Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet

Abstract

In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina $$\left( {{\text{Al}}_{{2}} {\text{O}}_{{3}} } \right)$$ Al 2 O 3 and Copper $$\left( {{\text{Cu}}} \right)$$ Cu nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids.

RETRACTED ARTICLE: Analysis of the Thomson and Troian velocity slip for the flow of ternary nanofluid past a stretching sheet

“…Wang et al 16 performed simulation to observe the flow pattern created by the hybrid nanofluid flowing inside a microchannel. Nadeem et al 17 analysed the thermal properties of second grade nanofluid using the fuzzy hybrid nanofluid model by considering the flow to be over a sheet. Chu et al 18 compared impact of various shapes of the suspended nanoparticles on the thermal properties of hybrid nanofluid flowing inside a channel made up of two infinitely long parallel walls.…”

Numerical investigation on the thermal transportation of MHD Cu/Al 2 O 3-H 2 O Casson-hybrid-nanofluid flow across an exponentially stretching cylinder incorporating heat source

“…[34] and Kierzenka et al [35] explained the Bvp4c technique with examples in MATLAB. Recently, Nadeem et al [36] numerically analysed the hybrid nanofluid flow and heat transfer through a porous stretching or shrinking sheet using Bvp4c techniques. Hina et al [37], Shah et al [38], Lv et al [39] have also successfully used the Bvp4c technique to establish their numerical investigations.…”

Magnetic Impact on the Unsteady Separated Stagnation-Point Flow of Hybrid Nanofluid with Viscous Dissipation and Joule Heating

“…In relation to the aim of this study, some related references on nanofluids and hybrid nanofluids in various applications can be found in Rabiei et al [4], Renuka et al [5], Ur Rehman et al [6], and Connolly et al [7]. We also mention some recently published papers by Kamis et al [8], Nadeem et al [9], Elsaid et al [10], Hassan et al [11], and Sheikholeslami [12], who presented a numerical simulation of boundary layer flow in a hybrid nanofluid considering various physical phenomena.…”