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Two-dimensional transient natural convective flow in a vertical tube of plain and uneven sidewalls containing cobalt-kerosene nanofluids is analyzed using a nonhomogeneous dynamic model. The vertical right wall of the enclosure is maintained at a constant low temperature and the left wall is heated by a uniform thermal condition whereas the horizontal side-walls are insulated. The Brownian motion and thermophoretic phenomena of the nanoparticles are considered in the model. The governing nonlinear momentum, energy, and concentration equations are solved numerically using a Galerkin weighted residual finite element method. The thermal, flow and concentration fields are obtained to understand the flow dynamics of cobaltkerosene nanofluid in two types of enclosures. The local and average Nusselt numbers are analyzed for plain and uneven side walls of the tube for different parameters of the problem. The simulated results are compared with the experimental as well as with the numerical data available in the literature for some special cases. The outcomes show that the tube of having uneven vertical side-walls give higher heat transfer for lower values of the thermal Rayleigh number; whereas for the higher values of the thermal Rayleigh number, the tube of plain vertical side-walls exhibit significantly higher heat transfer rate.

Numerical simulation of convective heat transport within the nanofluid filled vertical tube of plain and uneven side walls