Calculation Of Temperature Distribution Research Articles

Suppression of oxygen and carbon impurity deposition in the thermal system of Czochralski monocrystalline silicon

When preparing large monocrystalline silicon materials, severe carbon etching and silicide deposition often occur to the thermal system. Therefore, a suppression method that optimizes the upper insulation structure has been proposed. Assisted by the finite element method, we calculated temperature distribution and carbon deposition of heater and heat shield, made the rule of silicide and temperature distributing in the system, and we explained the formation of impurity deposition. Our results show that the optimized thermal system reduces carbon etching loss on heat components. The lowered pressure of the furnace brings a rapid decrease of silicide deposition. The increase of the argon flow rate effectively inhibits CO and back diffusion. The simulated results agree well with the experiment observations, validating the effectiveness of the proposed method.

CFD analysis on flow and heat transfer mechanism of a microchannel Ω-shape heat pipe under zero gravity condition

This paper utilizes the CFD approaches to investigate the unsteady flow, heat and mass transfer mechanisms in an axial microchannel Ω-shape aluminum-ammonia grooved heat pipe (GHP) under zero gravity condition. The established numerical model considers the spurious velocity due to discretizing the gradient term of phase volume fraction adjacent to the phase interface. The dynamic contact angle, which is a function of the local velocity, is also modeled based on the Hoffman function via user-defined function (UDF). The Lee model is used to calculate the mass transfer rate between the phases in the evaporator as well as condenser section, while the empirical coefficients in the model are calibrated by comparing the calculated temperature distributions with the experimental data by ourselves. The whole mathematical framework is also evaluated by the experiment. Different heat flux and filling ratios are modeled to probe the heat transfer mechanisms in the GHP. The results capture the pressure profiles along the axial direction and the pressure difference across the phase interface in the cross-section perpendicular to the axis, which is balanced by the surface tension with the different contact angles along the axis. It is found that the Ω-shape GHP is capable of transporting heat over relatively large distances with a minuscule temperature difference. The results give rich insights into the flow, heat and mass transfer mechanism of the studied heat pipe.

Evaluation of the thermal sensitivity of porcine liver in CT-guided cryoablation: an initial study.

To evaluate computed tomography (CT)-based thermometry in cryoablation, the thermal sensitivity of an ex-vivo porcine liver was determined in an initial study design. The CT-guided cryoablation was performed in three porcine liver samples over a period of 10min. Fiber optic temperature probes were positioned parallel to the shaft of the cryoprobe in an axial slice orientation. During ablation, temperature measurements were performed simultaneously with CT imaging at 5s intervals. On the CT images, the average CT number was calculated for a region of interest of 3×3 pixels just below the tip of each temperature probe. A linear regression analysis was performed using eleven data sets to determine the dependence of the CT number on the temperature. With decreasing temperature, an increasing hypodense area around the tip of the cryoprobe was observed on the CT images and decreasing values of the CT number were determined. Starting at a temperature of-40°C a linear relation between the CT number and the temperature was determined and a thermal sensitivity of 0.95HU/°C (R2 =0.73) was obtained. The thermal sensitivity was used to calculate color-coded temperature maps. The calculated temperature distribution corresponds quantitatively to the increasing hypodense area. A noninvasive CT-based temperature determination during cryoablation in a normal ex vivo porcine liver is feasible. A thermal sensitivity of 0.95HU/°C was determined by linear regression analysis. A color-coded map of the temperature distribution was presented.

Heat Transfer through Wire Cloth Micro Heat Exchanger

The main objective of this study is to calculate and determine design parameters for a novel wire cloth micro heat exchanger. Wire cloth micro heat exchangers offer a range of promising applications in the chemical industry, plastics technology, the recycling industry and energy technology. We derived correlations to calculate the heat transfer rate, pressure drop and temperature distributions through the woven structure in order to design wire cloth heat exchangers for different applications. Computational Fluid Dynamics (CFD) simulations have been carried out to determine correlations for the dimensionless Euler and Nusselt numbers. Based on these correlations, we have developed a simplified model in which the correlations can be used to calculate temperature distributions and heat exchanger performance. This allows a wire cloth micro heat exchanger to be virtually designed for different applications.

Thermal Radiation Influences on MHD Stagnation Point Stream over a Stretching Sheet with Slip Boundary Conditions

The present investigation manages the thermal radiation influences on MHD stagnation point stream over a stretching sheet with slip boundary conditions. The governing equations are reduced set of nonlinear ODEs with boundary conditions by using the similarity transformations and the numerical velocity and temperature distribution calculations are performed with the assistance of MATLAB in the built problem solver. The outcomes of the non-dimensional factors on velocity, temperature distributions are exhibited graphically.

A functional structural model of grass development based on metabolic regulation and coordination rules

Shoot architecture is a key component of the interactions between plants and their environment. We present a novel model of grass, which fully integrates shoot morphogenesis and the metabolism of carbon (C) and nitrogen (N) at organ scale, within a three-dimensional representation of plant architecture. Plant morphogenesis is seen as a self-regulated system driven by two main mechanisms. First, the rate of organ extension and the establishment of architectural traits are regulated by concentrations of C and N metabolites in the growth zones and the temperature. Second, the timing of extension is regulated by rules coordinating successive phytomers instead of a thermal time schedule. Local concentrations are calculated from a model of C and N metabolism at organ scale. The three-dimensional representation allows the accurate calculation of light and temperature distribution within the architecture. The model was calibrated for wheat (Triticum aestivum) and evaluated for early vegetative stages. This approach allowed the simulation of realistic patterns of leaf dimensions, extension dynamics, and organ mass and composition. The model simulated, as emergent properties, plant and agronomic traits. Metabolic activities of growing leaves were investigated in relation to whole-plant functioning and environmental conditions. The current model is an important step towards a better understanding of the plasticity of plant phenotype in different environments.

Process Analysis of the Hot Plate Welding of Drive Belts

Abstract Most industrial machines use belt transmission for power transfer. These mechanisms often use the round belts of several millimetres in diameter that are made of thermoplastic elastomers, especially polyurethane. Their production process calls for bonding the material, which is often performed by hot plate butt welding. In order to achieve proper design of an automatic welding machine, the authors analysed the hot plate welding process of round belts. This process consists of five phases. It is necessary to recognize all the physical phenomena that occur during welding, especially those connected with thermomechanical properties of material. This knowledge is necessary to determine the temperature distribution during each step of the process. The paper presents a standard welding cycle together with an explanation of the physical phenomena in each phase. An analysis of these fundamentals will be used to derivate the function of temperature distribution during all process phases. In addition, some assumptions for calculation of temperature distribution and some fundamental physic correlations were presented.

Effect of Pressure Fluctuations on the Temperature During Braking

Abstract The aim of this study is to develop the numerical–analytical model of frictional heating in a pad/disc system during braking including the pressure fluctuations, engendered by the pump in an anti-skid braking operation. For this purpose, the problem of motion and the one-dimensional thermal problem of friction for a semi-space/semi-space tribosystem were formulated and solved. Obtained solutions allow to calculate temperature distribution on the contact surface and inside the friction elements. Thermal analysis was performed for a metal–ceramic pad and a cast iron disc during one-time braking including the time-dependent, oscillating pressure. The influence of amplitude of pressure fluctuations on the temperature variations was investigated, especially on the value of maximum temperature achieved during braking.

Polygeneration Study of Low-to-Medium Enthalpy Geothermal Reservoirs in Mexico

This study combines the thermodynamic analysis of a polygeneration system along with the numerical modelling of the thermal behavior of geothermal reservoirs in Mexico to exploit their energy. Each reservoir was modeled as a porous medium assuming a five-spot well configuration and local thermal equilibrium. The heat conduction-convection along with the Laplace equations were solved to compute temperature distributions, the useful life and the optimum distance between injection-extraction wells. The predicted temperature and pressure of the geothermal fluid at the outlet of the reservoir were exploited in the polygeneration system consisting of: (1) a Rankine cycle, (2) an absorption refrigeration cycle, and (3) a heat exchanger. The developed approach allows calculating both the optimal distance between injection-extraction wells and the global (utilization) efficiency of six arrangements (each composed by a reservoir connected to a polygeneration system) by assuming that reservoirs have a lifespan of 30 years. Results also show that: (a) due to the low efficiency of the Rankine cycle, very little thermal energy is converted into electrical one; (b) not only the temperature and the size are important when evaluating the power production performance of reservoirs, but also the permeability plays a fundamental role; (c) the first law efficiency of the polygeneration system ranges from 41.9% to 43.7%; (d) the utilization efficiency of the six arrangements lies in the range between 25.8% and 31%.

Numerical prediction of a single phase Pressurized Thermal Shock scenario for crack assessment in an Reactor Pressure Vessel wall

A pressurized thermal shock (PTS) in a reactor pressure vessel (RPV) wall of a Pressurized Water Reactor (PWR) could eventually lead to reduced integrity of the RPV. A PTS scenario may be initiated by a Loss-of-Coolant Accident (LOCA) in which the Emergency Core Cooling (ECC) injection causes a thermal shock in the vessel wall while the RPV is still partially pressurized. The traditional Thermal-Hydraulic system codes fail to reliably predict the complex three-dimensional thermal mixing phenomena in the downcomer occurring during the ECC injection. Therefore, a three-dimensional computational fluid dynamics (CFD) simulation of the transient is required to provide an accurate temperature distribution for reliable probabilistic analyses. The assessment of the failure probability due to a single phase PTS initiated by postulated defects in the vessel wall requires the computation of a long transient solution. Since the CFD calculation is computationally expensive, the symmetry of a four-leg PWR geometry is utilized to reduce the computational domain.In the present work, several Unsteady Reynolds Averaged Navier-Stokes (URANS) CFD simulations are performed to select an optimal computational domain that is representative for a typical PWR. The computed temperature distribution is provided as input for the structural analyses to calculate the Stress Intensity Factor (SIF) along several postulated defects. The SIF is then used to evaluate the potential of crack propagation initiation of the defects.

Wear and fluid-solid-thermal transient coupled model for journal bearings

In this study, the transient interactions between the sliding wear behaviour and fluid–solid–thermal (FST) characteristics of journal bearings are revealed using an established mathematical model. The calculated temperature distribution is validated by a comparison with experimental results from the literature. Furthermore, a wear test for lubricated journal bearings is conducted to verify the predicted wear rate. The time-varying wear and FST performances of the journal bearing, including the wear rate, wear depth, fluid pressure, contact pressure, and maximum temperature are calculated numerically. Through numerical simulations, the effects of the boundary friction coefficient and surface roughness on the wear and FST performances are evaluated. To demonstrate the importance of considering the three-dimensional (3D) thermal effect during the wear analysis of lubricated journal bearings, the numerical results predicted by the isothermal model and the thermal model are compared systematically within a wide range of operating conditions. The numerical results reveal that the worn surface profile slightly decreases the maximum temperature. Additionally, the worn region is primarily located at both edges of the bearing, and the time-varying worn surface profile may be beneficial for improving the hydrodynamic effect. Furthermore, the effect of the 3D thermal characteristics on the wear prediction of journal bearings cannot be ignored when the external load, boundary friction coefficient, surface roughness are relatively large.

Study on heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source

A hybrid numerical method for heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source was studied. A weighted residual equation of heat conduction was considered under thermal boundary conditions. In order to calculate temperature distribution of functionally graded plate with variable gradient parameters, the Fourier transform and inverse Fourier transform were applied and the temperature field was obtained under the H(t) heat source. Results show that the influences of the gradient parameters on temperature distribution are dramatic. But with the increase of gradient parameters, the influences of parameters on the temperature distribution are gradually reduced. When the gradient parameters reach a certain critical value, the temperature does not change anymore. By comparing the temperature distribution of the upper and lower surfaces, it is seen that the temperature presents a gentle downward trend with the increase of the heat source distance, while the temperature does not change with the time in farther distance from heat source. Also, the results show that the influence of the heat source has only partial and limited influence on the temperature, which is in accordance with St. Venant’s Principle. The law of the temperature distribution of the lower surface varies with the gradient parameters, which is also discussed, an optimal gradient parameter with the thermal insulation effect of the functionally graded plate is obtained.

Numerical modeling of a benchmark experiment on equiaxed solidification of a Sn–Pb alloy with electromagnetic stirring and natural convection

A three-phase volume averaged equiaxed model is applied to simulation of an experiment on solidification of the binary alloy Sn-10 wt.% Pb subjected to the electromagnetic stirring. The experiment, whose description was published earlier, was performed in a parallelepiped cavity under controlled cooling conditions and with real-time two-dimensional temperature measurement over a lateral surface of the cavity co-planar with direction of solidification. Applied numerical model treats motion of the liquid and equiaxed grains whose growth kinetics is taken into account and uses a double time step scheme to accelerate solution. Growth of columnar dendrite is not considered. It is shown that electromagnetic force acting in a direction opposite to the natural convection flow creates moderately turbulent flow in pure liquid which is treated with a realizable kε−ε model. It is demonstrated that calculated temperature distribution in the cavity well reproduces temperature maps reconstructed from thermocouples measurements throughout the experiment. Final macrosegregation map and distribution of density grain number are qualitatively similar to those obtained in the experiment. Variation of intensity of electromagnetic stirring in numerical model shows that this affects shape and localization of positive segregation region at the bottom of the cavity.

A simplified semi-numerical model to simulate a U-pipe ground heat exchanger

A simplified semi-numerical model is developed to simulate a U-pipe ground heat exchanger (GHE), including a 2-D numerical model to simulate the radial and axial heat transfer in the borehole and an infinite cylindrical-source model to analyze the radial heat transfer in the soil. The proposed model is verified by comparing the calculated results with experimental data, simulation data, and the results of other models. The temperature distributions of the borehole and the soil calculated by the proposed model match well with experimental data and simulation data. The proposed model is demonstrated to have an accurate calculation of temperature distributions compared with other models.

Clarification of Temperature Distribution for Metals with Different Thermal Conductivity in Large-area Electron Beam Irradiation

High energy density of electron beam (EB) with diameter of about 60 mm is obtained in a large-area EB irradiation method. This method can be used for melting and evaporating material surface instantly, and highly efficient surface finishing of metals such as mold steels and biomaterials is possible. Furthermore, surface functions such as corrosion resistance, water repellency and wear resistance can be improved since a thin modified layer with fine microstructure is formed on the EB irradiated surface. It is expected that thick modified layer is effective to maintain their surface functions for long-term. However, the material surface is slightly removed in formation of modified layer. Therefore, control and prediction of removal and modified layer thickness are important in order to obtain appropriate modified layer thickness and to keep the shape accuracy for metals with different thermal properties. In order to predict the removal and modified layer thickness, it is necessary to clarify the temperature distribution in depth direction and its time variation in large-area EB irradiation. In this study, changes of removal and modified layer thickness on metal workpiece with different thermal conductivity are investigated by calculation of temperature distribution in large-area EB irradiation. It is made clear that the modified layer thickness of workpiece with low thermal conductivity is larger than that with high one, while the removal layer thickness is almost the same regardless of thermal conductivity. Furthermore, analytical removal and modified layer thickness obtained by our unsteady heat conduction analysis agree well with the experimental ones. Therefore, our unsteady heat conduction analysis model has high accuracy, and it is possible to predict variations of removal and modified layer thickness on workpiece with different thermal conductivity.

Numerical Calculation and Analysis of Temperature Distribution during Ultrasonic Welding Process for NiTi Shape Memory Alloy

Numerical Calculation and Analysis of Temperature Distribution during Ultrasonic Welding Process for NiTi Shape Memory Alloy

MODEL FOR CALCULATING THE TEMPERATURE IN THE FUEL RODS OF THE FA-X FUEL ASSEMBLY PRODUCED FOR SUBCRITICAL INSTILLATION AND REACTOR WWR-M

The TVS-X fuel rod model designed by NSC KIPT as an alternative fuel for subcritical assembly (SCA, KIPT, Kharkov) and research reactor (WWR-M, INR, Kiev) is described. The model is a program that allows calculating the temperature distribution on the radius and height of the fuel element containing both uranium oxide pellets and dispersion fuel based on the UO2+Al composition with different contents of the fuel phase, as well as the different geometric characteristics of the fuel element and the values of the coolant parameters: the temperature at the entrance to the hydraulic channel and the coolant speed. Comparative calculations of temperature distribution during operation are carried out. As a result, it has been shown that for conditions of operation in the SCA (linear power of fuel rod is 2.62 kW/m), the fuel center temperature reaches ~140 °C for UO2 and ~112 °C for the UO2+Al composition. For operating conditions in the WWR-M reactor (linear power of fuel rod is 12.1 kW/m), the fuel center temperature reaches ~626 °C for ceramic (UO2) and ~381 °C for metal-ceramic fuel (UO2+Al). The calculations show a significant effect of the type of fuel material (UO2 or UO2+Al dispersion composition) on the fuel center temperature, taking into account the operating conditions in the subcritical assembly and the WWR-M research reactor. The maximum temperature of the cladding for the WWR-M operating conditions was 86.5 °C, and the maximum temperature of the cladding for the SCA operating conditions is 27 °C, which does not exceed the boiling point (vaporization) under the nominal conditions of their operation. Cross-section area of fuel rods, heat transfer coefficient and temperature distribution of the coolant are calculated. The software module allowed to estimate the temperature distribution of fuel element with different types of nuclear fuel for the conditions of research nuclear assemblies.

Calculation of temperature distribution and rheological properties of the lithosphere along transect IV in the Western Carpathian-Pannonian Basin region

Abstract 2D integrated modelling algorithm was used to calculate the temperature distribution in the lithosphere along the transect IV located in the Western Carpathian-Pannonian Basin area. Based on the determined temperature field and given rheological parameters of the rocks, it was possible to calculate the strength distribution for both compressional and extensional regimes, construct the strength envelopes for chosen columns of the main tectonic units of the model, and thus construct a simple rheological model of the lithosphere along transect IV. The obtained results indicate decrease of the lithospheric strength from the European platform and the Western Carpathians towards the Pannonian Basin. The largest strength (valid for all tectonic units) can be observed within the upper crust with its maxima on the boundary between upper and lower crust, decreasing towards lower crust and disappearing in the lithospheric mantle, suggesting mostly rigid deformation occurring in the upper crust. A local increase in the values of strength can be observed in the eastern segment of the Western Carpathians where crustal thickening accompanies the lithospheric thickening (formation of the lithospheric root), unlike the previous models along transects I and II, that pass through the western segment of the Western Carpathians and their lithosphere-asthenosphere boundary is almost flat and therefore no accompanying crustal thickening is observed and the decrease in strength is slow and steady.

Monte Carlo Method of Shrinking Direction on Rectangular Slab of Fixed Boundary Condition

The study of heat transfer is crucial for its proper implementation in engineering design process. The Shrinking Boundary Monte Carlo Method was applied to evaluate temperature distribution in a Spiral, vertically up and vertically down running direction. The outcome was equated to normal Monte Carlo Method. The results revealed that increasing the size of the rectangular slab will increase the running time to compute temperature distribution. In a given direction of running, it has different temperature distribution for the different sizes of the slab. The computational run time for a rectangular slab in a portrait shape is greater than rectangular slab in a landscape pattern. The study proved that the average of the run time for various direction of movement indicates that spiral is shorter. It is the best ways of computing temperature dispersal in a rectangular slab of fixed boundary condition. The utilization of the shrinking boundary to analyse heat transfer was successful.

A hybrid strategy for solving radiation-conduction in irregular geometries filled with gray semitransparent medium using Monte Carlo method combined with blocked-off and embedded boundary treatments

Monte Carlo method (MCM) and finite volume method (FVM) are integrated to deal with combined conduction-radiation heat transfer problems in irregular geometries containing gray semitransparent media. The MCM is employed to get radiative heat source using blocked-off and embedded boundary treatments via Cartesian system. The FVM is adopted to solve the energy equation via unstructured grid system. The radiative heat source is implemented in the energy equation through geometrical mapping. The hybrid strategy is first validated regarding both pure radiation and conduction-radiation problems. Then, the features of the two boundary treatments are assessed through solving the conduction-radiation heat transfer problems in irregular geometries. The results show that both of them are highly satisfactory for calculating temperature distribution. In comparison with the embedded boundary treatment, the blocked-off treatment leads to obvious errors in predicting wall radiative heat flux for curved boundaries as well as the boundaries adjacent to the inner curved obstacle. Additionally, the hybrid strategy combined with embedded boundary treatment is promising in eliminating the ray effects.