A Bayesian inference approach: estimation of heat flux from fin for perturbed temperature data

Abstract

This paper reports the estimation of the unknown boundary heat flux from a fin using the Bayesian inference method. The setup consists of a rectangular mild steel fin of dimensions 250915096 mm 3 and an aluminium base plate of dimensions 250915098 mm 3. The fin is subjected to constant heat flux at the base and the fin setup is modelled using ANSYS14.5. The problem considered is a conjugate heat transfer from the fin, and the Navier-Stokes equation is solved to obtain the flow parameters. Grid independence study is carried out to fix the number of grids for the study considered. To reduce the computational cost, computational fluid dynamics (CFD) is replaced with artificial neural network (ANN) as the forward model. The Markov Chain Monte Carlo (MCMC) powered by Metropolis-Hastings sampling algorithm along with the Bayesian framework is used to explore the estimation space. The sensitivity analysis of the estimated temperature with respect to the unknown parameter is discussed to know the dependency of the temperature with the parameter. This paper signifies the effect of a prior model on the execution of the inverse algorithm at different noise levels. The unknown heat flux is estimated for the surrogated temperature and the estimates are reported as mean, Maximum a Posteriori (MAP) and standard deviation. The effect of a-priori information on the estimated parameter is also addressed. The standard deviation in the estimation process is referred to as the uncertainty associated with the estimated parameters.

Numerical Study of Performance of Porous Fin Heat Sink of Functionally Graded Material for Improved Thermal Management of Consumer Electronics

“…an operating condition where heat transfer coefficient at the base of the fin is high. However, several existing works investigate high and low heat flux to evaluate fin performance [33][34][35][36].…”

Performance Analysis of Metaheuristic Optimization Algorithms in Estimating the Interfacial Heat Transfer Coefficient on Directional Solidification

“…Markov Chain Monte Carlo (MCMC) method will be used in order to determine the statistical consistency of the results provided by the optimization algorithms under study. This method is widely used for estimations in materials and thermal science, such as thermal diffusivity of metals [20], heat flux [29], heat transfer coefficient [52] and metallic fatigue [4].…”

Simultaneous estimation of unknown parameters using a-priori knowledge for the estimation of interfacial heat transfer coefficient during solidification of Sn–5wt%Pb alloy—an ANN-driven Bayesian approach

“…Therefore, a combination of neural network with evolutionary algorithm has been found to drastically reduce the computational cost. ANN can serve as a fast forward model ensuring a reduction in computational time for the inverse approach [27,28]. Chanda et al [29] used combined ANN-GA to estimate the thermal conductivities of composite materials and close agreements between simulated and experimental temperatures were observed.…”