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In the present work, a theoretical model based on the full Navier-Stokes and energy equations for transient mixed convection in a vertical tube is extended to nanofluids with nanoparticle volume fraction up to 5 percent to ensure a Newtonian fluid behaviour. The paper aims to discuss these issues.

The nanofluids considered, alumina/water and CuO/water, flow inside a vertical tube of circular cross-section, which is subjected to convective heat exchange at the outer surface. The transient regime is caused by a sudden change of nanofluid temperature at the tube inlet. The range of the Richardson number (1.6=Ri=2.5) investigated in this study corresponds to classic cases of mixed convection flow.

Results have shown a significant reduction in the size of the recirculation zone near the wall when the particle volume fraction increases. This may be attributed to the viscosity increase with the volume fraction. Moreover, the flow structure clearly changes when the convective heat transfer coefficient is modified. A decrease of the wall temperature along the tube was found when increasing the convective heat transfer coefficient imposed at the tube external surface.

The problem formulation in 2D axisymmetric geometry includes the continuity, the Navier-Stokes and energy equations and is based on the stream function and vorticity; the numerical solution of equations is carried out using a finite difference method.

From an economic point of view, this research paper is innovative in the sense that it considers nanofluids as a new and more efficient way to transfer heat. This paper could find applications for heat exchange purposes of compact systems with high thermal loads.

Across the world, a still growing number of research teams are investigating nanofluids and their properties. Investigations concern several aspects such as the preparation of the nanofluids, as well as the applications of these nanofluids for convective heat transfer purposes. The dynamical study will consist in the instantaneous and spatial characterization of the dynamic flow field for different nanoparticle volume fractions.

The aim of this study is to present numerical analyses for combined effects of the inlet temperature (ΔT⁺) and the wall‐to‐fluid thermal capacitance ratio (a*) on the laminar mixed convection unsteady flows in a vertical pipe.

The full Navier‐Stokes and energy, coupled, unsteady state, two‐dimensional governing equations for ascending laminar mixed convection in a vertical pipe are solved numerically using a finite‐difference scheme.

The results show that the thermohydraulic flow behaviour is highly dependent on both parameters (ΔT⁺, a*). Moreover, the unsteady characteristics of the flow can involve oscillatory and reversed flow phenomena yielding the unstable flows. For the heating case, the reversed flow appears below the wave instability and the unsteady vortex is always significant in the vicinity of the wall, whatever ΔT⁺ and a*<100. For the cooling case, the reversed flow appears in the central region of the pipe; it develops on top of the wave instability.

This study should be very useful to improve heat transfer equipment.

The paper shows clearly the combined effects of both parameters (ΔT⁺, a*) on the laminar mixed convection flow.