The Buongiorno model is very considerably more sophisticated than the Tiwari and Das model. The former considers a large variety of effects to which a nanoparticle may be subject (do have a look at Buongiorno's paper), whereas the latter merely uses the viscosity and density of the nanofluid which is otherwise Newtonian in terms of its dynamics.
As Prof Andrew S Rees rightly said, the Buongiorno nanoliquid model incorporates Brownian motion and thermophoresis effects. No doubt it is sophisticated than Tiwari and Das model even though, the thermophysical properties are not incorporated in that model. Hence, we can combine models, and it is known as Modified Buongiorno nanoliquid model in the literature.
Article Numerical computation of natural convective heat transport w...
please find the attachment file which using mixed nanofluids model
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Numerical Analysis of the Unsteady Natural Convection MHD Couette Nanofluid Flow in the Presence of Thermal Radiation Using Single and Two-Phase Nanofluid Models for Cu–Water Nanofluids
Tiwari Das model is only for heat transfer analysis but combining both you can study heat and mass transfer analysis in a nanofluid flow with thermophysical properties as well as Brownian motion, thermophoresis and solid volume fraction of nanoparticle effects. Kohilavani Naganthran
The heat transfer features of nanofluids can be predicted by employing two main approaches, namely single-phase model (e.g., homogeneous nanofluid model) and the two-phase mixture model (e.g., non-homogeneous nanofluid model). First of all, the single phase model has been firstly proposed by Tiwari and Das for studying the heat transfer augmentation in nanofluids by expressing their thermo-physical properties as functions of the thermo-physical properties of the base fluids and the nanoparticles. Moreover, the nanoparticles are assumed to be in thermal equilibrium with the base fluid, distributed uniformly within the base fluid and move with the same velocity, in which the nanoparticle dynamics are neglected completely. Furthermore, the single-phase model adopts the momentum and energy balance equations of the base fluid as those of the nanofluid, only with the modification of thermo-physical properties caused by the nanoparticles. Beside the single-phase model, Buongiorno put forward another mathematical nanofluid model (i.e., Buongiorno’s twophase model), in which the nanofluid can be treated as a two-component non-homogeneous mixture, including the base fluid and the nanoparticles. In this model, the significant enhancement in the heat transfer rate is not just due to the improvement of the thermal conductivity, but also due to the thermal dispersion and intensified turbulence caused by the combined influence of Brownian diffusion and thermophoresis of nanoparticles
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