Abstract
Nano-suspensions (NS) exhibit unusual thermophysical behaviors once interparticle aggregations and the shear flows are imposed, which occur ubiquitously in applications but remain poorly understood, because existing theories have not paid these attentions but focused mainly on stationary NS. Here we report the critical role of time-dependent fractal aggregation in the unsteady thermal convection of NS systematically. Interestingly, a time ratio λ = tp/tm (tp is the aggregate characteristic time, tm the mean convection time) is introduced to characterize the slow and fast aggregations, which affect distinctly the thermal convection process over time. The increase of fractal dimension reduces both momentum and thermal boundary layers, meanwhile extends the time duration for the full development of thermal convection. We find a nonlinear growth relation of the momentum layer, but a linear one of the thermal layer, with the increase of primary volume fraction of nanoparticles for different fractal dimensions. We present two global fractal scaling formulas to describe these two distinct relations properly, respectively. Our theories and methods in this study provide new evidence for understanding shear-flow and anomalous heat transfer of NS associated non-equilibrium aggregation processes by fractal laws, moreover, applications in modern micro-flow technology in nanodevices.
Highlights
Nano-suspensions (NS) exhibit unusual thermophysical behaviors once interparticle aggregations and the shear flows are imposed, which occur ubiquitously in applications but remain poorly understood, because existing theories have not paid these attentions but focused mainly on stationary NS
A number of experimental measurements and numerical simulations have been reported on the heat conduction enhancements of these nano-suspensions containing small volume fraction of nanoparticles (NP) (Particle loading
According to natural convection boundary layer (NCBL) theories[28] (Zheng and coauthors have carried out some studies29–31), there are large velocity gradient and temperature gradient in NCBL and they are both coupled
Summary
According to natural convection boundary layer (NCBL) theories[28] (Zheng and coauthors have carried out some studies29–31), there are large velocity gradient (shear flow) and temperature gradient (heat transfer) in NCBL and they are both coupled. The velocity and temperature boundary layers both develop over time near the plate along the x-axis. It is applicable that the rheology and heat conducting constitutive models of NS with maximum particle loading 0.1 are addressed as Newtonian models within the circumstance of natural convection boundary layer[29,30,31]. The governing equations of this system can be written as
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