Solutions of an inverse laminar natural convection problem by subdomain and Galerkin methods

摘要

Reconstruction of the velocity field, for a laminar free convection flow, from the knowledge of the temperature distribution, within the flow, is an inverse heat transfer problem. In this investigation, the velocity profile for a laminar convective flow along an isothermal vertical plate is reconstructed using known temperature distributions. The temperature distributions used in this inverse problem were generated numerically from the direct similarity solutions. To solve this inverse problem, continuity, momentum and energy equations are considered. To obtain the velocity solutions (profiles), the Galerkin and subdomain weighted residual methods are employed. The velocity solutions are represented by the sum of n-term weak functions satisfying the boundary conditions. The solutions considered in this study belong to a family of sine and polynomial functions. Comparison of the inverse solutions with the direct solutions confirms that velocity profiles can be reconstructed from the knowledge of temperature distribution with good accuracy.