Boundary Heat Flux Estimation for Natural Convection in a Square Enclosure Containing a Cylinder: An Inverse Approach

In this study, the unknown boundary heat fluxes in a square enclosure containing a cylinder were estimated by an inverse technique. A series of computations was conducted for the two-dimensional, steady-state, and buoyancy-driven heat transfer in a square section containing a cylinder with variable heat fluxes and at a Rayleigh number (Ra) of 10⁶ and Prandtl number (Pr) of 0.7. The generated datasets were used to construct a physics-based neural network, which acted as a proxy model for natural convection to reduce the computational time for inverse estimation. The trained network was embedded in a genetic algorithm and Bayesian framework to estimate the boundary conditions of the heat fluxes from synthetic experimental temperatures. The results indicated that the genetic algorithm accurately predicted the heat flux, but the estimation failed with increasing measurement error/noise. The solutions of the genetic algorithm were then used as informative priors for the Bayesian framework, which outperformed the genetic algorithm at estimating unknown boundary heat fluxes with measurement noise. The estimated heat fluxes were then used as input for the direct problem and investigated the thermal and flow characteristics in an enclosure containing a cylinder.