Generalized fractional model of heat transfer in uncertain hybrid nanofluid with entropy optimization in fuzzy-Caputo sense

Abstract

In this paper, we present a new fuzzy-fractional (FF) transformation to recover FF differential model of hybrid nanofluid. The current study focuses on FF modeling of nanofluid with engine oil as base fluid, while ferrous oxide Fe2O3 and alumina Al2O3 are considered nanoparticles. In accordance to the real industrial phenomena, the flow is simulated between two squeezing plates with thermal radiation and magnetic effects. A generalized fuzzy-fraction flow problem is modeled by introducing new similarity transforms. Obtained model is validated both theoretically and numerically. At integer order Υ=1, the FF model reduces to the integer order fluid model existing in literature, proving theoretical validity. Fuzzy-valued functions are discriminated through triangular fuzzy numbers using r-cut approach. In order to solve, obtained highly non-linear FF nanofluid system, we apply He–Laplace–Carson (HLC) algorithm. Differential and convolution properties of Laplace–Carson Transform (LCT) are utilized for solution purpose. Error and convergence analysis is performed numerically to verify obtained results. Furthermore, graphical illustrations for upper and lower bound analysis on FF profiles is also presented. Analysis reveals that heat transfer in engine oil enhances with an increase in radiation at upper and lower bound in fuzzy-fractional environment. Moreover, entropy decreases with an increase in nanoparticle concentration of Fe2O3 and Al2O3 in engine oil.

Keywords

• Fractional-fuzzy (FF) modeling
• Hybrid nanofluid
• He–Laplace–Carson (HLC) algorithm