A numerical approach to study heat and mass transfer in porous medium influenced by uncertain parameters

Abstract

Heat and mass transfer is an essential phenomenon in various science and thermal engineering problems. In this direction, many research works are carried out with the absence of uncertainties by considering only exact parameters in the ideal conditions. But, the presence of uncertainties due to involved parameters, material properties, and boundary conditions cannot be ignored. As such, the present work discusses the modelling of heat and mass transfer in a porous medium with epistemic uncertainties. The said model is solved through the Fuzzy Finite Element Method (FFEM) and the convergence analysis of the same is performed with Triangular Fuzzy Number (TFN). Further, an example problem is taken to demonstrate the proposed model of heat and mass transfer in a porous medium. TFN convergence behaviour of stream function, temperature and concentration are performed in case 1, case 2 and case 3 by taking the non-dimensional parameters viz. modified Raleigh number (Ra), Radiation parameter (Rd) and Lewis number (Le). Then, the uncertain analysis and sensitiveness of these uncertain parameters are discussed in three different cases. It is found that if only one parameter is considered as fuzzy that is only Ra is fuzzy, only Rd is fuzzy, and only Le is fuzzy then stream function is more sensitive. If two parameters are fuzzy then concentration is more sensitive. Finally, for all three fuzzy parameters both the stream function and concentration are sensitive.