Analytical solution for quenching of hot rolled aluminium plates without passing through C-curve
- PDF / 1,454,802 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 58 Downloads / 213 Views
Analytical solution for quenching of hot rolled aluminium plates without passing through C‑curve Saravanakumar Palanisamy1 · Ashok Kumar Nallathambi1 · Eckehard Specht2 Received: 14 November 2019 / Accepted: 22 May 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
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. Keywords Quenching · Hot rolling · Precooling · C-curve · Process modelling · Analytical solution List of symbols a Function defined in Eq. (8) Bi Biot number C Specific heat capacity (kJ kg−1 K−1) Fo Fourier number f1 Fixed non-dimensional temperature (99% of initial temperature) f2 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) * Ashok Kumar Nallathambi [email protected] Saravanakumar Palanisamy [email protected] Eckehard Specht [email protected] 1
Department of Mechanical Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India
Institute of Fluid Dynamics and Thermodynamics, Otto von Guericke University Magdeburg, Magdeburg, Germany
2
Pe Peclect number s Thickness of the plate (mm) T Wall temperature (°C) Ti 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 θ0 Non-dimensional temperature at the interface of water cooling
Introduction Pr
Data Loading...
