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Heat and Mass Transfer

, Volume 45, Issue 10, pp 1247–1251 | Cite as

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

  • S. Amir Hossein A. E. TabatabaeiEmail author
  • Tinggang Zhao
  • O. Bamidele Awojoyogbe
  • Folorunsho O. Moses
Original

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.

Keywords

Welding Laser Welding Cooling Velocity Isothermal Expansion Welding Keyhole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

D

Thermal diffusivity (m2 s−1)

h

Keyhole height (m)

k

Thermal conductivity (Wm−1 K−1)

N0

Prefixed integer

P

Fluid pressure at mean temperature (Pa)

Qv

Power per unit volume (Wm−3)

T

Absolute temperature (K)

T0

Maximum absolute temperature (K)

T

Room absolute temperature (K)

Greek letters

αq

Boubaker polynomials minimal positive roots (dimensionless)

\( \varpi \)

Constant (dimensionless)

ρ

Density (Kg m−3)

γ

Heat capacity ratio (dimensionless)

ξq

Real coefficients (dimensionless)

Notes

Acknowledgment

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

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • S. Amir Hossein A. E. Tabatabaei
    • 1
    Email author
  • Tinggang Zhao
    • 2
  • O. Bamidele Awojoyogbe
    • 3
  • Folorunsho O. Moses
    • 4
  1. 1.Sadra Institute of Higher EducationTehranIran
  2. 2.College of MathematicsLanzhou City UniversityLanzhouPeople’s Republic of China
  3. 3.Department of PhysicsFederal University of TechnologyMinnaNigeria
  4. 4.Department of PhysicsFederal University of TechnologyAkureNigeria

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