Analytical Formulation for the Temperature Profile by Duhamel’s Theorem in Bodies Subjected to an Oscillatory Heat Source

2005 ◽  
Vol 129 (2) ◽  
pp. 236-240 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Heat Source ◽  
Temperature Profile ◽  
Rectangular Domain ◽  
Temperature Fields ◽  
Heat Sources ◽  
Point Heat Source ◽  
Analytical Formulation ◽  
Analytical Technique

An analytical technique is presented for treating heat conduction problems involving a body experiencing oscillating heat flux on its boundary. The boundary heat flux is treated as a combination of many point heat sources, each of which emits heat intermittently based on the motion of the flux. The working function of the intermittent heat source with respect to time is evaluated by using the Fourier series and temperature profile of each point heat source is derived by using the Duhamel’s theorem. Finally, by superposition of the temperature fields over all the point heat sources, the temperature profile due to the original moving heat flux is determined. Prediction results and verification using finite element method are presented for an oscillatory heat flux in a rectangular domain.

Development of Convective Heat Transfer Near Suddenly Heated, Vertically Aligned Horizontal Wires

1987 ◽  
Vol 109 (4) ◽  
pp. 912-918 ◽  
Author(s):  
J. R. Parsons ◽  
M. L. Arey
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Fluid Layer ◽  
Convective Motion ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Heat Sources ◽  
Transfer Coefficients ◽  
Vertically Aligned ◽  
The Wire

Experiments have been performed which describe the transient development of natural convective flow from both a single and two vertically aligned horizontal cylindrical heat sources. The temperature of the wire heat sources was monitored with a resistance bridge arrangement while the development of the flow field was observed optically with a Mach–Zehnder interferometer. Results for the single wire show that after an initial regime where the wire temperature follows pure conductive response to a motionless fluid, two types of fluid motion will begin. The first is characterized as a local buoyancy, wherein the heated fluid adjacent to the wire begins to rise. The second is the onset of global convective motion, this being governed by the thermal stability of the fluid layer immediately above the cylinder. The interaction of these two motions is dependent on the heating rate and relative heat capacities of the cylinder and fluid, and governs whether the temperature response will exceed the steady value during the transient (overshoot). The two heat source experiments show that the merging of the two developing temperature fields is hydrodynamically stabilizing and thermally insulating. For small spacing-to-diameter ratios, the development of convective motion is delayed and the heat transfer coefficients degraded by the proximity of another heat source. For larger spacings, the transient behavior approaches that of a single isolated cylinder.

The Green Function and Its Application to Heat Transfer in a Low Permeability Porous Channel

1999 ◽  
Vol 122 (3) ◽  
pp. 274-278 ◽  
Author(s):  
C. Cui ◽  
X. Y. Huang ◽  
C. Y. Liu
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Green Function ◽  
Porous Channel ◽  
Low Permeability ◽  
Heat Sources ◽  
Point Heat Source ◽  
Analytical Technique ◽  
Discrete Heat Sources ◽  
The Green Function

This paper describes an analytical technique for heat transfer in a low permeability porous channel with initially a point heat source and then multiple discrete sources. The solution of the temperature field for the point source is derived as a Green function, from which the temperature field for other geometrical heat sources can be obtained by using the Green integral. An application of the Green function and Green integral to the porous channel with discrete heat sources is presented. The results are compared with the existing numerical results and good agreements are achieved. [S1043-7398(00)01503-6]

Study on Welding Deformations of Shipboard of Container Vessel

2011 ◽  
Vol 488-489 ◽  
pp. 218-221
Author(s):  
Hong Li ◽  
Da Lu Qiu ◽  
Guang Lei Li ◽  
Hui Long Ren
Keyword(s):  
Heat Flux ◽  
Heat Source ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Transient Temperature ◽  
Plastic Strains ◽  
Out Of Plane ◽  
Inherent Strain ◽  
Nonlinear Behaviors ◽  
Plane Deformations

Residual plastic strains of the shipboard are the product of nonlinear behaviors during welding. Deformations of a welded shipboard injure the beauty of appearance of the ship, cause errors during the assembly of the shipboard and reduce the strength of the ship. Residual welding deformations of shipboard of a container vessel are studied in this paper. Nonlinear three dimensional transient temperature fields are analyzed by FEM first. The heat source is modeled as a moving heat flux following a Gaussian distribution. Then, applying the equivalent loads induced by the inherent strain on the shipboard, the final in-plane shrinkage and out-of-plane deformations are calculated. Being compared with the experimental results of deformations, the simulated results show mostly conformity.

Causes of the 1985-2014 Surface Warming over the Sanjiangyuan Region of the Tibetan Plateau from the Perspective of Energy Transport

2020 ◽  
Author(s):  
Yinglin Tian ◽  
Deyu Zhong
Keyword(s):  
Heat Flux ◽  
Tibetan Plateau ◽  
Heat Source ◽  
Energy Transport ◽  
Longwave Radiation ◽  
Warming Trend ◽  
The Tibetan Plateau ◽  
Heat Sources ◽  
The South ◽  
Downward Longwave Radiation

<p>The Tibetan Plateau (TP), known as the “World Roof”, has significant influences on hydrological and atmospheric circulation at both regional and global scale. As the Sanjiangyuan Region (SJY) supplies water resources to the adjacent river basin and the TP could exert strong thermal forcing on the atmosphere over Asian monsoon region, adequate understand of the climate change over this region and its underlying mechanisms is of great importance. Based on gridded data provided by China Meteorological Administration (CMA), a continuous warming trend higher than that over elsewhere in China has been observed over the TP during 1985-2014, especially in the cold season (0.69 K/decade) and over the SJY (1.0 K/decade). On the basis of ERA interim reanalysis datasets, this paper analyzed the factors facilitating this warming trend in the SJY from the perspective of energy transport. At first, the local processes involved were investigated by calculating partial temperature changes using the surface energy budget equation. Then the horizontal convection of heat was quantified by summing the heat flux across the boundaries of the SJY. Finally, a Lagrangian heat source diagnostic method was developed to identify the major heat source. As the results indicating, among all the local heat sources, the enhanced downward longwave radiation reflected to surface air and the increasing upward longwave radiation emitted by warmer land surface were responsible for the pronounced surface air warming. However, the changes in surface sensible and latent heat fluxes had a reduced warming effect on the surface air. As for the non-local horizontal heat sources, rising horizontal heat flux from the south, west and east boundaries into the SJY contributed to the higher surface temperature of the SJY. In winter season, the heat flows stemmed from the South Himalayan vein into the SJY played a dominant role. Moreover, the higher the temperature over the SJY was, the more inclined this heat source was to Nepal.</p>

scholarly journals Nonaxisymmetric Effects for Three-Dimensional Analysis of a Brake

1994 ◽  
Vol 116 (3) ◽  
pp. 401-407 ◽  
Author(s):  
A. Floquet ◽  
M. C. Dubourg
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Three Dimensional ◽  
Computer Time ◽  
Temperature Fields ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Fem Method ◽  
Validation Tests ◽  
Transient Heat Flux

A three-dimensional model of axisymmetric moving solids submitted to nonaxisymmetric transient heat flux conditions is presented in this paper. Temperature fields are obtained using a new hybrid FFT-FEM method that combines Fourier transform techniques and finite element method. A fast Fourier form algorithm is used which leads to inexpensive computer time. Validation tests are presented. Efficiency of the method is demonstrated.

The study of the temperature field in an infinite slab under line and plane heat source

2015 ◽  
Vol 25 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Wang Qing-Cheng ◽  
Wu Zhao-Chun ◽  
Zhu Xiang-Ping
Keyword(s):  
Temperature Field ◽  
Heat Source ◽  
Temperature Rise ◽  
Temperature Fields ◽  
Manufacturing Processes ◽  
Heat Sources ◽  
Content Type ◽  
Infinite Slab ◽  
Different Types ◽  
Changing Patterns

Purpose – The purpose of this paper is to reveal the characteristics of the temperature field under different types of heat sources, which are significant to the temperature control encountered in practical manufacturing processes. Design/methodology/approach – The temperature fields in an infinite slab under line or plane heat source are calculated numerically by control volume approach and ADI scheme, and the numerical results of the temperature rise have been compared among the different types of the heat sources. Findings – The numerical results show the different changing patterns of temperature fields under line and plane heat source, respectively, and demonstrate that the magnitude of temperature rise depends strongly on the type of the heat sources. The order of temperature rise from high to low is point, line and plane heat source base on the same input heat. Originality/value – The study is original and findings are new, which demonstrate the different changing patterns of temperature fields and the magnitude of temperature rise under line and plane heat source. The numerical solution is significant for the temperature control in practical manufacturing processes.

Magnetic Field Assisted Finishing of Ceramics—Part I: Thermal Model

1998 ◽  
Vol 120 (4) ◽  
pp. 645-651 ◽  
Author(s):  
Zhen-Bing Hou ◽  
R. Komanduri
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Thermal Model ◽  
Circular Ring ◽  
Heat Sources ◽  
Point Heat Source ◽  
Abrasive Finishing ◽  
Instantaneous Point ◽  
Magnetic Float ◽  
Transient And Steady State

A thermal model for magnetic field assisted polishing of ceramic balls/rollers is presented. The heat source at the area of contact between the balls and the abrasives where material removal takes place is approximated to a disk. The disk heat source is considered as a combination of a series of concentric circular ring heat sources with different radii. Each ring in turn is considered as a combination of a series of infinitely small arc segments and each arc segment as a point heat source. Jaeger’s classical moving heat source theory (Jaeger, 1942; Carslaw and Jaeger, 1959) is used in the development of the model, starting from an instantaneous point heat source, to obtain the general solution (transient and steady-state) of the moving circular ring heat source problem and finally the moving disc heat source problem. Due to the formation of fine scratches during polishing (on the order of a few micrometers long), the conditions are found to be largely transient in nature. Calculation of the minimum flash temperatures and minimum flash times during polishing enables the determination if adequate temperatures can be generated for chemo-mechanical polishing or not. This model is applied in Part II for magnetic float polishing (MFP) of ceramic balls and in Part III for magnetic abrasive finishing (MAF) of ceramic rollers.

Two-Phase Flow of Dusty Casson Fluid with Cattaneo-Christov Heat Flux and Heat Source Past a Cone, Wedge and Plate

2018 ◽  
Vol 387 ◽  
pp. 625-639 ◽  
Author(s):  
B. Mahanthesh ◽  
Oluwole Daniel Makinde ◽  
Bijjanal Jayanna Gireesha ◽  
Koneri L. Krupalakshmi ◽  
Isaac Lare Animasaun
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Heat Source ◽  
Regression Line ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Dust Particles ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Two Phase

This article addresses the boundary layer flow and heat transfer in Casson fluid submerged with dust particles over three different geometries (vertical cone, wedge and plate). The aspects of Cattaneo-Christov heat flux and exponential space-based heat source (ESHS) are also accounted. At first, the partial differential equations are transformed into a set of ordinary differential equations via appropriate similarity transformations. Resulting equations are solved via shooting method coupled with the Runge-Kutta-Fehlberg-45 integration scheme. The consequences of dimensionless parameters on velocity and temperature fields of both fluid and dust particles phase are analyzed. The rate of increment/decrement in the skin friction as well as the Nusselt number for various values of physical parameters are also estimated via slope of linear regression line using data points.

Mathematical Approaching and Experimental Assembly to Evaluate the Risks of In-Service Welding in Hot Tapping

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Ivo Andrei de O. L Lima ◽  
Alex Alisson Bandeira Santos
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Arc Welding ◽  
Numerical Models ◽  
Temperature Fields ◽  
Physical Situation ◽  
Rectilinear Motion ◽  
Heat Sources ◽  
The Mathematical Model ◽  
Burn Through

The welding onto in-service pipeline (operation condition) results in three possibilities of high risks: leaking and/or explosion by burn-through, chemical reactions to instability, or even explosion due to the heat on internal fluid and cracking in heat affected zone (HAZ). The numerical methods have a useful role in the assessment of welding conditions for the safe in-service welding of pipelines. Only limited published works have considered direct calculation of burn-through using a combination of thermal and stress analysis. The mathematical model of the heat source is the most important part of these numerical models, and actually the mathematical model which described better the heat distribution of the arc welding through gas-shielded tungsten arc welding (GTAW) process or shielded metal arc welding process is the double ellipsoidal heat source (DEHS) model of Goldak and Akhlaghi (2010, Computational Welding Mechanics, Springer Books, New York, pp. 32–35). However, that model has considered the heat source in rectilinear motion only, and it depends on three parameters (a, b, c) which are related with the weld bead size and shape to define the geometry and co-ordinates of heat source, and they are determined empirically or experimentally. Few researchers published works that could determine these parameters mathematically, from the welding data. The publication that best analytically addressed this issue was the work of Eagar and Tsai (1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355). First, this paper presents a new equation for heat source in double ellipsoid considering the circular motion, trying to develop a model closer to the physical situation of hot tapping onto pipeline. Second, a proposal for determination of the parameters a, b analytically from the Eagar model and Tsai (1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355), and third, an experimental facility to get the temperature field that was used to validate the numerical finite element models.

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