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Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme

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Abstract

The time dependent heating and cooling velocities are investigated in this paper. The temperature profile is found by using a keyhole approximation for the melted zone and solving the heat transfer equation. A polynomial expansion has been deployed to determine the cooling velocity during welding cut-off stage. The maximum cooling velocity has been estimated to be V max ≈ 83°C s−1.

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Abbreviations

D :

Thermal diffusivity (m2 s−1)

h :

Keyhole height (m)

k :

Thermal conductivity (Wm−1 K−1)

N 0 :

Prefixed integer

P :

Fluid pressure at mean temperature (Pa)

Q v :

Power per unit volume (Wm−3)

T :

Absolute temperature (K)

T 0 :

Maximum absolute temperature (K)

T ∞ :

Room absolute temperature (K)

α q :

Boubaker polynomials minimal positive roots (dimensionless)

\( \varpi \) :

Constant (dimensionless)

ρ :

Density (Kg m−3)

γ :

Heat capacity ratio (dimensionless)

ξ q :

Real coefficients (dimensionless)

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Acknowledgment

The authors would like to acknowledge help and assistance from Associate Professor Karem Boubaker from University of Tunisia.

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Authors and Affiliations

  1. Sadra Institute of Higher Education, Tehran, Iran

    S. Amir Hossein A. E. Tabatabaei

  2. College of Mathematics, Lanzhou City University, Lanzhou, Gansu, People’s Republic of China

    Tinggang Zhao

  3. Department of Physics, Federal University of Technology, Minna, Niger State, Nigeria

    O. Bamidele Awojoyogbe

  4. Department of Physics, Federal University of Technology, Akure, Ondo State, Nigeria

    Folorunsho O. Moses

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  1. S. Amir Hossein A. E. Tabatabaei
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  2. Tinggang Zhao
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  3. O. Bamidele Awojoyogbe
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  4. Folorunsho O. Moses
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Correspondence to S. Amir Hossein A. E. Tabatabaei.

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Tabatabaei, S.A.H.A.E., Zhao, T., Awojoyogbe, O.B. et al. Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme. Heat Mass Transfer 45, 1247–1251 (2009). https://doi.org/10.1007/s00231-009-0493-x

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  • DOI: https://doi.org/10.1007/s00231-009-0493-x

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