scholarly journals Simulation of differentiated thermal processing of railway rails by compressed air

2021 ◽  
Vol 63 (11-12) ◽  
pp. 907-914
Author(s):  
V. D. Sarychev ◽  
S. G. Molotkov ◽  
V. E. Kormyshev ◽  
S. A. Nevskii ◽  
E. V. Polevoi
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Thermal Processing ◽  
Heat Conduction Equation ◽  
Rail Steel ◽  
Rail Head ◽  
The Third ◽  
Forced Cooling

Mathematical modeling of differentiated thermal processing of railway rails with air has been carried out. At the first stage, onedimensional heat conduction problem with boundary conditions of the third kind was solved analytically and numerically. The obtained temperature distributions at the surface of the rail head and at a depth of 20 mm from the rolling surface were compared with experimental data. As a result, value of the coefficients of heat transfer and thermal conductivity of rail steel was determined. At the second stage, mathematical model of temperature distribution in a rail template was created in conditions of forced cooling and subsequent cooling under natural convection. The proposed mathematical model is based on the Navier-Stokes and convective thermal conductivity equations for the quenching medium and thermal conductivity equation for rail steel. On the rail – air boundary, condition of heat flow continuity was set. In conditions of spontaneous cooling, change in temperature field was simulated by heat conduction equation with conditions of the third kind. Analytical solution of one-dimensional heat conduction equation has shown that calculated temperature values differ from the experimental data by 10 %. When cooling duration is more than 30 s, change of pace of temperature versus time curves occurs, which is associated with change in cooling mechanisms. Results of numerical analysis confirm this assumption. Analysis of the two-dimensional model of rail cooling by the finite element method has shown that at the initial stage of cooling, surface temperature of the rail head decreases sharply both along the central axis and along the fillet. When cooling duration is over 100 s, temperature stabilizes to 307 K. In the central zones of the rail head, cooling process is slower than in the surface ones. After forced cooling is stopped, heating of the surface layers is observed, due to change in heat flow direction from the central zones to the surface of the rail head, and then cooling occurs at speeds significantly lower than at the first stage. The obtained results can be used to correct differential hardening modes.

scholarly journals Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

2021 ◽  
Vol 321 ◽  
pp. 03005
Author(s):  
George Kuvyrkin ◽  
Inga Savelyeva ◽  
Daria Kuvshinnikova
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Complex Structure ◽  
Modern World ◽  
Nonlocal Term ◽  
Material Structure ◽  
Two Dimensional ◽  
Differential Heat

Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship between micro and macro characteristics of materials. A mathematical model of thermal conductivity in nonlocal media is considered. The model is based on the theory of nonlocal continuum by A.K. Eringen. The interaction of material particles is described using local and nonlocal terms in the law of heat conduction. The nonlocal term describes the effect of decreasing the influence of the surrounding elements of the material structure with increasing distance. The effect of nonlocal influence is described using the standard non-locality function based on the Gaussian distribution. The nonlocality function depends on the distance between the elements of the material structure. The mathematical model of heat conduction in a nonlocal medium consists of an integro-differential heat conduction equation with initial and boundary conditions. A numerical solution to the problem of heat conduction in a nonlocal plate is obtained. The numerical solution of a two-dimensional problem based on the finite element method is described. The influence of nonlocal effects and material parameters on the thermal conductivity in a plate under highintensity surface heating is analyzed. The importance of nonlocal characteristics in modelling the thermodynamic behaviour of materials with a complex structure is demonstrated.

Study on Radial Temperature Distribution of Aluminum Dispersed Nuclear Fuels: U3O8-Al, U3Si2-Al, and UN-Al

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Jayangani I. Ranasinghe ◽  
Ericmoore Jossou ◽  
Linu Malakkal ◽  
Barbara Szpunar ◽  
Jerzy A. Szpunar
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Gradient ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Temperature Profiles ◽  
Nuclear Fuels ◽  
State Heat ◽  
Steady State Heat

The understanding of the radial distribution of temperature in a fuel pellet, under normal operation and accident conditions, is important for a safe operation of a nuclear reactor. Therefore, in this study, we have solved the steady-state heat conduction equation, to analyze the temperature profiles of a 12 mm diameter cylindrical dispersed nuclear fuels of U3O8-Al, U3Si2-Al, and UN-Al operating at 597 °C. Moreover, we have also derived the thermal conductivity correlations as a function of temperature for U3Si2, uranium mononitride (UN), and Al. To evaluate the thermal conductivity correlations of U3Si2, UN, and Al, we have used density functional theory (DFT) as incorporated in the Quantum ESPRESSO (QE) along with other codes such as Phonopy, ShengBTE, EPW (electron-phonon coupling adopting Wannier functions), and BoltzTraP (Boltzmann transport properties). However, for U3O8, we utilized the thermal conductivity correlation proposed by Pillai et al. Furthermore, the effective thermal conductivity of dispersed fuels with 5, 10, 15, 30, and 50 vol %, respectively of dispersed fuel particle densities over the temperature range of 27–627 °C was evaluated by Bruggman model. Additionally, the temperature profiles and temperature gradient profiles of the dispersed fuels were evaluated by solving the steady-state heat conduction equation by using Maple code. This study not only predicts a reduction in the centerline temperature and temperature gradient in dispersed fuels but also reveals the maximum concentration of fissile material (U3O8, U3Si2, and UN) that can be incorporated in the Al matrix without the centerline melting. Furthermore, these predictions enable the experimental scientists in selecting an appropriate dispersion fuel with a lower risk of fuel melting and fuel cracking.

Assessment of Models for Extracting Thermal Conductivity From Frequency Domain Thermoreflectance Experiments

2020 ◽  
Author(s):  
Siddharth Saurav ◽  
Sandip Mazumder
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Computational Domain ◽  
Fourier Heat Conduction

Abstract The Fourier heat conduction and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experimental setup. Numerical solutions enable use of realistic boundary conditions, such as convective cooling from the various surfaces of the substrate and transducer. The equations were solved in time domain and the phase lag between the temperature at the center of the transducer and the modulated pump laser signal were computed for a modulation frequency range of 200 kHz to 200 MHz. It was found that the numerical predictions fit the experimentally measured phase lag better than analytical frequency-domain solutions of the Fourier heat equation based on Hankel transforms. The effects of boundary conditions were investigated and it was found that if the substrate (computational domain) is sufficiently large, the far-field boundary conditions have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was also treated as a parameter, and was found to have some effect on the predicted thermal conductivity, but only in certain regimes. The hyperbolic heat conduction equation yielded identical results as the Fourier heat conduction equation for the particular case studied. The thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be 108 W/m/K, which is slightly different from previously reported values for the same experimental data.

Inverse determination of thermal conductivity in lumber based on genetic algorithms

Holzforschung ◽  
2016 ◽  
Vol 70 (3) ◽  
pp. 235-241 ◽  
Author(s):  
Jingyao Zhao ◽  
Zongying Fu ◽  
Xiaoran Jia ◽  
Yingchun Cai
Keyword(s):  
Thermal Conductivity ◽  
Genetic Algorithms ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Convective Heat Transfer Coefficient ◽  
Conduction Equation ◽  
New Equation ◽  
Volume Method ◽  
Good Agreement

Abstract A 3D numerical solution of the heat conduction equation is proposed based on the finite volume method to describe the heating of wood, where the thermal conductivity (ThC) is variable, and the convective heat transfer coefficient is constant. ThC parameters were found through an optimization process based on genetic algorithms. The objective function between measured and simulated curves is determined, and parameters with greatest correspondence between measured and estimated values were obtained. As a result, a new equation for ThC is proposed, which depends on moisture and temperature. The proposed coefficient is validated by experiments, and a good agreement was found between experimental heating curves and those obtained by simulation by means of the new heat conduction equation.

scholarly journals Parameterising continuum models of heat transfer in heterogeneous living skin using experimental data

2018 ◽  
Author(s):  
Sean McInerney ◽  
Elliot J Carr ◽  
Matthew J Simpson
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Layered Structure ◽  
Experimental Studies ◽  
Synthetic Data ◽  
Spatial Location ◽  
Recent Experimental Data ◽  
Data Set ◽  
Experimental Constraint

AbstractIn this work we consider a recent experimental data set describing heat conduction in living porcine tissues. Understanding this novel data set is important because porcine skin is similar to human skin. Improving our understanding of heat conduction in living skin is relevant to understanding burn injuries, which are common, painful and can require prolonged and expensive treatment. A key feature of skin is that it is layered, with different thermal properties in different layers. Since the experimental data set involves heat conduction in thin living tissues of anesthetised animals, an important experimental constraint is that the temperature within the living tissue is measured at one spatial location within the layered structure. Our aim is to determine whether this data is sufficient to reliably infer the heat conduction parameters in layered skin, and we use a simplified two-layer mathematical model of heat conduction to mimic the generation of experimental data. Using synthetic data generated at one location in the two-layer mathematical model, we explore whether it is possible to infer values of the thermal diffusivity in both layers. After this initial exploration, we then examine how our ability to infer the thermal diffusivities changes when we vary the location at which the experimental data is recorded, as well as considering the situation where we are able to monitor the temperature at two locations within the layered structure. Overall, we find that our ability to parameterise a model of heterogeneous heat conduction with limited experimental data is very sensitive to the location where data is collected. Our modelling results provide guidance about optimal experimental design that could be used to guide future experimental studies.NomenclatureA brief description of all variables used in the document are given in Table 1.Table 1:Variable nomenclature and description.

Thermal Conductivity of Nanochanneled Alumina

2000 ◽  
Author(s):  
A. R. Kumar ◽  
D.-A. Achimov ◽  
T. Zeng ◽  
G. Chen
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Experimental Study ◽  
Heat Conduction ◽  
Room Temperature ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Anisotropic Heat Conduction ◽  
3Ω Technique

Abstract We present an experimental study on the thermal conductivity of anodized alumina with regular nanochannels. Thermal conductivity values in both directions parallel and perpendicular to the nanochannel axis are measured at room temperature using the 3ω technique. An anisotropic heat conduction model is developed to analyze the experimental data.

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