A Darcy-Forchheimer Fluid Model with Fuzzy Norms in Variable Exponent Sequence Spaces

The Darcy-Forchheimer model extends Darcy's law to account for nonlinear inertial effects in fluid dynamics. This paper integrates fuzzy logic and variable exponent sequence spaces into the model to address the inherent uncertainties and heterogeneities in porous media. Through Fredholm operator theory and fixed-point theorems, we establish the existence and uniqueness of solutions to the nonlinear system. Numerical investigations highlight the impact of varying porous media conditions on fluid behavior. As a main outcome, we observe that solutions exhibit a smooth behaviour for moderate levels of permeability and porosity in the media, while for increased fuzzy norms in both media properties, the fluid velocity profile exhibits fluctuations due to the influence of the fuzzy terms.