Inverse analysis of forced convection in micro-channels with slip flow via integral transforms and Bayesian inference

Conjugated heat transfer in circular microchannels with slip flow and axial diffusion effects

“…As test case, the flow of air (k f = 0.0271 W/m °C, c p, f = 1.0049 kJ/ kgK, c v, f = 0.7178 kJ/kgK, ν f = 1.568 × 10 − 5 m 2 /s and ρ f = 1.177 kg/m 3 ) inside an acrylic microchannel (k s = 0.2 W/m °C) is considered, resulting in K s = k s /k f = 7.38. In the examples presented, it has been adopted β v = 1.5, β t = 2.0 and Kn = 0.025, which are representative values for these parameters [25,26].…”

Hybrid Approach in Microscale Transport Phenomena: Application to Biodiesel Synthesis in Micro-reactors

“…In the identification of properties and source terms, the direct problem solution is employed first for the sensitivity analysis of the quantities to be estimated and to produce simulated data, so as to evaluate the inverse problem solution ahead of employing actual experimental data. Bayesian inference has been preferred for the inverse analysis in the present context [45][46][47][48][49][50][51][52], first of all due to its inherent robustness, but also due to advantages in being able to account for a priori information on the parameters. The drawback of this statistical approach, associated with the usually large number of evaluations of the direct problem required for an appropriate statistical inference through the Monte Carlo Markov Chain method, is alleviated by the use of the present hybrid solution pathways with reduced computational cost.…”

“…Inverse problem analysis is an essential tool in engineering design for the identification of parameters, such as physical properties, and functions, such as equation and boundary condition source terms. Besides, such methodologies have evolved towards experimental planning and optimum design procedures [43][44][45][46][47][48][49][50][51][52].…”

Detection of contact failures with the Markov chain Monte Carlo method by using integral transformed measurements

“…The posterior ( 9) is a probability density model of the inverse problem, defined on a high dimensional space. In this study, inference on the posterior model is carried out by sampling based on Markov chain Monte Carlo (MCMC) integration that is implemented through the Metropolis-Hastings' algorithm [35][36][37][38][39][40][41][42][43][44][45][46]. In the Metropolis-Hasting algorithm, a proposal distribution p (P * ,P (t−1) ), which is used to draw a new candidate P * given the parameters in the current state P (t−1) of the Markov chain, must be selected by the user.…”