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Analytical solution for quenching of hot rolled aluminium plates without passing through C-curve

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Abstract

At the end of the hot rolling process, quenching is deployed for obtaining the desired microstructure and mechanical properties. During the quenching of aluminium plates, it is essential to optimize the process parameters such as the plate speed and cooling intensity for surpassing the C-curve. In this study, 1-D steady-state analytical model has been developed with the constant heat transfer boundary condition. The Eulerian computational domain contains the precooling and water cooling regions. Temperature drop starts in the precooling region itself due to back diffusion of heat, which originates from the water cooling region. Based on the analytical solution, the effect of plate speed and heat transfer coefficient on the cooling time has been investigated with the three non-dimensional parameters such as Peclect, Biot, and Fourier numbers. Typically, for the 2xxx (Al–Cu) alloys, every material point in the plate has to reach 350 °C within 0.2 s, which surpasses the nose of the C-curve where the phase transformation (CuAl2) severity can be reduced. This sets the limit for the maximum Fourier number and while keeping Peclect number as the independent variable, the minimum required water cooling in terms of Biot number is identified. The presented analytical solution provide the guidelines for selecting the appropriate combinations of plate speed and heat transfer coefficient for the quenching of continuously moving hot rolled plates. The results indicate that the nose of the C-curve can be surpassed easily by increasing the plate speed instead of reducing which contradicts the common notion.

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Abbreviations

a :

Function defined in Eq. (8)

Bi :

Biot number

C :

Specific heat capacity (kJ kg−1 K−1)

Fo :

Fourier number

f 1 :

Fixed non-dimensional temperature (99% of initial temperature)

f 2 :

Required non-dimensional temperature (C-Curve nose temperature)

h :

Heat transfer coefficient (HTC) (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

Pe :

Peclect number

s :

Thickness of the plate (mm)

T :

Wall temperature (°C)

T i :

Initial temperature of the plate (°C)

T ∞ :

Ambient temperature (°C)

t :

Time (s)

u :

Speed of the plate (m min−1)

X :

Non-dimensional length coordinate

α :

Thermal diffusivity (m2 s−1)

θ :

Non-dimensional temperature

θ 0 :

Non-dimensional temperature at the interface of water cooling

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India

    Saravanakumar Palanisamy & Ashok Kumar Nallathambi

  2. Institute of Fluid Dynamics and Thermodynamics, Otto von Guericke University Magdeburg, Magdeburg, Germany

    Eckehard Specht

Authors
  1. Saravanakumar Palanisamy
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  2. Ashok Kumar Nallathambi
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  3. Eckehard Specht
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Correspondence to Ashok Kumar Nallathambi.

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Palanisamy, S., Nallathambi, A.K. & Specht, E. Analytical solution for quenching of hot rolled aluminium plates without passing through C-curve. J Therm Anal Calorim 141, 2665–2671 (2020). https://doi.org/10.1007/s10973-020-09874-7

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