Steady Temperature Field Research Articles

Cooling Roller Steady-state Heat Flux and Temperature Analysis in Amorphous Ribbon Preparing Process

Temperature of cooling roller is a key issue affecting the quality of the amorphous ribbon. To this end, heat flux distribution acting on cooling roller outer wall was calculated by fluid dynamics software Fluent. Cooling roller steady temperature field was analyzed with a finite element method with heat flux boundary conditions. The cooling roller inner and outer wall temperature distribution was obtained and the temperature of cooling roller as a function of cooling roller thickness and water passage height was discussed. Results show that cooling roller outer wall temperature decreases with roller thickness and the cooling water passage height decrease; cooling roller inner wall temperature decreases with roller thickness increases and the cooling water passage height decreases. Meantime, the appropriate roller thickness and passage height were selected to keep both inner and outer wall temperature of cooling roller within the certain range. The study result provides theoretical support for cooling roller design and optimization.

Study of thermo‐elastic cruciform crack with unequal arms in an orthotropic elastic plane

The objective of this article is concerned with a study of a static cruciform crack problem in an infinite orthotropic elastic medium opened by prescribed normal pressure distributions subjected to steady state temperature field. The problem is reduced to Fredholm singular integral equations of first kind, which are solved using Chebyshev polynomials. Analytical expressions of the stress intensity factors and crack energies are found and the numerical computations for the orthotropic elastic material Boron‐epoxy composite for different particular cases are depicted through figures. The striking feature of the article is the graphical presentation of possibility of crack arrest and variations of crack energies with the variations of the arms of the cruciform crack.

An analytical solution of three-dimensional steady thermodynamic analysis for a piezoelectric laminated plate using refined plate theory

Based on the refined plate theory, an analytical solution of three-dimensional thermodynamic analysis for a piezoelectric laminated plate under 3D steady temperature field is given in this paper. The refined plate theory has a lot in common with classical plate theory in many aspects, and the involved variables can be expressed as certain function type comparing with other shear deformation theories and exact solution, besides it does not need to use shear correction factor. In this study, the method of separation of variables is used to process the 3D temperature field, subsequently the Galerkin method in conjunction with the double Fourier serial method and Newmark method are applied to determine the closed-form solutions of deflection for thermodynamic problem. The results of this paper show that the fiber orientation, number of layers for laminated plate, thickness ratio between total thickness and thickness of piezoelectric layer, temperature distributed function and geometrical nonlinearity have great influence on the deflection, normal stress and shear stresses of the piezoelectric laminated plate.

Analysis of thermal temperature fields and thermal stress under steady temperature field of diesel engine piston

With the improvement of the diesel engine power and performance, the piston in the combustion chamber is subjected to higher thermal load and the thermal stress decreases its working life. Therefore, it is necessary to analyze the subsequent thermal stress on the piston during design process to reach the optimum one. This paper tries to present a new calculation method for the theoretical design of the piston. In this study, the 3D solid model of piston in 16V280 diesel engine was developed and the simulation calculation of the steady-state and the transient-state temperature field is carried out. Based on calculation results, the maximum temperature fluctuation of the piston temperature field is less than 20°, so the steady-state temperature field was used as boundary condition for the thermal stress calculation and the thermal mechanical decoupling method was used to calculate the thermal stress caused only by the uneven temperature distribution. The results show that the maximum temperature is 354°C, which appears at the edge of the combustion chamber. The steady-state temperature field of finite element simulation shows a good agreement with the experimental results. The thermal stress obtained from thermal mechanical decoupling method was within the allowable range, since the maximum value is 270MPa. Danger zone appears at the combustion chamber throat, the contact area of piston head and skirt.

The Study Physical-Chemical Properties of Water Treated by Contact Heating Method

The influence of contact heat and mass- transfer processes of combustion products at bubbling at immersed combustion apparatuses action was studied. The gaseous fuel was used. The main points of water quality were compared at different temperatures with standard points, such as colour, turbidity, hardness, oxidability, alcalinity. The mentioned standards were not changed. Concentration of nitrates and nitrites were lower then the limit concentration by 10 and 3 times respectively, sulfates – by 2 times and chlorides – by 12 times. The influence of contact time of combustion products with liquid phase upon the 9 main water quality standards was also studied. The obtained data show the possibility and safety of contact water heating. The steady temperature field through the surface and through the volume of the bath with liquid was observed. And there was no additional metal tube corrosion in the heating systems.

Unsteady MHD convective flow of Second grade fluid through a porous medium in a Rotating parallel plate channel with temperature dependent source

In this paper, we make an initial vale investigation of hydromagnetic convective flow of a viscous electrically conducting second grade fluid through a porous medium in a rotating parallel plate channel in the presence of a temperature dependent heat source. The perturbations in the flow are created by a constant pressure gradient along the plates in addition to non-torsional oscillations of the lower plate. The exact solutions of the velocity and the temperature fields consist of the steady state and the transient components using Laplace transform technique. The time required for the transient effects to decay is discussed in detail and the ultimate steady state consists of boundary layers on the plates and an interior. Attention is focused on the physical nature of the solutions, and the structure of the various kinds of boundary layers formed on the plates. The final steady state velocity and temperature fields are numerically discussed for different values of the governing parameters. The shear stresses and the Nusselt number are tabulated. Particular case when both the plates are at rest has also been computed and analyzed.

Determination of time of death in forensic science via a 3-D whole body heat transfer model

This study is focused on developing a whole body heat transfer model to accurately simulate temperature decay in a body postmortem. The initial steady state temperature field is simulated first and the calculated weighted average body temperature is used to determine the overall heat transfer coefficient at the skin surface, based on thermal equilibrium before death. The transient temperature field postmortem is then simulated using the same boundary condition and the temperature decay curves at several body locations are generated for a time frame of 24h. For practical purposes, curve fitting techniques are used to replace the simulations with a proposed exponential formula with an initial time delay. It is shown that the obtained temperature field in the human body agrees very well with that in the literature. The proposed exponential formula provides an excellent fit with an R2 value larger than 0.998. For the brain and internal organ sites, the initial time delay varies from 1.6 to 2.9h, when the temperature at the measuring site does not change significantly from its original value. The curve-fitted time constant provides the measurement window after death to be between 8h and 31h if the brain site is used, while it increases 60–95% at the internal organ site. The time constant is larger when the body is exposed to colder air, since a person usually wears more clothing when it is cold outside to keep the body warm and comfortable. We conclude that a one-size-fits-all approach would lead to incorrect estimation of time of death and it is crucial to generate a database of cooling curves taking into consideration all the important factors such as body size and shape, environmental conditions, etc., therefore, leading to accurate determination of time of death.

An Investigation of Hot Forging Die Wear Based on FEA

Taking the forging die of an automobile differential shell as example, the influence of some die forging process parameters and die structure parameters on the die wear was investigated. Based on a modified Archard wear model and the application of finite element method simulation, the die wear depth was calculated under a steady state temperature field. Within the scope of the experimental data, the research shows that: with the increase of billet preheating temperature, the wear is reduced gradually. Improving die preheating temperature, the wear increases gradually. When the forming speed is 300mm/s~400mm/s, the wear value decreases first and then increases.When the forming speed is over than 400mm/s, the change of wear value is not obvious. Increasing flash thickness and round radius, the wear value reduces gradually.

Three-dimensional steady thermodynamic analysis for a double-layer plate with a local heat source and harmonic load

Based on the three-dimensional heat conduction theory, von Karman equation and laminated plate theory, the three-dimensional steady thermodynamic behavior for a double-layer (coating/FGM) plate subjected to a local heat source and harmonic load is investigated in this paper. The exact three-dimensional steady temperature field has been obtained previously by using Poisson method and layer wise method, and then governing equations of the double-layer plate are solved by applying the finite difference method and Newmark method in space domain and time domain, respectively. Numerical results denote that functionally graded index, selected coating layer’s heat conduction coefficient, thickness ratio between total layers and coating layer, width of heat source strip, geometrical condition and boundary condition of the structure have great influence on the deflection and stresses for the double-layer plate.

Temperature solution in composites by domain decomposition

This paper considers the conduction of heat in composite media in the steady-state. The original domain is subdivided into part domains and it is investigated how a part domain influences the complementary structure and the temperature field. This can be represented by two interfacial effects. Firstly, a part domain acts as a perfect thermal sink which effect is described by a homogeneous interface condition of the first kind on its interface(s), which enables to separate the part domains and to establish a temperature part solution within them independently. Secondly, the temperature field is corrected for the finite conductivity of the part domains which effect is described by re-forming the original structure and feeding back the opposite of the fluxes, which had been “sunk” previously, at the interfaces. At this step, all the other external and internal excitations are homogenized. A general, non-iterative procedure for obtaining the steady temperature field in composite media is thus also established. Practical applications of the developed procedure are discussed, e.g., improvements and extension of analytical and coupled (numerical combined with analytical) solution techniques for the heat equation. An illustrative example is also presented.

Analysis of bulk temperature field and flash temperature for locomotive traction gear

Sliding velocity variation for gear meshing surface was researched based on theories of gear tribology, heat transfer and Hertz contact, and a model of contact stress considering friction force was derived. The model design process culminated in a comparison of theoretical values and simulated values. Heat flux of friction for different meshing positions and the convective heat transfer coefficient at gear tooth surface and tooth face were initially calculated accurately. The finite element method was then adopted to establish the gear bulk temperature field model and, after the steady state temperature field of the locomotive traction gear was obtained, the distribution law of the steady-state temperature for the gear teeth was analyzed. Transient thermal analysis on the gear was implemented utilizing the steady-state thermal analysis to obtain the transient temperature field of the locomotive traction gear. Applying the Blok flash temperature criterion, theoretical value of the transient temperature rise for the gear tooth surface was calculated. Comparison of the simulation values and the theoretical values for the transient temperature rise indicated that the theoretical values were higher than the simulation values as the Blok flash temperature criterion considers the heat conduction only in the direction vertical to the tooth surface and disregards heat conduction in other directions. The simulation results were then concluded to be superior in practicality and accuracy.

Analysis of Temperature Field in a Composite Functionally Graded Material Plate by Finite Element Method

A finite element model is constructed to analyze the effects of steady state temperature field on FGM layer thickness. The first-order shear deformation model is exploited to investigate the uncoupled thermal behavior of functionally graded plates in Abacus environment. The continuum is divided into 540 elements and 541 nodes using two node linear elements. The results show that the temperature distribution in the composite plate is more reasonable with increase in the thickness of FGM layer. The comparison with the non-graded two layered composite plate, the temperature field of the Zirconia/FGM/Aluminum three layered composite plate is in the form of a curve but in case of non-graded two layered composite plate the temperature field is in the form of inclined straight line with sharp bend at the interface of metal and ceramic phase.

Constitutive modelling and creep life prediction of a directionally solidified turbine blade under service loadings

The high pressure turbine (HPT) blade of a heavy duty gas turbine operates under the interaction of complex aerodynamic, centrifugal and thermal loadings. The reliability of continuous working at elevated temperatures is a major limitation in service application of these materials. Therefore, it is essential to build the constitutive equations for predicting and analysing the creep deformation and creep lifetime of the blade. In present work, the creep deformation and lifetime of a HPT blade made of a nickel-based directionally solidified (DS) superalloy was numerically predicted. The θ-projection method was used to characterize the creep deformation of DZ125 under different temperatures and stress levels. The uniaxial equations of the θ-projection method were expanded into multi-axial form which was implemented into ABAQUS/UMAT (User MATerial subroutine) by an Euler method. A modified θ-projection method was employed to promote the adaptability of the original model to both steady state and transient temperature fields. Transient stress, strain and displacement distribution of the critical position inside the blade were obtained for service loading. The Larson–Miller parameter was employed to predict the creep lifetime of the blade. Simulation and results of the θ-projection method may also provide suggestions for the safety and life evaluation of HPT blade and other turbine blades.

Accessory gearbox temperature field analysis considering fuel injection lubrication

Accessory gearbox is a major component of aero-engine,and the heat production and heat dissipation problems of accessory gearbox are complex. Previous studies have focused only on solid domains thermal analysis,however oil cooling effect has not been taken full account of. Aiming to complement this,a fluid simulation based on the steady-state temperature field thinking method of analysis was proposed. Firstly,basic rules and characteristics of the heat production and heat dissipation problems of the accessory gearbox were analyzed. Then we applied the k-e turbulence model to simulation,applied the multiphase flow model to simulate the oil,and used multiple reference coordinate system to simulate heat transfer with gear rotation. Finally,the application of a specific case of accessory gearbox verified the correctness and feasibility of the method,which formed a set of effective models and methods using FLUENT software to simulate accessory gearbox's steady state temperature field. The result plays an important supporting role for subsequent research on accessory gearbox reliability and lifetime analysis.

Method of Lines to Solve the Linear Temperature Field of LENS

This article introduces a semi-analytical numerical method ——method of lines(MOLs) to solve steady temperature field of Laser Engineered Net shaping (LENS). The main idea of MOLs is to semi-discretized the governing equation of thermal transfer problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The steady linear temperature fields of functionally graded materials were obtained using MOLs and the regularities of different temperature functions were also found. The effects of thermal conductivity coefficient under different formal functions on thermal temperature fields were analys. Numerical results showed that different material thermal conductivity function had obvious different effect on the temperature field.

Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions

An approximate analytical solution to the axisymmetric heat conduction equation for a hollow cylinder made of functionally graded material with temperature-dependent heat conductivity is presented. General linear boundary conditions are considered. The Poincare method for regular perturbation problems is employed to obtain an analytical closed-form approximate solution for the temperature field. The hierarchical asymptotic problems are solved up to the second-order approximation. A numerical example is worked out, i.e., the one-dimensional heat conduction in the radial direction with prescribed temperatures at the boundaries. The approximate temperature profiles are compared with a numerical solution of the full nonlinear problem which provides the reference “exact” solution. A good agreement between the approximate and reference solutions is established. The convergence of the asymptotic series as well as the properties of the temperature field are studied.

Three Dimensional Steady State Thermal Stress Analyses in a Clamped Solid Sphere

The present work deals with the three dimensional axisymmetric problem in a spherical coordinate system. A clamped solid sphere is subjected to heat flux on its plane boundary surface. Heat is generated within the sphere. The attempt made to analyze heat transfer and thermal stresses of solid sphere under steady temperature field. The Legendre's transforms are used for the solution of governing heat conduction equation. The solution of Navier's equation in terms of Goodier's thermoelastic displacement potential and the Boussinesq's harmonic function for spherical co-ordinate system have been used to determine displacement and thermal stresses within solid. The results for temperature change, displacement and stresses have been computed numerically and illustrated graphically.

Modelling of heat transfer in composite bodies reinforced with tubes with incompressible liquid coolant moving in laminar regime

The equations were obtained for description of heat transfer in composite bodies with reinforcement with a set of smooth tubes with pumping of incompressible liquid coolant. The appropriate boundary-value problem of heat transfer was formulated with the following qualitative analysis. The steady temperature fields in cylindrical shells with spiral-shaped tube reinforcement (with liquid coolant flow) were simulated. The influence on the temperature fields from the side of reinforcement geometry parameters, flow direction and velocity, tubes cross sections was studied. It was found that these characteristics allow significant variation of temperature field in its gradients within the composite item: this open ways for effective control of temperature fields.

The BEM-FDM model of thermal processes proceeding in the domain of the human finger.

The problem of the numerical modeling of thermal processes proceeding in the non-homogeneous domain of the human finger is discussed. The domain considered constitutes the assembling of soft and bone tissues and the system of supplying blood vessels (arteries and veins). The mathematical description of the process analyzed corresponds to the so-called vascular models. At the stage of numerical modeling the algorithm being the composition of the boundary element method (BEM) and the finite difference method (FDM) is applied. The algorithm presented allows one to determine the steady state temperature field in the finger domain in natural convection conditions. To verify the effectiveness and exactness of the method of the problem solution, the thermal imaging measurements of the finger surface temperature have been done. The compatibility of numerical and experimental results (the natural convection conditions) has proved to be quite satisfactory. It is possible to use the algorithm proposed for the modeling of thermal processes proceeding in the conditions of low or high ambient temperatures and the big values of heat transfer coefficients. The impact of protective clothing on the temperature field in the domain of the finger can also be analyzed.

Temperature Field Analysis of 400 MN Heavy Die Forging Press Based on Finite Element Method

Heat conduction and thermal radiation of workpiece could increase temperature of the steel wire wound frame and the moving beam, which may lead to huge creep deformation, pre-stress loss of steel wire and performance degradation of the hydraulic oil. So it is practically important to analyze the temperature field of the die forging press. Steady and transient temperature field analyses are performed for 400 MN forging press by using ABAQUS to study the temperature field characteristics of the ejection cylinder and steel wires of the moving beam and the frame. The results show that when working temperature of the die is 300 ℃,wire temperature is below 75 ℃ after 48 h, while oil temperature is above 70 ℃ after 8.4 h, the latter exceeds the permit limit. Since the improvement of heat dissipation could not decrease temperature effectively, scheme A in which the heat insulation gaskets are added to the bottom and the top of the cylinder and scheme B in which the insulation gaskets are added between the die and the die holder are proposed. It is verified by the simulation that the latter could decrease oil temperature effectively and meet the design requirements, the oil temperature could keep below 70 ℃ after 48 h. The FEM results agree well with the experimental data, which verifies the validity of the FEM modeling. This work provides beneficial reference for structural design and forging process design.