A new hybrid approach to study heat and mass transfer in porous medium influenced by imprecisely defined parameters

Abstract

The present work discusses a hybrid approach of Successive Overrelaxation (SOR) with Finite Element Method (FEM) in presence of non-probabilistic uncertainties. In order to address the heat and mass transfer problem in porous media with fuzzy environment, the proposed SOR FFEM has been applied. Here, the imprecise parameters have taken in terms of TFNs and the convergence analysis of the proposed technique is performed. The parameters viz. Rayleigh number (Ra), Radiation parameter (Rd) and Lewis's number (Le) are considered as uncertain and discussed in case study. Different combinations of uncertain parameters are considered for investigation and the sensitivity analysis of the same is observed. It is noted that the stream function (ψ‾) is sensitive when Ra is fuzzy. Similarly, the stream function (ψ‾) and temperature (T‾) both are exhibiting sensitivity when Rd is fuzzy. Additionally, the stream function (ψ‾) is sensitive when Le is fuzzy. As comparing all the cases, it is observed that, stream function (ψ‾) is more sensitive in all three circumstances that is a small change in value can be affect more.

Keywords

• Successive Overrelaxation (SOR) method
• Fuzzy Finite Element Method (FFEM)
• Triangular Fuzzy Number (TFN)
• Uncertain parameters
• Porous media