Steady Temperature Distribution Research Articles

On opto-thermally excited parametric oscillations of microbeam resonators. I

The present article is the first part of the work devoted to investigation of the nonlinear dynamics of parametrically excited flexural vibrations of a clamped-clamped microbeam - the basic sensitive element of a promising class of microsensors of various physical quantities - under laser thermooptical action in the form of periodically generated pulses acting on a certain part of the surface of the beam element. An analytical solution of the heat transfer problem is found for the steady harmonic distribution of temperature in the volume of the resonator. The static and dynamic components of temperature-induced axial force and bending moment are determined. Using the Galerkin method, the discretization of nonlinear coupled partial differential equations describing the longitudinal-flexural oscillations of the resonator is performed. Using the asymptotic method of multiple time-scales, an approximate analytical solution is obtained for the nonlinear dynamics problem under the conditions of primary parametric resonance.

Applications of distributed fiber Bragg gratings to the measurements of in-tube fluid temperature distribution

The temperature distribution information of the two-phase fluid inside a tube can effectively reflect the heat transfer of the fluid, which is the key information in the study of the heat transfer of flowing fluid in a tube. This article aims to develop a method for measuring the temperature distribution of fluid inside a tube based on distributed fiber Bragg gratings (DFBGs). It is more convenient than traditional measurement methods using thermocouples that are impossible to be installed to the inner tube of a double tube heat exchanger. By using a stainless steel seamless tube, ϕ1.0 × 0.2 mm in size, and a hose to seal and protect the optical fiber with Bragg grating sensors inside, we successfully shielding the stress effects from the thermal effects, and also enhance the durability of the fiber. Since the seal leads to extra thermal resistance to the DFBGs, obtaining the response performance of the sealed DFBGs to a temperature change is essential for reliable applications. The performance characterization shows that the temperature measurement repeatability of the sealed DFBGs is within 0.2 °C for a period up to 35 months. The time constants of the DFBGs are not longer than 0.25 s, capable of measuring the temperature oscillations with frequency less than 2 Hz. Comparison with commercial thermocouples supports the feasibility and the reliability that the sealed DFBGs can be used as temperature sensors. To obtain the equivalent thermal conductivity between the tube that sealed the fiber and the fiber, κ¯air, the response to a temperature jump was also calculated based on a simplified model, which can comprehensively reflect the heat transfer of the air inside the sealed tube and provide the reference for design optimization of a sealed FBG for dynamic measurements. Finally, the capillary tube with sealed DFBGs was placed in the condenser tube of a two-phase circulation loop to exhibit the feasibility of the steady and dynamic temperature distribution measurements of the fluid inside a tube.

Thermal-structural reduced order models for unsteady/dynamic response of heated structures in large deformations

This paper focuses on applications of recently developed thermoelastic reduced order models (ROMs) for the geometrically nonlinear response and temperature of heated structures. In these ROMs, both displacements and temperature fields with respect to the undeformed, unheated configuration are expressed in a reduced order modeling format, i.e., as modal-type expansions of the spatial and temporal variables with constant basis functions. Accordingly, the time varying generalized coordinates of the response and temperature expansions satisfy a generic set of coupled nonlinear differential equations derived from finite deformations thermoelasticity using a Galerkin approach. Finally, the coefficients of these governing equations, which characterize the structure considered and its loading conditions, are determined from structural and thermal finite element models non intrusively so that commercial finite element software can be used. This approach is considered here for the prediction of the displacements and stress fields in the presence of unsteady temperature distributions to enrich previous investigations limited to steady temperature distributions. Specifically considered here are: (i) a panel undergoing rapid heating and (ii) an oscillating flux on a panel. These problems not only demonstrate the extension of the thermal-structural reduced order framework to unsteady problems but also show the importance of the selection of the basis functions. It is also noted that the temperature dependence of the linear stiffness coefficients on temperature can induce in the unsteady situation the existence of a parametric-type excitation of the structure. This behavior is studied in the oscillating flux example and a strong sub-harmonic resonance is in particular found. The computational benefit of using ROMs is discussed and demonstrated.

Steady-state thermal model based on new dedicated boundary conditions – application in the simulation of laser powder bed fusion process

Analytical and numerical methods have been widely used to predict the melt pool morphology and temperature distribution of thermomechanical processes involving a moving heat source, such as welding or additive manufacturing. Compared to analytical methods (based on the Rosenthal equation), the finite element method (FEM) provides more realistic results because it allows the consideration of more physical phenomena involved in the laser powder bed fusion (LPBF) process. However, its computation time is significantly longer than that of the analytical methods. In this context, this study proposes a new FE thermal model based on a steady-state simulation and analytically inspired boundary conditions to predict the melt pool morphology and temperature distribution. This proposed model possibly considers temperature-dependent material properties, Gaussian distribution of heat source, convective and radiative heat losses, powder-compact transition, enthalpy due to solid-liquid transition, and effect of heat convection in the melt pool, while allowing fast and accurate predictions of the melt pool size and steady-state temperature distribution. Single-track LPBF simulations were carried out for two most used materials (AlSi10Mg and Inconel 718). The melt pool sizes simulated by the proposed model are compared to those of a transient model and experimental results (melt pool morphology), and a relative error of less than 5% was observed for all the numerical and experimental validation tests. Furthermore, it is shown that the proposed boundary conditions allow accurate prediction of the steady temperature distribution, even with a short geometry in the source moving direction, which drastically reduces the computational cost and greatly facilitate the utilization of steady-state model.

One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

Development of an effective TE cooler box for food storage

The development of a cooling system with a low power supply and evenly distributed temperature for food storage is challenging. This paper proposed a thermoelectric (TE) cooler box that adopt both conduction and convection heat transfer to solve the problems. The cooler box is made of three-layer wall, six TE modules (TEC1-12706), six inner heatsinks with fan, six outer heatsinks with fan, six top fans, two-power supply, a contactor, a switch, and a thermostat. With the six TE modules power consumption of 37.7 W at 3.18 A, the obtained results showed steady temperature distributions with time at various points of the layers including the cold and hot region. Meanwhile, the cooling capacity changes and became steady with the time. The conduction heat transfer is the dominant of the total heat transfer (Qc). The theoretical COP(coefficient of performance) using Carnot decreases with constant time, where COPsink of heatsink is approximately 1.6 higher than COPc of TE module. Furthermore, the experimental COPexp increases sharply before actualizing stability with experimental time compared to previous findings. Therefore, the TE cooler box is applicable for fruits and vegetable storage, and in areas of limited power supply.

Application of conduction heating on hot stamping of front bumper

The conduction heating device for full-scale automobile safety parts was investigated and developed in the present study. The heating and forming tests of the blanks of ultra-high-strength steel were conducted on the device. The influence of unequal radiation heat transfer strategy on the steady temperature distributions of the blanks was studied. The forming accuracy, mechanical properties, and microstructure of the front bumper parts via conduction heating were also investigated. The results showed that the material utilization rate of the blanks increased by 31.1% in the unequal radiation heat transfer condition. The forming accuracy of the front bumper parts fluctuated within the range of + 0.595 mm and − 0.845 mm. The Vickers hardness of the uniform temperature regions was more than 480 HV. The balance of strength and ductility of the uniform temperature regions was more than 11.1 GPa%. The full martensite microstructure was obtained in the front bumper parts.

Influence of PT-CT contact on PHWR fuel channel thermal behaviour under accident condition – An experimental study

An experimental investigation has been performed to simulate a scenario of a beyond design basis accident like LOCA along with the un-availability of ECCS. The investigation is aimed to study the thermal behaviour of a single channel of PHWR during sagging deformation. The sagging deformation of PT was simulated by making a direct physical contact between PT and CT. The fuel channel assembly of a length of 1.4 m was immersed in water which simulates Moderator. The decay heat liberated after reactor shutdown was simulated by Joule heating of the 37-fuel pin elements. The steady state circumferential temperature distribution in the 37-fuel pin bundle simulator, PT and CT at different axial position has been obtained. It was found that there is a significant circumferential temperature gradient in the fuel channel. The maximum and minimum temperature was obtained respectively at top and bottom nodes of PT. However, an opposite trend was observed in CT. The maximum temperature difference of 185.7 °C and 10.2 °C has been found between top and bottom surfaces of PT and CT respectively. A similar behaviour to that of PT was discerned in the 37-pin fuel element. However, fuel pin of ring-1 has an insignificant effect of PT-CT contact. It was observed that around 84 percent of simulated decay heat is transferred to the simulated moderator.

Temperature distribution inside Ising system confined by fixed boundary temperatures

In this paper, a two dimensional Ising model system in which the two boundaries of it are confined by two fixed boundary temperatures has been taken into consideration, obviously, the temperature inside the system is self-adjusting. To investigate the temperature evolutionary process of this Ising model system, the energy-exchange has been introduced in the Monte Carlo steps, and then the temperature variation of a local region is determined by the energy-exchange. Making use of above modified Monte Carlo method, a final steady temperature distribution of the system has been determined, and the obtained results suggest that this temperature distribution is nonlinear: from the constant temperature of the boundary to the critical temperature, the temperature variation is almost linear; however, lots of the local temperatures near the critical value remain almost unchanged and a temperature platform is obtained. Furthermore, the length of the temperature platform is much larger than that of the linear variation part. Meanwhile all the physical quantities and their fluctuations were also obtained by the Monte Carlo simulations, and the results show that, near the critical temperature, the fluctuations of magnetization are much larger than that of the energy, specific heat and magnetic susceptibility.

Dual variational model of a thermal breakdown of a dielectric layer at an alternating voltage

The article constructs the dual variational form of the model based on the presented differential form of a mathematical model describing the steady-state process of thermal conductivity in a plane or circular cylindrical layer of a solid dielectric at an alternating voltage. This form includes the main and alternative functionals, whose stationary points analysis makes it possible to establish a combination of the determining parameters corresponding to the occurrence of thermal breakdown of the dielectric layer. An example of the analysis of stationary points for two variants of test functions that are admissible for these functionals and approximating the steady temperature distribution in the dielectric layer is given. The estimation of the approximation error, which makes it possible to choose the function closest to the limiting temperature distribution in the layer preceding the thermal breakdown of the dielectric, is presented.

Temperature State of a Hollow Cylinder Made of a Polymer Dielectric with Temperature-Dependent Characteristics

A mathematical model is constructed to describe a steady one-dimensional temperature distribution in a hollow circular cylinder made of a polymer dielectric with a constant difference in the electric field potentials on the cylinder surfaces. Based on systematized data on the dependence of the thermal conductivity and electrical conductivity of polymer materials used as dielectrics in engineering on temperature, a qualitative analysis of the model is performed for a prescribed density of the heat flux supplied to the inner surface of the cylinder and intensity of convective heat transfer on the outer surface The results obtained in the study allow one to determine the area of applicability of polymer dielectrics used in various electrical engineering applications, including electrical insulation of DC high-voltage cables, and to formulate the conditions for the thermal breakdown of the cylindrical layer of the dielectric.

Thermal management of epidermal electronic devices/skin system considering insensible sweating

Thermal management of the system consisting of epidermal electronics devices (EEDs) and skin is critically important since a few degrees in temperature increase may induce thermal discomfort. In this paper, considering insensible sweating, a three-dimensional analytical thermal model, validated by finite element analysis, is developed to derive analytical expressions for the steady temperature distributions in the EED/skin system. The influences of various parameters including the thickness and thermal conductivity of the substrate in EEDs on the maximum skin temperature are investigated. The comfort analysis is then carried out based on the model to provide design guidelines for optimizing the geometric and material properties of EEDs to avoid the adverse thermal effects. These results pave the theoretical foundation for thermal management of EEDs/skin system in practical applications.

Tailored properties of hot stamping steel by resistance heating with local temperature control

Local austenization by local heating temperature control of blanks is one of the methods to obtain hot stamping parts with tailored properties. Resistance heating is a novel heating technology with high efficiency and rapid heating rate. In this paper, a heat transfer model was firstly developed to describe the steady temperature distribution of the blank during resistance heating. Then two resistance heating schemes to achieve tailored properties of hot stamping steel were investigated by experiments. One scheme is local resistance heating by adjusting the electrode position. And the other scheme is resistance heating with middle insulation. The results showed that the developed model could provide adequate accuracy in calculating the blank temperature field. For the local resistance heating, the percentage of high temperature region in heating zone was about 70 %. From the non-heating region to the middle heating region, hardness increased from 200 to 515 HV10. And the length ratio between high and low hardness regions could he controlled by adjusting electrode positions. For the resistance heating with middle insulation, a 340~360 HV10 medium hardness region with the length of 80mm was observed. The total length of transition hardness regions was about 60 mm. In summary, the local resistance heating scheme showed more advantages including shorter transition region and significant hardness difference.

Parametric study on the characteristics of a SDBD actuator with a serrated electrode

Active flow control based on surface dielectric barrier discharge (SDBD) has become a focus of research in recent years, due to its unique advantages and diverse potential applications. Compared with the conventional SDBD with straight electrodes, the serrated electrode-based SDBD has a great advantage due to its 3D flow topology. It is believed that the boundary layer separation of moving objects can be controlled more effectively with this new type of SDBD. In SDBD with a serrated electrode, the R (tip sharpness) and N (tip number per unit length) have a great influence on the discharge and induced airflow characteristics. In this paper, a parametric study of the characteristics of SDBD with a serrated electrode has been conducted with different ranges of R and N. Aspects of the power consumption, the steady medium temperature distribution, and the maximum induced airflow velocity have been investigated. The results indicate that there is a critical value of R and N where the maximum power consumption and induced airflow velocity are achieved. The uniformity of the steady temperature distribution of the medium surface is found to be more dependent on N. We found that the accelerating effects of the induced airflow can be evaluated with the Schlieren technique, which agree well with the results from the pitot tube.

Modelling fracture of aged graphite bricks under radiation and temperature

The graphite bricks of the UK carbon dioxide gas cooled nuclear reactors are subjected to neutron irradiation and radiolytic oxidation during operation which will affect thermal and mechanical material properties and may lead to structural failure. In this paper, an empirical equation is obtained and used to represent the reduction in the thermal conductivity as a result of temperature and neutron dose. A 2D finite element thermal analysis was carried out using Abaqus to obtain temperature distribution across the graphite brick. Although thermal conductivity could be reduced by up to 75% under certain conditions of dose and temperature, analysis has shown that it has no significant effect on the temperature distribution. It was found that the temperature distribution within the graphite brick is non-radial, different from the steady state temperature distribution used in the previous studies [1,2]. To investigate the significance of this non-radial temperature distribution on the failure of graphite bricks, a subsequent mechanical analysis was also carried out with the nodal temperature information obtained from the thermal analysis. To predict the formation of cracks within the brick and the subsequent propagation, a linear traction–separation cohesive model in conjunction with the extended finite element method (XFEM) is used. Compared to the analysis with steady state radial temperature distribution, the crack initiation time for the model with non-radial temperature distribution is delayed by almost one year in service, and the maximum crack length is also shorter by around 20%.

Simplified approach for steady thermal analysis of chips with variable power based on spatial autocorrelation

Due to their growing power and shrinking size, thermal management and analysis have become one of the most critical concerns for power devices. Though finite element (FE) method is commonly employed in thermal analysis now, the uncertainty of material properties and the redundancy of repeat modeling still nag analyzers. In this paper, a simplified approach for steady thermal analysis of chips with variable power is proposed. Based on spatial autocorrelation and undetermined method, the steady temperature distribution could be directly determined with power distribution and example temperature measurement result, without identifying environment factors or material properties. The theory of the simplified approach is introduced at first in this paper. The characteristics of the simplified approach are discussed afterwards. Eventually, a case study is given to illustrate the procedure, of which the analytical result coincides with the actual measurement well.

On numerical heat transfer characteristic study of flat surface subjected to variation in geometric thickness

Thermal management in the looming world of electronic packaging system is the most prior and conspicuous issue as far as the working efficiency of the system is concerned. The cooling in such systems can be achieved by impinging air jet over the heat sink as jet impingement cooling is one of the cooling technologies which are widely studied now. Here the modulation in impinging and geometric parameters results in the establishment of the characteristic cooling rate over the target surface. The characteristic cooling curve actually resembles non-uniformity in cooling rate. This non-uniformity favors the area average heat dissipation rate. In order to study the non-uniformity in cooling characteristic, the present study takes an initiative in plotting the local Nusselt number magnitude against the non-dimensional radial distance of the different thickness of target surfaces. For this, the steady temperature distribution over the target surface under the impingement of air jet is being determined numerically. The work is completely inclined towards the determination of critical value of geometric thickness below which the non-uniformity in the Nusselt profile starts. This is done by numerically examining different target surfaces under constant Reynolds number and nozzle-target spacing. The occurrences of non-uniformity in Nusselt profile contributes to over a 42% enhancement in area average Nusselt magnitude. The critical value of characteristic thickness (t/d) reported in the present investigation approximate to 0.05. Below this value, the impingement of air jet generates a discrete pressure zones over the target surface in the form of pressure spots. As a result of this, the air flowing in contact with the target surface experiences a damping potential, in due of which it gets more time and contact with the surface to dissipate heat.

A Novel Hybrid Heating Method for Mechanical Testing of Miniature Specimens at Elevated Temperature

A novel hybrid heating method which combines the conventional electric-resistance specimen heating with microcoil heating of specimen ends to achieve uniform heating over the gauge length is presented. Resistive heating of a miniature specimen develops a parabolic temperature profile with lowest temperature at the grip ends because of the heat loss to the gripper. Coil heating at the specimen ends compensates for this heat loss resulting in uniform temperature distribution over the central segment of the specimen. Thermo-electric finite element simulations were carried out to analyze the transient and steady temperature distribution in miniature specimens followed by experimental validation.

Heat transfer coefficient as parameter describing ability of insulating liquid to heat transfer

The paper presents the results of the measurements of heat transfer coefficient of insulating liquids used in transformers. The coefficient describes an ability of the liquid to heat transport. On the basis of the coefficient, effectiveness of cooling system of electric power devices can be estimated. Following liquids were used for the measurements: mineral oil, synthetic ester and natural ester. It was assumed that surface heat load is about 2500 W·m -2 , which is equal the load of transformer windings. A height of heat element was 1.6 m, because it makes possible steady distribution of temperature on its surface. The measurements of heat transfer coefficient was made as a function of various position of heat element (vertical, horizontal). In frame of horizontal position of heat element, three suppositions were analysed: top, bottom, and side.

Investigation on temperature uniformity of blanks by conduction heating

Abstract The austenitizing process of ultra-high strength steel by radiation heating occupied most of the cycle time, which would affect the application of hot stamping in automotive industry. The conduction heating had the advantages of rapid heating, high energy efficiency and good flexibility, which solved the deficiencies of radiation heating. However, the steady temperature distribution of the blanks by conduction heating in the regions closed to the copper electrodes was lower than that of the middle regions, which would affect the mechanical properties of the hot stamping parts. According to the principle of heat transfer, the unequal radiation heat transfer technology was proposed to solve the problem of the inhomogeneous temperature distribution of the blanks. The tests were carried out on the conduction heating test line to investigate the influence of the technology on the steady temperature distribution of the blanks. The results shown that the homogeneous temperature distribution of the blanks was achieved by the local and continuous unequal radiation heat transfer technologies, satisfying the requirement of hot stamping. And the material utilization ratio of the blanks was also improved. The tensile strength, elongation and the balance of strength and ductility of the high temperature regions exceeded 1490 MPa, 6% and 11 GPa•%, respectively. The technology solved the application deficiencies of conduction heating in hot stamping.