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Journal of Heat Transfer | Volume 133 | Issue 6 | Technical Brief
Technical Briefs

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

[+] Author and Article Information
Mohsen Akbari1

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T 0A3, Canadamohsen_akbari@sfu.ca

David Sinton

Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 2Y2, Canada

Majid Bahrami

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T 0A3, Canada

1

Corresponding author.

J. Heat Transfer 133(6), 064502 (Mar 02, 2011) (10 pages) doi:10.1115/1.4003155 History: Received February 26, 2010; Revised November 24, 2010; Published March 02, 2011; Online March 02, 2011
Article
References
Figures
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Citing Articles

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.
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References

1
Sun, Y., Kwok, Y. C., and Nguyen, N. T., 2006, “Low-Pressure, High-Temperature Thermal Bonding of Polymeric Microfluidic Devices and Their Applications for Electrophoretic Separation,” J. Micromech. Microeng., 16 , pp. 1681–1688.  [CrossRef]
2
Kricka, L. J., Fortina, P., Panaro, N. J., Wilding, P., Alonso-Amigo, G., and Becker, H., 2002, “Fabrication of Plastic Microchips by Hot Embossing,” Lab Chip, 2 (1), pp. 1–4.  [CrossRef]
3
Halling, J., 1975, "Principles of Tribology", Macmillan, London.
4
Williams, J. A., 2005, "Engineering Tribology", Cambridge University Press, Cambridge, UK.
5
Winer, W. O., and Cheng, H. S., 1980, “Film Thickness, Contact Stress and Surface Temperatures,” "Wear Control Handbook", ASME, New York, pp. 81–141.
6
Tian, X., and Kennedy, F. E., 1994, “Maximum and Average Flash Temperatures in Sliding Contacts,” ASME J. Tribol., 116 , pp. 167–174.  [CrossRef]
7
Hou, Z. B., and Komanduri, R., 2000, “General Solutions for Stationary/Moving Plane Heat Source Problems in Manufacturing and Tribology,” Int. J. Heat Mass Transfer, 43 (10), pp. 1679–1698.  [CrossRef]
8
Laraqi, N., Baīri, A., and Segui, L., 2004, “Temperature and Thermal Resistance in Frictional Devices,” Appl. Therm. Eng., 24 (17–18), pp. 2567–2581.  [CrossRef]
9
Carslaw, H. S., and Jaeger, J. C., 1959, "Conduction of Heat in Solids", Oxford University Press, New York.
10
Muzychka, Y. S., and Yovanovich, M. M., 2001, “Thermal Resistance Models for Non-Circular Moving Heat Sources on a Half Space,” ASME J. Heat Transfer, 123 (4), pp. 624–632.  [CrossRef]
11
Rosenthal, D., 1946, “The Theory of Moving Sources of Heat and Its Application to Metal Treatments,” Trans. ASME, 68 (11), pp. 849–866.
12
Weichert, R., and Schonert, K., 1978, “Temperature Distribution Produced by a Moving Heat Source,” Q. J. Mech. Appl. Math., 31 (3), pp. 363–379.  [CrossRef]
13
Terauchi, Y., Nadano, H., and Kohno, M., 1985, “On the Temperature Rise Caused by Moving Heat Sources. II: Calculation of Temperature Considering Heat Radiation From Surface,” Bull. JSME, 28 (245), pp. 2789–2795.
14
Yovanovich, M. M., 1997, “Transient spreading resistance of arbitrary isoflux contact areas-development of a universal time function,” presented at the 32nd AIAA Thermophysics Conference , Atlanta, GA.
15
Yovanovich, M. M., Negus, K. J., and Thompson, J. C., 1984, “Transient Temperature Rise of Arbitrary Contacts With Uniform Flux by Surface Element Methods,” presented at the 22nd AIAA Aerospace Sciences Meeting , Reno, NV, Jan. 9–12.
16
www.maplesoft.com
17
Simms, D. L., 1960, “Ignition of Cellulosic Materials by Radiation,” Combust. Flame, 4 , pp. 293–300.  [CrossRef]
18
Koohyar, A. N., 1967, "Ignition of Wood by Flame Radiation", University of Oklahoma, Norman, OK.
19
Kashiwagi, T., 1979, “Experimental Observation of Radiative Ignition Mechanisms,” Combust. Flame, 34 , pp. 231–244.  [CrossRef]
20
Kashiwagi, T., 1979, “Effects of Attenuation of Radiation on Surface Temperature for Radiative Ignition,” Combust. Sci. Technol., 20 (5), pp. 225–234.  [CrossRef]
21
Wesson, H. R., 1970, "The Piloted Ignition of Wood by Radiant Heat", University of Oklahoma, Norman, OK.
22
Taylor, J. R., 1997, "An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements", University Science Books, Herndon, VA.
23
Jaeger, J. C., 1942, “Moving Sources of Heat and the Temperature at Sliding Contacts,” J. Proc. R. Soc. N. S. W., 76 , pp. 203–224.
24
Vick, B., and Furey, M. J., 2003, “An Investigation Into the Influence of Frictionally Generated Surface Temperatures on Thermionic Emission,” Wear, 254 (11), pp. 1155–1161.  [CrossRef]
25
Xu, X., and Malkin, S., 2001, “Comparison of Methods to Measure Grinding Temperatures,” ASME J. Manuf. Sci. Eng., 123 , pp. 191–195.  [CrossRef]
26
Takazawa, K., 1966, “Effects of Grinding Variables on Surface Structure of Hardened Steel,” Bull. Jap. Soc. Grind Eng., 6 , pp. 14–19.
27
Paek, U. -C., and Gagliano, F., 1972, “Thermal Analysis of Laser Drilling Processes,” IEEE J. Quantum Electron., 8 (2), pp. 112–119.  [CrossRef]
28
Eagar, T. W., and Tsai, N. S., 1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J. (Miami, FL, U.S.), 62 (12), pp. 346–355.
29
Zhang, H. J., 1990, “Non-Quasi-Steady Analysis of Heat Conduction From a Moving Heat Source,” ASME Trans. J. Heat Transfer, 112 , pp. 777–779.  [CrossRef]
30
Manca, O., Morrone, B., and Naso, V., 1995, “Quasi-Steady-State Three-Dimensional Temperature Distribution Induced by a Moving Circular Gaussian Heat Source in a Finite Depth Solid,” Int. J. Heat Mass Transfer, 38 (7), pp. 1305–1315.  [CrossRef]
31
Yevtushenko, A. A., Ivanyk, E. G., and Ukhanska, O. M., 1997, “Transient Temperature of Local Moving Areas of Sliding Contact,” Tribol. Int., 30 (3), pp. 209–214.  [CrossRef]
32
Zeng, Z., Brown, J. M. B., and Vardy, A. E., 1997, “On Moving Heat Sources,” Heat Mass Transfer, 33 (1–2), pp. 41–49.  [CrossRef]
33
Zubair, S. M., and Chaudhry, M. A., 1998, “A Unified Approach to Closed-Form Solutions of Moving Heat-Source Problems,” Heat Mass Transfer, 33 (5–6), pp. 415–424.  [CrossRef]
34
Zubair, S. M., and Chaudhry, M. A., 1996, “Temperature Solutions Due to Time-Dependent Moving-Line-Heat Sources,” Heat Mass Transfer, 31 (3), pp. 185–189.  [CrossRef]
35
Kato, T., and Fujii, H., 1997, “Temperature Measurement of Workpiece in Surface Grinding by PVD Film Method,” ASME J. Manuf. Sci. Eng., 119 , pp. 689–694.  [CrossRef]
36
Kaebernick, H., Bicleanu, D., and Brandt, M., 1999, “Theoretical and Experimental Investigation of Pulsed Laser Cutting,” CIRP Ann., 48 (1), pp. 163–166.  [CrossRef]
37
Neder, Z., Varadi, K., Man, L., and Friedrich, K., 1999, “Numerical and Finite Element Contact Temperature Analysis of Steel-Bronze Real Surfaces in Dry Sliding Contact,” Tribol. Trans., 42 (3), pp. 453–462.  [CrossRef]
38
Baīri, A., 2003, “Analytical Model for Thermal Resistance Due to Multiple Moving Circular Contacts on a Coated Body,” C. R. Mec., 331 (8), pp. 557–562.  [CrossRef]
39
Li, J. F., Li, L., and Stott, F. H., 2004, “Comparison of Volumetric and Surface Heating Sources in the Modeling of Laser Melting of Ceramic Materials,” Int. J. Heat Mass Transfer, 47 (6–7), pp. 1159–1174.  [CrossRef]
40
Kuo, W. L., and Lin, J. F., 2006, “General Temperature Rise Solution for a Moving Plane Heat Source Problem in Surface Grinding,” Int. J. Adv. Manuf. Technol., 31 (3–4), pp. 268–277.  [CrossRef]
41
Bianco, N., Manca, O., Nardini, S., and Tamburrino, S., 2006, “Transient Heat Conduction in Solids Irradiated by a Moving Heat Source,” presented at the Proceedings of COMSOL Users Conference , Milan.
42
Wen, J., and Khonsari, M. M., 2007, “Analytical Formulation for the Temperature Profile by Duhamel’s Theorem in Bodies Subjected to an Oscillatory Heat Source,” ASME J. Heat Transfer, 129 , pp. 236–240.  [CrossRef]
43
Levin, P., 2008, “A General Solution of 3-D Quasi-Steady-State Problem of a Moving Heat Source on a Semi-Infinite Solid,” Mech. Res. Commun., 35 (3), pp. 151–157.  [CrossRef]
44
Laraqi, N., Alilat, N., de Maria, J. M., and Baīri, A., 2009, “Temperature and Division of Heat in a Pin-on-Disc Frictional Device—Exact Analytical Solution,” Wear, 266 (7–8), pp. 765–770.  [CrossRef]
45
Xu, H., Chen, W. W., Zhou, K., Huang, Y., and Wang, Q. J., 2010, “Temperature Field Computation for a Rotating Cylindrical Workpiece Under Laser Quenching,” Int. J. Adv. Manuf. Technol., 47 (5–8), pp. 679–686.  [CrossRef]

Figures

Grahic Jump Location
+Schematic of a symmetrical moving plane heat source with arbitrary shape
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Schematic of a symmetrical moving plane heat source with arbitrary shape
Figure 1

Schematic of a symmetrical moving plane heat source with arbitrary shape

Grahic Jump Location
+Hyperellipse as a general symmetric geometry covers an array of source geometries: (a) star shape (n<1), (b) rhombic (n=1), (c) elliptical (n=2), (d) rectangular with round corners (n=4), and (e) rectangular (n→∞)
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Hyperellipse as a general symmetric geometry covers an array of source geometries: (a) star shape (n<1), (b) rhombic (n=1), (c) elliptical (n=2), (d) rectangular with round corners (n=4), and (e) rectangular (n→∞)
Figure 2

Hyperellipse as a general symmetric geometry covers an array of source geometries: (a) star shape (n<1), (b) rhombic (n=1), (c) elliptical (n=2), (d) rectangular with round corners (n=4), and (e) rectangular (n→∞)

Grahic Jump Location
+Schematic diagram of the laser beam, the engraved groove, and cross-sectional image of the wooden substrate (red oak) following laser exposure at the typical relative beam speed of U∗=U/Umax=0.6 and relative power of P∗=P/Pmax.=0.4. Image is taken by an inverted microscope (Unitron, Commack, NY) with a 10× magnification.
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Schematic diagram of the laser beam, the engraved groove, and cross-sectional image of the wooden substrate (red oak) following laser exposure at the typical relative beam speed of U∗=U/Umax=0.6 and relative power of P∗=P/Pmax.=0.4. Image is taken by an inverted microscope (Unitron, Commack, NY) with a 10× magnification.
Figure 3

Schematic diagram of the laser beam, the engraved groove, and cross-sectional image of the wooden substrate (red oak) following laser exposure at the typical relative beam speed of U∗=U/Umax=0.6 and relative power of P∗=P/Pmax.=0.4. Image is taken by an inverted microscope (Unitron, Commack, NY) with a 10× magnification.

Grahic Jump Location
+Effect of heat source shape on the quasi-steady maximum temperature for two typical aspect ratios, 0.1 and 0.5, and Peclet number of Pe=10
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Effect of heat source shape on the quasi-steady maximum temperature for two typical aspect ratios, 0.1 and 0.5, and Peclet number of Pe=10
Figure 4

Effect of heat source shape on the quasi-steady maximum temperature for two typical aspect ratios, 0.1 and 0.5, and Peclet number of Pe=10

Grahic Jump Location
+Effect of the aspect ratio on the maximum temperature of a plane moving heat source at various source speeds (Peclet number)
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Effect of the aspect ratio on the maximum temperature of a plane moving heat source at various source speeds (Peclet number)
Figure 5

Effect of the aspect ratio on the maximum temperature of a plane moving heat source at various source speeds (Peclet number)

Grahic Jump Location
+Maximum temperature as a function of Peclet number for aspect ratio of εm=1, a typical value. Note that two asymptotes for stationary, Pe→0, and fast moving heat source, Pe→∞, can be recognized in the present plot.
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Maximum temperature as a function of Peclet number for aspect ratio of εm=1, a typical value. Note that two asymptotes for stationary, Pe→0, and fast moving heat source, Pe→∞, can be recognized in the present plot.
Figure 6

Maximum temperature as a function of Peclet number for aspect ratio of εm=1, a typical value. Note that two asymptotes for stationary, Pe→0, and fast moving heat source, Pe→∞, can be recognized in the present plot.

Grahic Jump Location
+Variation in θmax∗/θmax,0∗ as a function of dimensionless depth for elliptical (n→2) and rectangular (n→∞) heat sources with Pe=10 and various aspect ratios
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Variation in θmax∗/θmax,0∗ as a function of dimensionless depth for elliptical (n→2) and rectangular (n→∞) heat sources with Pe=10 and various aspect ratios
Figure 7

Variation in θmax∗/θmax,0∗ as a function of dimensionless depth for elliptical (n→2) and rectangular (n→∞) heat sources with Pe=10 and various aspect ratios

Grahic Jump Location
+Maximum dimensionless temperature in a half-space. Rectangular heat source with Pe=2.86 and aspect ratio of εm=4.39; experimental data from Ref. 25; see Table 4 for the experiment parameters.
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Maximum dimensionless temperature in a half-space. Rectangular heat source with Pe=2.86 and aspect ratio of εm=4.39; experimental data from Ref. 25; see Table 4 for the experiment parameters.
Figure 8

Maximum dimensionless temperature in a half-space. Rectangular heat source with Pe=2.86 and aspect ratio of εm=4.39; experimental data from Ref. 25; see Table 4 for the experiment parameters.

Grahic Jump Location
+Effect of laser beam speed on the depth of engraved channels using single pass ablation. Square (◻) and delta (△) symbols are the present experimental measurements for percentage powers of 20% and 40%, respectively. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.
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Effect of laser beam speed on the depth of engraved channels using single pass ablation. Square (◻) and delta (△) symbols are the present experimental measurements for percentage powers of 20% and 40%, respectively. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.
Figure 9

Effect of laser beam speed on the depth of engraved channels using single pass ablation. Square (◻) and delta (△) symbols are the present experimental measurements for percentage powers of 20% and 40%, respectively. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.

Grahic Jump Location
+Effect of laser power on the depth of engraved channels using single pass ablation at maximum beam speed. Square (◻) symbols are the present experimental measurements maximum beam speed. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.
View Large  |  Save Figure  |  Download Slide (.ppt)
Effect of laser power on the depth of engraved channels using single pass ablation at maximum beam speed. Square (◻) symbols are the present experimental measurements maximum beam speed. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.
Figure 10

Effect of laser power on the depth of engraved channels using single pass ablation at maximum beam speed. Square (◻) symbols are the present experimental measurements maximum beam speed. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.

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