Moving Heat Sources in a Half Space: Effect of Source Geometry

2009 ◽  
Author(s):  
Mohsen Akbari ◽  
David Sinton ◽  
Majid Bahrami
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Half Space ◽  
Source Area ◽  
Heat Sources ◽  
Shape Variation ◽  
Wide Range ◽  
Space Effect ◽  
Moving Plane ◽  
Transient And Steady State

The time dependent temperature distribution due to a moving plane heat source of hyperelliptical geometry is analytically studied in this work. The effect of the heat source shape is investigated starting from the general solution of a moving heat source on a half space. Selecting the square root of the heat source area as a length scale, it is observed that the temperature distribution becomes a weak function of the heat source shape. Variation of temperature field with respect to the source aspect ratio, velocity and depth is studied. The analysis presented in this work is valid for both transient and steady-state conditions. In addition, the hyperellipse formulation provided here covers a wide range of shapes including star, rhombic, ellipse, circle, square, rectangle and rectangle with rounded corners.

Geometrical Effects on the Temperature Distribution in a Half-Space Due to a Moving Heat Source

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Mohsen Akbari ◽  
David Sinton ◽  
Majid Bahrami
Keyword(s):  
Aspect Ratio ◽  
Heat Source ◽  
Half Space ◽  
Fundamental Problem ◽  
Laser System ◽  
Numerical Data ◽  
Source Area ◽  
Maximum Temperature ◽  
Moving Heat Source ◽  
Wide Range

Fundamental problem of heat transfer within a half-space due to a moving heat source of hyperelliptical geometry is studied in this work. The considered hyperelliptical geometry family covers a wide range of heat source shapes, including star-shaped, rhombic, elliptical, rectangular with round corners, rectangular, circular, and square. The effects of the heat source speed, aspect ratio, corners, and orientation are investigated using the general solution of a moving point source on a half-space and superposition. Selecting the square root of the heat source area as the characteristics length scale, it is shown that the maximum temperature within the half-space is a function of the heat source speed (Peclet number) and its aspect ratio. It is observed that the details of the exact heat source shape have negligible effect on the maximum temperature within the half-space. New general compact relationships are introduced that can predict the maximum temperature within the half-space with reasonable accuracy. The validity of the suggested relationships is examined by available experimental and numerical data for the grinding process, for medium Peclet numbers. For ultrafast heat sources, an independent experimental study is performed using a commercial CO2 laser system. The measured depth of the engraved grooves is successfully predicted by the proposed relationships.

Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

2007 ◽  
Vol 129 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Heat Source ◽  
Oscillation Amplitude ◽  
The Body ◽  
Transient Temperature ◽  
Dimensionless Frequency ◽  
Heat Sources ◽  
Infinite Body ◽  
Fitting Method ◽  
Wide Range ◽  
Analytical Expressions

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency ω¯=ωl2∕4α and the dimensionless oscillation amplitude A¯=A∕l, whose product can be interpreted as the Peclet number involving oscillatory heat source, Pe=ω¯A¯. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

Analytical Thermal Models of Oblique Moving Heat Source for Deep Grinding and Cutting

2000 ◽  
Vol 123 (2) ◽  
pp. 185-190 ◽  
Author(s):  
T. Jin ◽  
G. Q. Cai
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
High Efficiency ◽  
Orthogonal Cutting ◽  
Heat Sources ◽  
Thermal Models ◽  
Creep Feed ◽  
Moving Direction ◽  
Transfer Problems ◽  
Zone Temperature

Three related analytical thermal models of plane heat source moving obliquely along the surface of a semi-infinite solid are presented. The temperature distribution of grinding zone under deep-cut conditions is investigated with these models. It is proposed that the oblique angle of the heat source plane to its moving direction has an essential influence on the grinding zone temperature rise and its distribution of high efficiency deep grinding (HEDG). Compared with that in creep-feed grinding, HEDG has a different form of heat flux distribution in grinding zone and should be treated with different thermal models. The temperature distribution at the shear zone of orthogonal cutting is also briefly discussed with the thermal models. The models developed in the paper provide a more rational and integrated analytical basis for dealing with the heat transfer problems of inclined moving heat sources.

An Experimental Study of Transient Heat Transfer From Discrete Heat Sources in Water Cooled Vertical Rectangular Channel

2004 ◽  
Vol 127 (3) ◽  
pp. 193-199 ◽  
Author(s):  
H. Bhowmik ◽  
K. W. Tou
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Source ◽  
Rectangular Channel ◽  
Convection Heat Transfer ◽  
Uniform Heat Flux ◽  
Heat Sources ◽  
Discrete Heat Sources ◽  
Wide Range ◽  
Transfer Behavior

Experiments are performed to study the single-phase transient forced convection heat transfer on an array of 4×1 flush-mounted discrete heat sources in a vertical rectangular channel during the pump-on transient operation. Water is the coolant media and the flow covers the wide range of laminar flow regime with Reynolds number, based on heat source length, from 800 to 2625. The applied uniform heat flux ranges from 1 to 7W∕cm2. For flush-mounted heaters the heat transfer characteristics are studied and correlations are presented for four chips as well as for overall data in the transient regime. The experimental results indicate that the heat transfer coefficient is affected strongly by the number of chips and the Reynolds number. Finally the general impacts of heat source protrusions (B=1, 2 mm) on heat transfer behavior of four chips are investigated by comparing the results obtained from flush-mounted (B=0) heaters.

scholarly journals Interactions due to Moving Heat Sources in Generalized Thermoelastic Half-Space using L-S Model

2013 ◽  
Vol 18 (3) ◽  
pp. 815-831 ◽  
Author(s):  
N. Sarkar ◽  
A. Lahiri
Keyword(s):  
Half Space ◽  
Heat Sources ◽  
Dimensional Problem ◽  
Eigenvalue Approach ◽  
One Dimensional ◽  
Coupled Equations ◽  
The Laplace Transform ◽  
Moving Plane ◽  
Generalized Thermoelastic ◽  
S Model

Abstract A one-dimensional problem for a homogeneous, isotropic and thermoelastic half-space subjected to a moving plane of heat source on the boundary of the space, which is traction free, is considered in the context of Lord- Shulaman model (L-S model) of thermoelasticity. The Laplace transform and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the temperature, thermal stress, and displacement distributions are represented graphically and discussed

Mixed Convection Heat Transfer From Thermal Sources Mounted on Horizontal and Vertical Surfaces

1990 ◽  
Vol 112 (4) ◽  
pp. 975-987 ◽  
Author(s):  
S. S. Tewari ◽  
Y. Jaluria
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Source ◽  
Mixed Convection ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Finite Width ◽  
Heat Sources ◽  
Wide Range ◽  
Thermal Sources

An experimental study is carried out on the fundamental aspects of the conjugate, mixed convective heat transfer from two finite width heat sources, which are of negligible thickness, have a uniform heat flux input at the surface, and are located on a flat plate in the horizontal or the vertical orientation. The heat sources are wide in the transverse direction and, therefore, a two-dimensional flow circumstance is simulated. The mixed convection parameter is varied over a fairly wide range to include the buoyancy-dominated and the mixed convection regimes. The circumstances of pure natural convection are also investigated. The convective mechanisms have been studied in detail by measuring the surface temperatures and determining the heat transfer coefficients for the two heated strips, which represent isolated thermal sources. Experimental results indicate that a stronger upstream heat source causes an increase in the surface temperature of a relatively weaker heat source, located downstream, by reducing its convective heat transfer coefficient. The influence of the upstream source is found to be strongly dependent on the surface orientation, especially in the pure natural convection and the buoyancy dominated regimes. The two heat sources are found to be essentially independent of each other, in terms of thermal effects, at a separation distance of more than about three strip widths for both the orientations. The results obtained are relevant to many engineering applications, such as the cooling of electronic systems, positioning of heating elements in furnaces, and safety considerations in enclosure fires.

scholarly journals A Study on the Thermal Effect by Multi Heat Sources and Machining Characteristics of Laser and Induction Assisted Milling

Materials ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1032 ◽  
Author(s):  
Jae-Hyeon Ha ◽  
Choon-Man Lee
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Thermal Effect ◽  
Measured Temperature ◽  
Heat Sources ◽  
High Productivity ◽  
Measurement Experiment ◽  
Laser Induction ◽  
Machining Characteristics

Thermally assisted machining (TAM) is an effective method for difficult-to-cut materials, and works by locally preheating the workpiece using various heat sources, such as laser, induction, and plasma. Recently, many researchers have studied TAM because of its low manufacturing costs, high productivity, and quality of materials. Laser assisted machining (LAM) has been studied by many researchers, but studies on TAM using induction or plasma heat sources, which are much cheaper than lasers, have been carried out by only a few researchers. Lasers have an excellent preheating effect, but are expensive, and the temperature of the heated workpiece drops quickly. Here, multi heat sources were used to solve the shortage in supplied heat source with a single heat source. Induction was applied as an additional heat source. The purpose of this study is to analyze the thermal effect and temperature distribution of single heat source and multi heat sources, and compare the machining characteristics according to heat source types. In order to analyze the preheating effect according to the feed rate of the heat sources, a temperature measurement experiment using thermocouples was carried out, and the efficiency of the thermal effect using multi heat sources was verified. In addition, the effectiveness of the thermal analysis results was verified by comparison with the measured temperature distribution. The machining characteristics of Inconel 718 and Ti-6Al-4V with laser, induction, and laser-induction assisted milling (LIAMill) were analyzed, by cutting force and surface roughness.

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.

2D Axisymmetric Problem for a Sphere with Heat Sources in the Theory of Generalized Thermoviscoelasticity

2017 ◽  
Vol 09 (02) ◽  
pp. 1750028
Author(s):  
Hany H. Sherief ◽  
Allam A. Allam
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Axisymmetric Problem ◽  
Solid Sphere ◽  
Heat Sources ◽  
Inner Sphere ◽  
Axisymmetric Temperature

A solid sphere composed of a thermoviscoelastic material is subjected to an axisymmetric temperature distribution on its surface that is traction free. A distributed heat source acts inside an inner sphere. The problem is solved analytically and numerically. The solutions are represented graphically for different cases.

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