isothermal contact processes, involving bodies with uniform temperatures and no heat transmitted or generated through or near the contact interface. This paper addresses the problem of frictional heating in non-conforming or rough contacts by investigating the thermoelastic behaviour of asperities. The heat generated in a sliding contact by interfacial friction leads to thermoelastic distortion of the contact surface, further modifying contact parameters such as pressure, gap or temperature. The thermal expansion of the contacting bodies must therefore be accounted for when solving the contact problem. The thermoelastic displacement is computed with the aid of the half-space theory and of fundamental solutions for point sources of heat located at the free surface, derived in the literature of heat conduction in solids. The linearity of conduction equations encourages the use of superposition principle in the same way as for the elastic displacement. As the thermoelastic displacement is expressed mathematically as a convolution product, methods derived in contact mechanics for elastic displacement calculation are adapted to the heat conduction equations. The influence coefficients needed to efficiently compute the convolution products are derived, and the Discrete Convolution Fast Fourier Transform technique is applied to improve the algorithm computational efficiency. A similar method is then advanced for the temperature rise on the contact interface due to arbitrary heat input. The predictions of the newly advanced computer programs are tested against existing closed-form solutions for uniform circular or ring heat sources, and a good agreement is found.

Identification of the anisotropic thermal conductivity by an inverse solution using the transient plane source method

The identification of the anisotropic thermal conductivity of material was performed using the transient plane source (TPS) method coupled with an inverse solution. The proposed method requires three measurements to be performed on three orthogonal planes of the cubic samples. Transient finite element analysis was used to solve a direct problem: three-dimensional heat conduction in anisotropic media due to a circular planar heat source. 3D printing technology was used to manufacture two sets of samples, isotropic samples were used to identify intrinsic properties of the polymer, and samples with specially designed anisotropic microstructure were used for the identification of an anisotropic conductivity tensor by the proposed method. To validate obtained results, the thermal conductivity was calculated using a finite element solution for a periodic unit cell, representing the microstructure of the material. Good agreement was observed between conductivity values obtained by two different methods, with a difference of ≤10 %.

A simplified modelling approach for thermal behaviour analysis in hybrid plasma arc-laser additive manufacturing

Hybrid plasma transferred arc (PTA)-laser additive manufacturing (AM) has the potential to build large-scale metal components with high deposition rate and near-net shape. However, the process is complex with many parameters adjustable for process control, which determine the thermal behaviour and thus the final structure and properties of the deposited components. In this study, a three-dimensional steady-state finite element model with two independent circular surface heat sources was developed, validated, and used to analyse the thermal behaviour in hybrid PTA-laser AM of Ti-6Al-4V. Artificial conductivity in three orthogonal directions was applied in the melt pool to compensate for the melt pool convection effect. The predicted melt pool geometry, heat-affected zone and thermal cycles had good agreement with the corresponding experimental data. This model has advantages over the widely used volumetric heat source model, since it is more representative of the energy sources used, giving accurate thermal prediction for a wide range of process parameters. As the heat source parameters in this model are directly linked to the actual arc/laser size, it enables to capture heat source size effect on the hybrid process. In addition, it is easier to calibrate compared to the model with volumetric heat sources due to the fewer empirical parameters involved. It was found that in the investigated ranges of all the parameters, the melt pool geometry is more sensitive to laser power and travel speed compared to arc-laser separation distance and laser beam size. The full-field distributions of the cooling rate and temperature gradient in the hybrid process were obtained and the roles that different process parameters played on them were also studied, which provided useful thermal information for metallurgical analysis.

DYNAMICAL EFFECTS OF A HOT DISK ON THE DEVELOPMENT OF A NATURAL CONVECTION FLOW BETWEEN CYLINDRICAL WALLS

This study numerically investigates the problem of natural convection flow ina vertical cylinder. The importance of this issue mainly stems from thermal systems (e.g. chimneys, hot air generators, solar collectors, and many others.). Despite the numerous studies on the modeling of free convection flow between two perpendicular plates, there are very few studies that have investigated regarding the convective flow between two cylindrical walls. Therefore, the study is limited to vertical cylinders with different heating modes.The first configuration includes heated walls of thermosiphon flow in a cylindrical channel.The second configuration introduces a circular heat source at the channel entrance, and the third configuration includes an ended vertical cylinder with a heat source centered in the cylinder (zs = 0.04). The flow comparison from the three configurations demonstrates how the hot disk affects the flow from a dynamic point of view.Furthermore, details about the flow and dynamical fields can be obtained from the solution equation of the conservation of momentum and energy, considering the differences between the boundary conditions of the studied configurations. The study covers Rayleigh numbers and focuses on the effect of the cylinders geometry on the characteristic of the flow as well as dynamical and thermal field characteristics and variations in Nusselt number. The studied flow is natural convection, laminar, steady, two-dimensional, and incompressible flow. Solutions were obtained using a numerical model based on the finite volume method and the Navier–Stokes equations. The velocity–pressure coupling was resolved using the SIMPLER algorithm. The temperature and vertical velocity profiles of the flow showed the existence of a boundary layer regime along the heated channel wall without a heat source. The layer continued along the cylindrical wall with the introduction of the heat source at the channel inlet. However, introducing the heat source caused a considerable change in the flow structure at the channels central part.Calculations were performed for the channel aspect ratio R* = 0.2 and different Rayleigh numbers (Ra = 105, 107, 108, 109 and 1010). Numerical results included velocity, temperature, and Nusselt number profiles.

Thermal constriction resistance of an axisymmetric plate subjected to a circular heat source and mixed boundary conditions. Semi-analytical solutions and simple and accurate correlations

This article deals with a complex problem of thermal constriction induced by mixed boundary conditions. Recently (Laraqi et al., 2021) [1], we have developed a set of new analytical solutions to solve some thermal constriction problems for the particular case of semi-infinite axisymmetric media under mixed boundary conditions. In this article, we propose a study extended to media of finite thickness to cover other applications related to thermal problems such as electronic cards equipped with chips, and other assemblies involving thin plate. The problem of finite thickness is much more complex to solve. In this article we consider a plate subjected to a circular heat flux density while the rest of the same face is isothermal. Two configurations concerning the rear face are studied. In the first one the surface is adiabatic and in the second one it is isothermal. The analytical developments are carried out until obtaining a Fredholm integral equation of the second kind with finite limits and explicit and converging kernel. Its resolution is done numerically in an easy way (a simple linear system to solve). Comparison with some available results is performed and shows an excellent agreement. Furthermore, on the basis of a judicious study of the asymptotic behavior, simple and accurate correlations are proposed to calculate the thermal constriction resistance for the both considered configurations.

An analytical approach of heat transfer modelling with thermal stresses in circular plate by means of Gaussian heat source and stress function

In the proposed research work we have used the Gaussian circular heat source. This heat source is applied with the heat flux boundary condition along the thickness of a circular plate with a finite radius. The research work also deals with the formulation of unsteady-state heat conduction problems along with homogeneous initial and non-homogeneous boundary condition around the temperature distribution in the circular plate. The mathematical model of thermoelasticity with the determination of thermal stresses and displacement has been studied in the present work. The new analytical method, Reduced Differential Transform has been used to obtain the solution. The numerical results are shown graphically with the help of mathematical software SCILAB and results are carried out for the material copper.

New findings in vorticity dynamics of turbulent buoyant plumes

The vorticity dynamics of turbulent, buoyant, and pure plumes released into the quiescent ambience has been investigated using large-eddy simulations with plume Reynolds number in the range of 6 × 107 to 108. The plume is generated by a circular heat source and sustained by buoyancy forcings generated by heating. As the starting plume rises vertically, it expands radially, entraining ambient fluid into the plume and two distinct stages of evolution are evident. During stage one (initial stage), in the near-source region the plume is accelerating characterized by developing turbulence. During the next stage (mixing stage), the plume is significantly altered by turbulence resulting in significant entrainment and expansion in the radial direction. As turbulent intensities decay during the mixing stage, the enstrophy decays in an exponential manner with height with an exponent of −7/4. The turbulent kinetic energy budget analysis reveals—baroclinic torque, stretching, and compression—as the three dominant mechanisms for the plume growth. The probability distribution function (PDF) of vorticity shows that vorticity is mainly aligned along the transverse direction near the source and slowly reaches to a quasi-isotropy state downstream. Turbulence spectra demonstrate the presence of a buoyancy-regime with a −3 spectral slope. The PDF of vorticity further shows extreme dominance of the strain rate rather than rotation within the plume. Consistent with studies in the literature, the vorticity fluctuations align with the intermediate eigen-vector of strain-rate tensor.

Analytical solutions for rapid prediction of transient temperature field in powder-fed laser directed energy deposition based on different heat source models

The present paper aims to develop an effective analytical solution for laser directed energy deposition through powder feeding (LDED-PF). Three heat source models are introduced and compared to analytically describe the transient temperature field in the process. These models are known as point (1D) heat source, circular (2D) heat source, and semi-spherical (3D) heat source. For the validation tests, single-track deposition of Ti-5Al-5 V-5Mo-3Cr powder on Ti-6Al-4 V substrate is conducted at different laser powers, scanning speeds, and powder feed rates. The temperature field is validated using the measurement of melt-pool/deposit geometry. In order to improve the model fidelity, the enhanced thermal diffusivity and heat source radius are calibrated in terms of linear functions. It is found that the 2D Gaussian heat source model, which is in agreement with the underlying physics of the process, establishes a better match between the predicted and experimental data. The developed model only needs the basic information from the LDED-PF setup and material thermal properties to predict the thermal history and melt-pool geometry at different processing parameters.

Effects of Boundary Conditions and Operating Parameters on Temperature Distribution during the Friction Stir Welding Process

This work deals with a numerical simulation of the friction stir welding FSW process of alloy material AA2195-T8. A 3D transient thermal model for simulating the heat transfer phenomena in the welding phase is applied. In this model, the FSW tool is considered as a circular heat source moving in a rectangular plate having a cooling surface and subjected to non-uniform and non-homogeneous boundary conditions. The thermal problem is solved using the finite element method as part of a Lagrangian formulation. The obtained results allow us to determine the maximum value of the temperature in the Nugget zone of the welded joint. During this process, the thermal cycle and the temperature distribution were determined for different values of the welding process parameters. The obtained numerical results are in good agreement with the one available in the literature.

New developments and explicit results for the thermal constriction resistance of a circular contact under mixed axisymmetric boundary conditions

This article presents a study of the thermal constriction resistance developed in a semi-infinite medium subjected to a circular heat source with mixed boundary conditions. The problem is considered axisymmetric and stationary. Two cases of mixed boundary conditions are considered. The contact area can be subjected to a non-uniform axisymmetric heat flux density while the remainder of the surface is isothermal, or the contact is subjected to a non-uniform axisymmetric surface temperature while the remainder of the surface is adiabatic. The thermal constriction resistance is determined analytically. It takes a simple form and can be used for various problems. To offer a wide choice of applications, a general distribution law for the heat flux density or the temperature of the contact area is considered. Verifications of the proposed solutions are carried out by comparison with some analytical results available in the literature. An analysis of the results according to the kind of boundary conditions and the curvature of the axisymmetric source is also performed.

Расчет температур в алюминиевой пластине по диаметрам расплавленных точек

The concept of equilibrium effective power of welding heat sources is substantiated. This is the difference between the total effective power and loss of ablation for heat transfer to the environment and to the equipment. The use of equilibrium power allows determining the parameters of the heat source and thermophysical coefficients in a mathematical model by the size of the weld pool. A computer program has been developed for calculating the size of the weld pool and thermal cycles during the action of a normal circular heat source on the plate surface. An example is given of determining the parameters of a normal-circular source using the diameters of the molten points on a plate made of an aluminum alloy by a compressed arc with opposite current pulses. Thermal cycles are calculated for a point on the axis of the heat source at different times of its action. Estimates of the time of crystallization of the molten metal after switching off the arc were made. The calculated radial temperature distribution was obtained. With this model, the temperatures in the center of the weld pool are close to two aluminum melting points. The developed method of calculating temperatures can be used to determine the optimal modes of spot arc welding, precluding the formation of crystallization cracks

Numerical investigation of mixed convection heat transfer behavior of nanofluid in a cavity with different heat transfer areas

The main purpose of this research is the numerical modeling of laminar mixed convection heat transfer inside an open square cavity with different heat transfer areas. In the considered geometry, cold fluid enters the cavity. At the middle of the cavity, there is a hot isothermal circular heat source. For increasing the heat transfer, solid silver nanoparticles with volume fractions (φ) of 0, 2 and 4% are added to water. Studied Re numbers are 10, 50, 120 and 200. The location of the hot zone changes the temperature distribution in the fluid layers. If the heat transfer area is located in an appropriate location, temperature distribution becomes more uniform. Increasing Re leads to smaller temperature gradients in regions near the hot surface and higher temperature at fluid layers close to the surface. By increasing fluid velocity, backflows do not improve heat transfer but it is able to change the heat transfer mechanism. By decreasing the fluid velocity, the effects of velocity gradients and extension of the velocity boundary layer increase and friction coefficient attains the maximum value.