Simultaneous Estimation of Pr and Ra in a Natural Convective Flow Using Inverse Technique

The present research proposes an inverse natural convection algorithm for simultaneous estimation of correct values of Prandtl number (Pr) and Rayleigh number (Ra). The inverse problem is formulated as the minimization of appropriate functional and is solved iteratively using conjugate gradient algorithm. Since the inverse technique requires temperature data as the input parameter, this work uses schlieren experiments to measure the temperature in a water-filled, differentially heated, cubic cavity. While the proposed inverse technique may be applied for a variety of thermofluidic problems, the simulations are restricted to two-dimensional (2D), laminar-free convective flows in a 50 $×$ 50 $×$ 50 mm³ cavity. The present experiments restrict the wall temperature difference to 6.3 K, allowing the use of Boussinesq approximation in the inverse formulation. The proposed inverse algorithm is found to be highly accurate with an estimation error less than 10% when the measurement data contain about 5% noise.