Effects of imprecisely defined parameters on heat and mass transfer in a vertical annular porous cylinder

Abstract

The present research provides a numerical study of heat and mass transfer in a vertical annular porous cylinder with uncertainties. In this study, a 5% error in Raleigh number (Ra), Radiation parameter (Rd), and Buoyancy ratio (N) are considered. The coupled differential equations are transformed into algebraic equations using the fuzzy finite element method that is simplified with the fuzzy Gauss-Seidel iterative approach. A parameter study is performed with different cases and the sensitivity of the involved uncertainties is discussed. The sensitivity of a parameter suggests the stability of the system over the change in parametric values. If a parameter is more sensitive, then the system is unstable with a change in parametric values. Similarly, if a parameter is less sensitive, then the system is stable with a change in parametric values. When we take a single parameter as uncertain, it is found that Ra is more sensitive. Similarly, if two parameters are taken as uncertain, then it is observed that the combination of Ra and N becomes more sensitive. The overall study provides an approach to deduce the sensitivity of the system parameters. This procedure can also be used in solving many other science and engineering problems.