Research Papers: Conduction

Scaling Analysis of a Moving Point Heat Source in Steady-State on a Semi-Infinite Solid

[+] Author and Article Information
Patricio F. Mendez

Chemical and Materials Engineering,
University of Alberta,
Donadeo ICE 12-332 9211 116 St,
Edmonton, AB T6G 2V4
e-mail: pmendez@ualberta.ca

Yi Lu

Chemical and Materials Engineering,
University of Alberta,
Edmonton, AB T6G 2R3, Canada
e-mail: ylu13@ualberta.ca

Ying Wang

Chemical and Materials Engineering,
University of Alberta,
Edmonton, AB T6G 2R3, Canada
e-mail: wang18@ualberta.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 1, 2017; final manuscript received February 1, 2018; published online April 11, 2018. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(8), 081301 (Apr 11, 2018) (9 pages) Paper No: HT-17-1725; doi: 10.1115/1.4039353 History: Received December 01, 2017; Revised February 01, 2018

This paper presents a systematic scaling analysis of the point heat source in steady-state on a semi-infinite solid. It is shown that all characteristic values related to an isotherm can be reduced to a dimensionless expression dependent only on the Rykalin number (Ry). The maximum width of an isotherm and its location are determined for the first time in explicit form for the whole range of Ry, with an error below 2% from the exact solution. The methodology employed involves normalization, dimensional analysis, asymptotic analysis, and blending techniques. The expressions developed can be calculated using a handheld calculator or a basic spreadsheet to estimate, for example, the width of a weld or the size of zone affected by the heat source in a number of processes. These expressions are also useful to verify numerical models.

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Grahic Jump Location
Fig. 1

Point heat source moving with constant velocity on a semi-infinite solid

Grahic Jump Location
Fig. 2

Characteristic values ymax and xmax for a point heat source moving with constant velocity on a semi-infinite solid

Grahic Jump Location
Fig. 3

Dimensionless isotherm width ymax* as a function of Ry

Grahic Jump Location
Fig. 4

Blending error for isotherm width ymax as a function of Ry for exponents n at or near the optimal value

Grahic Jump Location
Fig. 5

Maximum blending error for isotherm width ymax as a function of blending parameter n

Grahic Jump Location
Fig. 6

Correction factors for maximum isotherm width ymax

Grahic Jump Location
Fig. 7

Dimensionless location xmax of maximum isotherm width as a function of Ry

Grahic Jump Location
Fig. 8

Error of blending for location xmax of maximum isotherm width as a function of Ry for blending parameter n at or near the optimal value

Grahic Jump Location
Fig. 9

Maximum blending error for location xmax of maximum isotherm width as a function of blending parameter n

Grahic Jump Location
Fig. 10

Correction factors for location xmax of maximum isotherm width

Grahic Jump Location
Fig. 11

Weld bead corresponding to Ry = 20.84. Scale is in mm.




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