An upper bound on the steady flow velocity of solvent-free nanofluids

The rheological properties and limited flow velocities of solvent-free nanofluids are crucial for their technologically significant applications. In particular, the flow in a solvent-free nanofluid system is steady only when the flow velocity is lower than a critical value. In this paper, we establish a rigid-flexible dynamic model to investigate the existence of the upper bound on the steady flow velocities for three solvent-free nanofluid systems. Then, the effects of the structural parameters on the upper bound on the steady flow velocities are examined with the proposed structure-preserving method. It is found that each of these solvent-free nanofluid systems has an upper bound on the steady flow velocity, which exhibits distinct dependence on their structural parameters, such as the graft density of branch chains and the size of the cores. In addition, among the three types of solvent-free nanofluids, the magnetic solvent-free nanofluid poses the largest upper bound on the steady flow velocity, demonstrating that it is a better choice when a large flow velocity is required in real applications.