Dual solution of thin film flow of fuzzified MHD pseudo-plastic fluid: numerical investigation in uncertain environment

Abstract

The pseudoplastic fluids have wide range of applications in industrial areas including cyclone separation, bearings, paper fibre separation, heat exchangers and also in food industry. In this regard, the current manuscript investigates the impact of transverse magnetic field on thin pseudo-plastic film flow on a vertical wall in a fuzzy (uncertain) environment. The uncertainty in a model is characterized through triangular fuzzy numbers (TFNs) along with $ \mathbbm {r} $ r-cut approach, which is computationally effective in capturing the uncertainties in physical phenomena. This results in the modelling of highly nonlinear fuzzified problem. For solution and analysis purposes, Runge-Kutta Fehlberg (RKF) is utilized. Also, RKF solutions are validated by comparing them to homotopy perturbation solutions in the current manuscript. The impact of $ \mathbbm {r} $ r-cut, and fluid parameters including non-Newtonian parameter beta, magnetic field M and Stoke's number $ \mathcal {S}_{t} $ St on the upper and lower velocity profiles are captured and analysed numerically and graphically. Analysis reveals that velocity profile decreases with an increase in applied magnetic field at upper and lower bounds. Also, increase in $ \mathcal {S}_{t} $ St and beta increases the velocity profile at lower bound, while inverse behaviour is recorded in the case of upper bound. The results also indicate that as $ \mathbbm {r} $ r goes from 0 to 1, the crisp solution always lies between upper and lower profiles, and becomes coherent at 1. Moreover, all fuzzy level set values of $ \mathbbm {r} \in [0,1] $ r is an element of[0,1] satisfy the fuzzy solution in the form of TFN.