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

Mohsen Akbari

,
Mohsen Akbari

Mechatronic Systems Engineering, School of Engineering Science,

mohsen_akbari@sfu.ca
Simon Fraser University

, Surrey, BC, V3T 0A3, Canada
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David Sinton

,
David Sinton

Department of Mechanical Engineering,

University of Victoria

, Victoria, BC, V8W 2Y2, Canada
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Majid Bahrami

Majid Bahrami

Mechatronic Systems Engineering, School of Engineering Science,

Simon Fraser University

, Surrey, BC, V3T 0A3, Canada
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Mohsen Akbari

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

Simon Fraser University

, Surrey, BC, V3T 0A3, Canada*J. Heat Transfer*. Jun 2011, 133(6): 064502 (10 pages)

**Published Online:**March 2, 2011

Article history

Received:

February 26, 2010

Revised:

November 24, 2010

Online:

March 2, 2011

Published:

March 2, 2011

Citation

Akbari, M., Sinton, D., and Bahrami, M. (March 2, 2011). "Geometrical Effects on the Temperature Distribution in a Half-Space Due to a Moving Heat Source." ASME. *J. Heat Transfer*. June 2011; 133(6): 064502. https://doi.org/10.1115/1.4003155

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