Theoretical expectation of strip thickness in planar flow casting process

Abstract The objective of this study is to obtain a simple analytical solution that will predict the strip thickness with given planar flow casting (PFC) processing variables. Mass balance and the Bernoulli equation are used to formulate the final analytical solution. The focus is on the evaluation of the friction loss (dissipation of mechanical energy over the volume of the entire flow field) in the Bernoulli equation. Friction loss in the PFC process can be attributed to (1) a sudden contraction of the melt path (crucible to slit), (2) flow through a slit and, finally (3) an abrupt change in the size and direction of the melt path at the gap between the nozzle and the roll. Among these causes, friction loss resulting from an abrupt change in the size and direction of the melt path at the gap is the most significant factor under PFC conditions. Our experimental results show that the effects of the gap on the friction loss factor can be expressed as e f,gap = 0.172 ( h / b ) −2.5 , where h and b represent the gap size between the nozzle and the roll, and the slit breadth respectively. The accuracy of our formulation is evaluated by comparing the experimental data with theoretical expectation.