Uncertainty Quantification Through use of the Monte Carlo Method in a One-Dimensional Heat Conduction Experiment

Abstract

The correct expression of temperature measurement results is of the utmost importance for experimental research in thermal sciences. Temperature measurements are used in heat transfer models to estimate various parameters, either in direct or inverse problems. The reliability of these parameter values depends mainly on the uncertainty associated with the measured temperature. This paper deals with the application of Monte Carlo method for uncertainty quantification, in an experimental model of heat transfer that describes the behavior of a homogeneous, isotropic and linear solid. Temperature measurements were carried out using a type K thermocouple, considering a nominal measuring range from − 5 °C to 110 °C, at a given point in an AISI 304 stainless steel sample, specifically a massive cylindrical billet. The sample was placed in an experimental setup, and it was submitted to a one-dimensional steady-state thermal field, with boundary conditions of prescribed temperature and prescribed heat flux. The uncertainty associated with temperature was assessed using the Monte Carlo method, and the obtained results were compared with those calculated by the Guide to the Expression of Uncertainty in Measurement (GUM). Noteworthy in this study was that the temperature simulated values follow a Gaussian probability distribution function. The expanded uncertainty (k =2.00) associated with temperature (in Kelvin) was 0.42 % about the measured average temperature. The results presented herein can be useful for those cases when the mechanical component is not fully accessible physically. Therefore, using the temperature measured in a particular region and since the heat conduction problem is unidimensional in a steady state, it is possible to estimate the temperature in any section.