Analytical model of the temperature distribution and the thermally induced birefringence in laser rods with cylindrically symmetric heating

2000 ◽  
Vol 17 (8) ◽  
pp. 1398 ◽  
Author(s):  
M. Schmid ◽  
Th. Graf ◽  
H. P. Weber
2020 ◽  
Vol 9 (2) ◽  
pp. 359
Author(s):  
Ugwuanyi Donald Chidiebere ◽  
Okafor Fidelis Onyebuchi

Thermally induced cracks have far-reaching implications on the durability of concrete structures. When cement mixes with water, the reaction is exothermic implying the release of heat. In the case of mass concrete structures, quite a substantial increase in internal temperature may be experienced depending on the ambient temperature and cement content in the mix. The objective of the paper is to develop a mathematical model to predict the time dependent temperature profile in early age mass concrete. Mass concrete block was used to verify the model. Type-K thermocouples placed at various positions and digital thermometer was used to monitor the temperature distribution within the mass concrete block at intervals. The highest temperature values occurred within the core of the mass concrete after one day of concrete placement. Analytical model was developed by applying method of separation of variables and orthogonality relation to two dimensional unsteady state heat conduction equations. The model equation was evaluated and using MATLAB based computer programe. The model successfully predicted the temperature variation within the mass concrete with time. It is therefore suitable for use in the assessment of thermal cracks potential in mass concrete structures. 


2017 ◽  
Vol 47 ◽  
pp. 33-45 ◽  
Author(s):  
Shaochuan Feng ◽  
Chuanzhen Huang ◽  
Jun Wang ◽  
Hongtao Zhu ◽  
Peng Yao ◽  
...  

2020 ◽  
Author(s):  
Zhu Linhui ◽  
Shen Jienan ◽  
Zeng Yibo ◽  
Guo Hang

Abstract Particle velocity sensor (PVS) plays an important role in determining the type and location of a sound source. In this presentation, analytical model of heat transfer in PVS with a three-wire (SHS) configuration was first presented. By comparing with the thermal diffusion motion, the forced convection exerts a smaller influence on the temperature distribution. Thus, variation in forced convection could induce the formation of a thermal perturbation field. The overall temperature distribution model of a PVS is made up of a steady temperature field and a thermal perturbation field. With the derived model, PVS with SHS configuration has smaller thermal noise and higher signal-to-noise ratio in comparision with a two-wire (SS) configuration under the same conditions. Optimized parameters of structure design and heating power could be obtained via the analysis model. Also, this model gives optimal output performance and frequency-dependent characteristic curve. Numerical results are found to be in good agreement with the analytical solutions and experimental data, which verify the correctness of analytical model and numerical method. The study provides a basis for a theoretical and numerical analysis.


Author(s):  
M. Naser Reda ◽  
Markus Spinnler ◽  
Rajib Mahamud ◽  
Thomas Sattelmayer

Abstract The measurement of soil temperature profiles for different locations or climates is essential for calculating the thermal performance of applications connected with the soil, e.g., underground heat storage systems. Estimating soil temperature profiles is identified as crucial knowledge for plant and crop growth as well as for germination in all agricultural tasks. The ground temperature depends on weather conditions (ambient temperature, solar irradiation, wind velocity, sky radiation, etc.) that contribute to the resulting temperature distribution within the soil close to the surface. In literature, several approaches have been discussed to predict soil temperature in different climates and locations, such as data-driven models, wavelet transform artificial neural networks, statistical models, etc. However, these models require extensive data sets from literature and high computational efforts. In the present study, a one-dimensional analytical model will be presented, which is based on the Green’s Function (GF) method. The model can estimate the daily and annual variation of the soil temperature distribution at different depths from real-time weather data sets. The model was experimentally validated with an accuracy of more than 96%. The significant advantage of the presented analytical method is the low computational cost, which is lower than that of numerical models by approximately two orders of magnitude.


1991 ◽  
Vol 113 (4) ◽  
pp. 373-380 ◽  
Author(s):  
G. Subramani ◽  
M. C. Whitmore ◽  
S. G. Kapoor ◽  
R. E. DeVor

In this paper, an analytical model is developed for computation of the temperature distribution in a hollow cylindrical workpiece during machining with a single point tool. Such a model is useful for prediction of machined surface error arising from thermal expansion of the workpiece during machining. The model considers the interface between the tool and the workpiece to be a helically moving volumetric heat source. The governing equation satisfied by the temperature field, along with the appropriate boundary and initial conditions, is solved using the method of integral transforms. The experimental test facility used for the conduct of experiments for measurement of the temperature response in a cylindrical workpiece, namely a cylinder bore, during machining is discussed. The results from tests conducted using a laser as a heat source to verify the analytical model for temperature field are then presented. Several cylinder boring tests have been conducted, and the results from these tests along with the analysis performed with the temperature data to calibrate the temperature model are then discussed. Comparisons between predicted and measured temperature response in a cylinder bore during machining show good agreement.


Author(s):  
Zakarya Djelloul Khedda ◽  
Kamel Boughrara ◽  
Frédéric Dubas ◽  
Baocheng Guo ◽  
El Hadj Ailam

Purpose Thermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction of temperature distribution based on the formal resolution of thermal partial differential equations (PDEs) by the harmonic modeling technique (or the Fourier method) is uncommon in electrical machines. Therefore, this paper aims to present a two-dimensional (2D) analytical model of steady-state temperature distribution for permanent-magnet (PM) synchronous machines (PMSM) operating in generator mode. Design/methodology/approach The proposed model is based on the multi-layer models with the convolution theorem (i.e. Cauchy’s product theorem) by using complex Fourier’s series and the separation of variables method. This technique takes into the different thermal conductivities of the machine parts. The heat sources are determined by calculating the different power losses in the PMSM with the finite-element method (FEM). Findings To validate the proposed analytical model, the analytical results are compared with those obtained by thermal FEM. The comparisons show good results of the proposed model. Originality/value A new 2D analytical model based on the PDE in steady-state for full prediction of temperature distribution in the PMSM takes into account the heat transfer by conduction, convection and radiation.


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