A non-probabilistic approach to study the effect of imprecisely defined parameters on heat transfer in a conical porous cylinder

Purpose In this study a numerical investigation of the heat transfer within a vertical conical porous cylinder has considered epistemic type uncertainties and accordingly, the problem is modelled. Because in this problem the uncertainties may arise due to defined boundary conditions, insufficient information about the system, experimental errors etc. Design/methodology/approach The study aims to handle uncertain involved systems. The uncertain involved coupled momentum and energy equations are solved through the proposed fuzzy finite element method (FFEM). The converted coupled algebraic equations are resolved through the Gauss–Seidel iterative approach. Also, the uncertain parametric effect is investigated for finding the stability of the system. Findings A case study is presented to demonstrate the utility and efficiency of the proposed method. The effects of Ra and Rd on the stream function and temperature distribution are analysed for different Alpha-cut values. Furthermore, the sensitivity of the imprecise parameters involved is examined. The results indicate that both Ra and Rd are the most influential parameters in determining the temperature and stream function of the system when only two parameters are considered uncertain. Practical implications The proposed method can be included in different practical application problems to analyse the parametric effects like geothermal analysis, nuclear reactor system and different porous structured problems. Originality/value The novelty of the system is the implementation of the proposed method like FFEM and Gauss–Seidel method in the conical porous cylinder. Also, the sensitivity of the uncertain parametric effect is analysed to study the stability of the system. This kind of structure is found in real-life applications like gas thermal analysis, geothermal analysis etc.