Viscosity and effusion rate identification from free surface data

Abstract

Based on new explicit expressions for sensitivity coefficients, this study proposes a new method to solve two inverse problems in time-dependent three-dimensional gravity-driven thin film flow down an inclined plane governed by free-surface lubrication approximation. The flow is developed by time-dependent injection through a circular hole in the plane. The first inverse problem, a parameter estimation problem, consists in simultaneously estimating the temperature-dependent viscosity and a constant injection. The second inverse problem, a function estimation problem, involves the determination of the time-dependent injection. It is shown here that using the derived sensitivity coefficients, a parameter estimation approach can still be used for the second inverse problem, efficiently and accurately, and without the need to solve the adjoint and sensitivity problems as well as additional direct problem solutions.

Keywords

• Gravity-driven flow
• Lubrication approximation
• Temperature-dependent viscosity
• Inverse problem
• Parameter estimation
• Sensitivity analysis