Inverse natural convection problem with radiation in rectangular enclosure

Inverse thermal problem is applied to natural convective flow with radiative heat transfer. The bottom wall temperature in the 2-D cavity domain is estimated by using gas temperature measurements in the flow field. The inverse problem is solved through a minimization of an objective function using the conjugate gradient method with adjoint problem. The effects of functional form of bottom wall temperature profile, the number and the position of measurement points, and the measurement errors are investigated and discussed. The conjugate gradient method is found to work well in estimating the bottom wall temperature, even when natural convection with radiation phenomena is involved.