Transient and steady state free convection from a horizontal cylinder

Estimating parameters in steady state, homogeneous systems is a well-developed process, usually involving the least squares technique or the Bayesian statistical approach. When the parameters vary with time or space, the process is more difficult. The function specification method was developed to estimate time varying surface fluxes for inverse heat conduction problems. Electrical and systems engineers tend to utilize the Kalman filter approach in such situations. The two approaches have much in common and the Kalman filter can often be applied to conduction/convection problems. It is particularly useful when multiple parameters vary with time. In addition, it lends itself conveniently to situations in which the measured data are noisy and/or correlated. This article describes the application of both methods to the problem of transient and steady state free convection from a horizontal cylinder. The problem involves noisy data and an exceptionally strong early time variation of the heat transfer coefficient. Because of the inherent smoothing effect of the Kalman filter, it is possible to estimate the heat flux with greater precision. The article discusses both approaches and compares the resulting estimates of the parameters.