Scripta METALLURGICA Vol. 14, pp. 861-864, 1980 Pergamon Press Ltd. Printed in the U.S.A. All rights reserved. THEORETICAL ANALYSIS OF RIBBON THICKNESS FORMATION DURING MELTSPINNING L. Katgerman III Aluminum Company of America, Alcoa Center, PA 15069, U.S.A. on leave of absence from Laboratory of Metallurgy, Delft University of Technology 2628 AL Delft, The Netherlands. (Received May 2, 1980) (Revised June 16, 1980) Introduction In recent studies [1-3] the effect of meltspinning process variables on ribbon thickness formation has been determined. It has been recognized that the hydrodynamic and thermal conditions in the liquid puddle play a dominant role in the formation of the ribbon dimensions. The liquid puddle consists of a zone (boundary-layer) in which the thermal and momentum effects of the chill surface (substrate) are strongly felt. Outside the boundary-layer the effects of the substrate are not yet developed. To calculate the thickness of the ribbon the thermal and momentum boundary-layer must be determined. In all analyses so far the momentum and thermal boundary-layers are calculated independently [1-2] or steady state conditions were assumed [2]. In the present calculation the interaction of the solidifying boundary with the velocity profile has been taken into account for non-steady state conditions. For the case of Newtonian and ideal cooling conditions analytical solutions of the velocity profile can be obtained. Mathematical Analysis In order to treat the problem quantitatively the following assumptions and simplifications have been made. The puddle is considered to be a semi-infinite body of liquid metal with constant density and viscosity bounded by a flat chill surface (Fig. i). Initially the liquid metal and the chill surface are at rest. At time t=O the chill surface is set in motion in the positive x-direction with a velocity Vo; heat is extracted from the liquid metal by the substrate and the metal starts to solidify. It can be assumed that the solid metal is at surface velocity. This is an expression in which the velocity at the solid-liquid interface is equal to Vo. The interface velocity or solidification rate R is determined by the cooling conditions. Three regions of cooling can be distinguished in terms of the Nusselt- number Nu=h.dt/k , where h is the heat-transfer coefficient, d t the thickness and k the thermal conductivity of the solid metal. The cooling is Newtonian for Nu 30 and intermediate for 0.015<Nu<30 [4]. For Newtonian and ideal cooling analytical expressions are available for plane front solidification: (i) R=h(Tm-To)/(p.H) (Newtonian) (2) R=¥~aT~ (Ideal), where y is implicitely given by y.exp(y2)erf(y)=Tm-To)Cp/H~ [5], and p is the density of the solid, a is the thermal diffusivity of the solid, Cp is the specific heat of the solid, H is the latent heat of fusion per unit mass, T m is the melting temperature, and T o is the substrate temperature. Approximate analytical solutions can be derived for intermediate cooling conditions. 801 0036-9748/80/080861-04502.00/0 Copyright (c) 1980 Pergamon Press Ltd.