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Research Papers: Conduction

# Temperature Created by a Tilted Moving Heat Source: Heating Line and Cylinder

[+] Author and Article Information
Valerian Nemchinsky

Keiser University, 1500 Northwest 49 Street, Fort Lauderdale, FL 33309nemchinsky@bellsouth.net

J. Heat Transfer 133(2), 021301 (Nov 02, 2010) (7 pages) doi:10.1115/1.4002601 History: Received January 10, 2010; Revised July 28, 2010; Published November 02, 2010; Online November 02, 2010

## Abstract

Temperatures created by a moving tilted line and a moving tilted cylinder are considered. Analytical expressions for low Peclet $(Pe⪡1)$ and high Peclet $(Pe⪢1)$ numbers are obtained for the whole range of possible tilt angles. These expressions almost overlap: It is shown that these analytical expressions describe very well the results of numerical calculations at any Peclet numbers except for a very narrow range of Pe close to unity. A method of calculation of the cut shape (variation of the tilt angle inside the cut) is discussed.

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## Figures Figure 4

Ratio of F2D(Pe,0,0)/F2D(Pe,β,0) for different Peclet numbers; for Pe⪢1, this ratio should be proportional to cos β (formula 36); bold line is cos β Figure 3

Geometry used to calculate temperature in the case of 2D MHS (cylinder); observation point is by Δ ahead of the cylinder Figure 5

(a) Nondimensional temperature created by a vertical MHS in the case of no liquid layer separating MHS and solid metal (Δ=0); points are the numerical calculations of the integral (Eq. 19); lines are the approximations (Eqs. 24,34). (b) Nondimensional temperature created by a tilted MHS: tilt angle is 45 deg and thickness of the liquid layer separating MHS and solid metal is 20% of the cylinder radius (δ=0.2). Points are the numerical calculations of the integral (Eq. 19); lines are the approximations (Eqs. 24,34). Figure 6

Relative gain in heat per unit plate thickness by tilting the MHS (ratio of the heat per unit plate thickness to the one of the vertical MHS) Figure 7

Shape of a cut: distance of the front of the melting edge from the MHS center as a function of the cut depth; initial tilt of the cut β0=0 and Pe⪢1 Figure 1

Geometry used to calculate temperature in the case of 1D MHS (line), angle θ is the azimuth of the observation point Figure 2

(a) Nondimensional temperature created by 1D MHS: tilt angle β=22.5 deg, θ=0; points are the numerical calculation of the integral (Eq. 4), solid line is the approximation Pe⪢1 (Eq. 15); dashed line is the approximation Pe⪡1 (Eq. 12). (b) Nondimensional temperature created by 1D MHS: tilt angle β=45 deg, θ=0; points are the numerical calculation of the integral (Eq. 4); solid line is the approximation Pe⪢1 (Eq. 15); dashed line is the approximation Pe⪡1 (Eq. 12).

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