Liancun Zheng | Searcharxiv

arXiv2023

Rheological synergistic thermal conductivity of CMC-based Fe3O4 and Al2O3 nanofluids in shear flow fields

In this paper, considering the variation of the viscous dissipative heat in the transfer direction, a new theoretical formula for thermal conductivity measurement was proposed based on the energy equation of the rotational Couette flow field. This theoretical formula shows that thermal conductivity and rheology have a synergistic effect. Based on this theoretical formula, the rheological synergistic thermal conductivity of CMC-based Fe3O4 nanofluids and Al2O3 nanofluids was experimentally investigated. The experimental results show that the thermal conductivity rises with the increase of shear rate and volume fraction, moreover, volume fraction and shear rate have mutually reinforcing effects on thermal conductivity enhancement. Non-Newtonian effects of rheology and heat transfer reduce with shear rate and increase with volume fraction, with consistent synergistic effects. According to the experimental data, the expressions of the thermal conductivity and dynamic viscosity of these two nanofluids as functions of shear rate and volume fraction were presented.

physics.flu-dyn↗

arXiv2019

Novel numerical analysis of multi-term time fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid

In recent years, non-Newtonian fluids have received much attention due to their numerous applications, such as plastic manufacture and extrusion of polymer fluids. They are more complex than Newtonian fluids because the relationship between shear stress and shear rate is nonlinear. One particular subclass of non-Newtonian fluids is the generalized Oldroyd-B fluid, which is modelled using terms involving multi-term time fractional diffusion and reaction. In this paper, we consider the application of the finite difference method for this class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete $H^1$ norm and prove that their accuracy is of $O(τ+h^2)$ and $O(τ^{\min\{3-γ_s,2-α_q,2-β\}}+h^2)$, respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.

math.NA↗