Duel Solutions in Hiemenz Flow of an Electro-Conductive Viscous Nanofluid Containing Elliptic Single-/Multi-Wall Carbon Nanotubes With Magnetic Induction Effects

Modern magnetic nanomaterials are increasingly embracing new technologies including smart coatings, intelligent lubricants, and functional working fluids in energy systems. Motivated by studying the manufacturing magnetofluid dynamics of electroconductive viscous nanofluids, in this work, we analyzed the magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid containing carbon nanotubes (CNTs) past a stretching sheet. Magnetic induction effects are included. Similarity solutions are derived where possible in addition to dual branch solutions. Both single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are considered taking water and kerosene oil as base fluids. The governing continuity, momentum, magnetic induction, and heat conservation partial differential equations are converted to coupled, nonlinear systems of ordinary differential equations via similarity transformations. The emerging control parameters are shown to be Prandtl number (Pr), nanoparticle volume fraction parameter (φ), inverse magnetic Prandtl number (λ), magnetic body force parameter (β) and stretching rate parameter (A), and the type of carbon nanotube. Numerical solutions to the ordinary differential boundary value problem are conducted with the efficient bvp4c solver in matlab. Validation with earlier studies is included. Computations of reduced skin friction and reduced wall heat transfer rate (Nusselt number) are also comprised in order to identify the critical parameter values for the existence of dual solutions (upper and lower branch) for velocity, temperature, and induced magnetic field functions. Dual solutions are shown to exist for some cases studied. The simulations indicate that when the stretching rate ratio parameter is less than 1, SWCNT nanofluids exhibit higher velocity than MWCNT nanofluids with increasing magnetic parameters for water- and kerosene-oil-based CNT nanofluids. Generally, SWCNT nanofluids achieve enhanced heat transfer performance compared to MWCNT nanofluids. Water-based CNT nanofluids also attain greater flow acceleration compared with kerosene-oil-based CNT nanofluids.