Abstract
Unsteady flow of thin Cu-water nanoliquid film over a horizontal rotating disk is studied numerically using finite difference technique under the assumption of planar interface. It is also assumed that the disk is cooling axisymmetrically from below. The effects of the nanolayer thickness and nanoparticle radius are considered for investigation. It is found that the film thinning rate decreases with increase of the nanoparticle volume fraction. It is also found that thickness of liquid decreases with increase of the thermocapillary parameter. The results show that the rate of film thinning is more for the thermal conductivity model of Yu and Choi [47] compared to the model of Maxwell [46]. It is observed that the film thinning rate increases with increase of nanolayer thickness but it decreases with the nanoparticle radius. A curve R=R_c(z,t) in R-z plane is delineated along which temperature gradient T_z is zero and positive or negative according to R<R_c or R >R_c respectively. Furthermore, it is shown that the region for T_z>0 enlarges with increase of the nanoparticle volume fraction and the nanolayer thickness.
Highlights
The process of development of thin liquid film over a horizontal rotating disk by the action of the centrifugal force is known as spin coating in the literature
It is evident from the figure that the thickness of the nanoliquid film decreases with increase of the tharmocapillary parameter a
We have investigated the flow and heat transfer within a thin nanoliquid film containing the Cu nanoparticles on an rotating disk and the disk is assumed to be cooled axisymmetrically from below
Summary
The process of development of thin liquid film over a horizontal rotating disk by the action of the centrifugal force is known as spin coating in the literature. Dandapat and Singh [25] studied the unsteady two-layer liquid film flow on a horizontal rotating disk using asymptotic method for small values of Reynolds number. They showed that the viscous force dominates over centrifugal force, and the upper layer film thins faster than the lower layer at large time. Viscous Cu-water nanoliquid film of uniform thickness h0 on the surface of a horizontal rotating disk whose radius is quite large compared with the thickness of the film At this stage of the nanoliquids development, the enormous increase of thermal conductivity is not known precisely, but researchers proposed two different models of nanoliquids to resolve this issue. P1FjnÀþ11 þ Q1Fjnþ þ R1Fjnþþ11 1⁄4 ðS1Þnj ; P1GnjÀþ11 þ Q1Gjnþ þ R1Gjnþþ11 1⁄4 ðS2Þnj ; P2MjnÀþ11 þ Q2Mjnþ þ R2Mjnþþ11 1⁄4 ðS3Þnj ; P2NjnÀþ11 þ Q2Njnþ þ R2Njnþþ11 1⁄4 ðS4Þnj ; ð45Þ ð46Þ ð47Þ ð48Þ
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