Inverse Problem of Parameter Estimation in Natural Convection of an Iron Oxide—Distilled Water Nanofluid

Nanofluids have been used to facilitate the transport of nanoparticles to tumor regions for different purposes, such as drug delivery, promotion of antioxidant effects, and selective absorption of energy from external sources for thermal treatments. The characterization of nanofluids by solving an inverse parameter estimation problem was the main objective of this work. A nanofluid of Fe₂O₃ nanoparticles dissolved in distilled water was heated by a diode laser, causing natural convection currents during the experiment. The parameter estimation problem was solved within the Bayesian framework of statistics by applying the Metropolis–Hastings algorithm of the Markov Chain Monte Carlo method, thus demanding large computational times associated with stochastic simulations of a natural convection problem. A multivariate linear regression model was then trained with the high-fidelity natural convection model, to speed up calculations during the solution of the inverse problem. It is shown that the multivariate linear regression low-fidelity model can be used as an accurate representation of the temperatures at the heated surface of the nanofluid, thus resulting in estimated parameters with small uncertainties.