Markov Chain Monte Carlo (MCMC) approach for the determination of thermal diffusivity using transient fin heat transfer experiments

A simultaneous estimation of fin parameter “m” and thermal diffusivity “α” of a fin material is accomplished by conducting in-house unsteady experiments on a fin of constant area losing heat to still air by natural convection. The material of the fin is mild steel and the surface is highly polished. The fin protrudes from an aluminium base and beneath the aluminium base, a heater is provided to heat the fin. Upon reaching steady state, the power is switched off, transient cooling takes place and the temperature distribution for various time intervals is recorded using a data logger. The temperature varies along the height of the fin and also with respect to time. Bayesian inference is then applied to statistically determine the unknown parameters “m” and thermal diffusivity “α” simultaneously. Markov chain Monte Carlo method (MCMC) is used for sampling the fin parameter “m” and thermal diffusivity “α” of the material. The parameters are retrieved with and without MCMC using a wealth of temperatures generated from experiments with minimum number of time instances. The usefulness of priors in improving the estimates of parameters is investigated. The uncertainity in the form of standard deviation of the parameters estimated, an inherent output of the Bayesian frame work is also reported.

► Temperature-time histories of a cooling fin experimentally determined.
►  Measured temperatures combined with a mathematical model using MCMC.
► Estimation of fin parameter and thermal diffusivity done.
► Effect of prior information systematically investigated.
► Proposed method novel, inexpensive and general enough.