Dimensionless diagrams for the temperature distribution in direct-chill continuous casting

Depicting Aluminium DC Casting by Means of Dimensionless Numbers

“…[23], which for the semi-continuous casting of aluminium has the form [24]: and T is the temperature [K]. The z coordinate relates to the casting velocity through the casting time, so it can be expressed as z = u × time [25].…”

“…The term on the right-hand side represents the latent heat removal due to the solidification itself [24]. Eq.…”

“…Eq. (3) can be solved numerically [17,22,24,[26][27][28][29]. Temperature fields can be computed from this equation as well as stress and deformation fields; however, further discussions on the latter are beyond the scope of this entry.…”

“…According to Hakonsen and Myhr [24], heat transfer in aluminium casting operation can be described by using the dimensionless Péclet and Biot numbers. Péclet number represents the ratio of convective to conductive heat transfer [30] and is defined as Similarly, Biot number is defined as the ratio of the internal thermal resistance to the surface film thermal resistance [30]; this is expressed as In view of the former, it has been proposed that Eq.…”

“…Péclet number represents the ratio of convective to conductive heat transfer [30] and is defined as Similarly, Biot number is defined as the ratio of the internal thermal resistance to the surface film thermal resistance [30]; this is expressed as In view of the former, it has been proposed that Eq. (3) can be rewritten as [24] …”