Non-Probabilistic Uncertainty Analysis of Analytical and Numerical Solution of Heat Conduction

Fuzzy set theory is applied to quantify the non-probabilistic uncertainty alternatively termed as epistemic uncertainty. An algorithm “Fuzzy Centered Radius” has been developed for quantification of epistemic uncertainty. Uncertainty analysis is also carried out using fuzzy vertex method. Analytical solution of one dimension heat conduction and numerical solution of heat removal from circular fin are applied to quantify the uncertainty of the temperature distribution using the proposed algorithm. Heat transfer coefficient and thermal conductivity are considered as fuzzy parameter due to their imprecise measured values. Results of uncertainty of temperature distribution based on FCR algorithm in case of analytical solution of heat conduction is compared with that obtained on the basis of fuzzy vertex method. Finite element method with the specified fuzzy parameters is adopted to obtain the membership values of the temperature at the specified node and the heat removal rate from the fin. Uncertainty in both the cases is estimated in terms of fuzziness measure.