modeling and numerical simulations of fuzzy-fractional oldroyd 6-constant nanofluid

This article contains analysis of thin film flow of fuzzy-fractional oldroyd-6 constant nanofluid in lift and drain cases. the fluid has ability to model both viscous and elastic behaviors accurately in different complex flow regimes and geometries. due to these features, this fluid is very important in food cosmetics industries. typically, the variables in these models are assumed to have crisp values regardless of uncertainties or memory effects in the phenomena. to incorporate uncertainty in the current modeling, triangular fuzzy numbers (tfns) are used in the boundary conditions and volume fraction of nanoparticle along with a consideration of caputo derivative. we examine effects of obtained fuzzy numbers for more accurate and realistic analysis of flow regime. to further improve the model accuracy, fuzzy based numerical methods are used to solve the obtained system, which helps in precise quantification of uncertainty associated with each parameter. furthermore, effect of different parameters on the velocity profiles is analyzed numerically and graphically. the validation and convergence of the obtained solutions are checked by capturing residual errors in each case. analysis reveals that in draining case, increase in material parameter ς1 leads to a less pronounced and more diffuse fuzzy velocity profile. on the other hand, increase in material parameter ς2 and gravitational parameter gr amplifies the fuzzy velocity field, indicating a stronger and faster flow; however, opposite behavior is observed in lifting case. the end result of this modeling is more accurate and realistic portrayal of nanofluidic flow, which reflects the complexities of phenomena more closely.