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This investigation aims to find entropy production and to determine the existence of a dual solution in magnetohydrodynamic (MHD) thermal radiative tri-hybrid nanofluid flow over an exponentially shrinking surface by considering suction effects at the surface. Furthermore, the effects of Smoluchowski temperature and Maxwell velocity slip are considered. The products on various flow fields are examined for three different types of fluid: mono nanofluid (Fe3O4/H2O), hybrid nanofluid (Fe3O4-Al2O3/H2O), and tri-hybrid nanofluid (Fe3O4-Al2O3-Cu/H2O). The similarity transformation translates the nonlinear partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). The numerical MATLAB function bvp4c is utilized to construct and solve governing higher-order nonlinear ODEs. A tabular and graphical analysis is conducted on the impact of emergent factors on velocity, temperature, skin friction coefficient, Nusselt number, and entropy generation. The acceptable parameter ranges for the computation are as follows: 0.01<ϕ1<0.1, 0.01<ϕ2<0.1, 0.01<ϕ3<0.1, −0.7<ξ<1.6, 2.0<S<3.0, 0.0<M<0.2, 0.5<Nr<1.5, 0.1<ω<0.5, and 0.1<ε<0.5. Due to the contraction of the surface, dual solutions are found, but dual solutions cannot be found beyond the critical values. The critical values ξλ are −1.44285, −1.44804, and 1.51550 for mono nanofluid, hybrid nanofluid, and tri-hybrid nanofluid, respectively. Including Al2O3 and Cu nanoparticles inside Fe3O4 nanoparticles containing nanofluid depicted an accelerating effect on skin friction and Nusselt number rates. The skin friction coefficient and heat transference rate in both the solution branches improved as the suction parameter S was increased. It has been demonstrated that the fluid’s temperature is enlarged by the thermal radiation parameter Nr and increasing nanoparticle volume fractions ϕ1,ϕ2,ϕ3. However, the temperature is reduced greatly by the suction parameter S and Smoluchowski temperature slip parameter ε. Since dual solutions are present, stability analysis is performed by finding the minimum eigenvalue. A positive minimum eigenvalue (β1) denotes the upper stable solution branch, whereas a minimal eigenvalue that is negative indicates the bottom branch is unstable. The entropy of the flow was found to increase with thermal radiation parameter Nr and magnetic field parameter M in a physically stable solution. Still, it decreased with a higher nanoparticle volume fraction (ϕ1,ϕ2,ϕ3). The current optimization technique offers a new and beneficial insight through numerous applications in various fields, i.e. polymer engineering, extrusion of polymer, plastic sheet compression, glass production, fiber, metallic furnace, medicine, and the field of biomedical technology.
Gopinath Mandal (Thu,) studied this question.