Impacts of entropy generation in second-grade fuzzy hybrid nanofluids on exponentially permeable stretching/shrinking surface

Abstract

Abstract The present investigation aims to use entropy analysis to analyze the unsteady Magnetohydrodynamic (MHD) flow in a second-grade fuzzy hybrid $$\left( {{\text{Al}}_{{2}} {\text{O}}_{{3}} - {\text{Cu/SA}}} \right)$$ Al 2 O 3 - Cu/SA nanofluid over an exponentially shrinking/stretching surface. The model for hybridization of the mixture of alumina $$\left( {{\text{Al}}_{{2}} {\text{O}}_{{3}} } \right)$$ Al 2 O 3 and copper (Cu) nanoparticles in the sodium alginate (SA) base fluid under heat source/sink, nonlinear thermal radiation, and viscous dissipation. The fundamental partial differential equations (PDEs) are simplified using an appropriate similarity conversion to generate the ordinary differential equations (ODEs). The analytical computation occurs in the MATHEMATICA program implementing the homotopy analysis method (HAM). In terms of code validity, our results are preferable to previous findings. The features of several parameters against the velocity, surface friction coefficient, entropy, temperature, and Nusselt number are described through graphs. According to our findings, the rise in the Brinkman and Reynolds numbers enhanced the total entropy of the system. Furthermore, the nanoparticle volume fraction and viscus dissipation magnifies the fluid temperature while retards the flow profile throughout the domain. Fluid velocity declined due to the Lorentz force using magnetic impact applications. The imprecision of nanofluid and hybrid nanofluid volume fractions was modelled as a triangular fuzzy number (TFN) [0%, 1%, 2%] for comparison. The double parametric approach was applied to deal with the fuzziness of the associated fuzzy parameters. The nonlinear ODEs convert into fuzzy differential equations (FDEs) and use HAM for the fuzzy solution. From our observation, the hybrid nanofluid displays the maximum heat transfer compared to nanofluids. This important contribution will support industrial growth, particularly in the processing and manufacturing sectors. The percentage increase in skin friction factor is 18.3 and 15.0 when $$\alpha$$ α and $$\beta$$ β take input in the ranges of 0 ≤ $$\alpha$$ α ≤ 0.8 and 0 ≤ $$\beta$$ β ≤ 1, respectively.