We develop a model to study the natural convection of a nanofluid between a square enclosure and a circular, an elliptical, or a rectangular cylinder. Using super elliptic functions, the dimensionless governing equations of two-dimensional rectangular coordinates have been transformed into a system of equations valid for the above geometry. The resulting equations are then solved utilizing finite difference technique. We illustrate the flow and heat transfer characteristics of nanofluids with streamlines and isotherms as well as the Nusselt number at the inner and outer cylinders. It is found that the intensity of streamlines becomes stronger with the increase in the volume fraction of nanoparticles and the Rayleigh number. The Nusselt number at the inner and outer cylinders is almost linearly increased for higher values of the volume fraction of nanoparticles while an exponentially increasing tendency is observed with the increase in the Rayleigh number. The distinct findings are that the intensity of the streamlines increases with rectangular, circular, and elliptical inner shapes. Moreover, the Nusselt number at the inner and outer cylinders diminishes with circular, elliptical, and rectangular inner shapes. The acquired knowledge from the results could be used to augment or control the heat transfer of nanofluids and for the advancement of existing technology. Moreover, the present concept of introducing super elliptic functions might be useful to formulate a model for more complex geometry.
In this study, Stokes' second problem for Cu-Al2O3/water hybrid nanofluid is considered along with the effects of buoyancy force and a heat source. Using Laplace transforms, transient velocity, skin friction coefficient, and local Nusselt number are established in closed forms involving exponentials and error functions. The exact solutions have been compared with the numerical solutions as well as with available exact solutions, which show excellent agreement. It is found that the temperature, skin friction coefficient, and local Nusselt number are strongly affected and increased owing to the increase in the volume fractions of copper and alumina nanoparticles and heat source parameter. On the other hand, the mixed convection parameter noticeably enhances the flow velocity. When the heat source is absent, the skin friction coefficients are oscillating and the heat transfer approaches an asymptotic value. However, for a higher heat source parameter, when time increases, the amplitude of oscillation of the skin friction coefficients gradually increases and the magnitude of heat transfer exponentially increases. Both eventually go to infinity after a long period of time.
The natural convection boundary layer flow with conduction-radiation interaction of a viscous incompressible fluid along a vertical plate to surface temperature oscillations has been studied. Three distinct methods are used in the investigation, namely (a) the perturbation method for low frequency range and the asymptotic series expansion method for high frequency range, (b) the direct finite difference method for primitive variable formulations, and (c) the implicit finite difference method for stream-function formulation together with the Keller-box elimination technique for the entire frequency range. The effects of varying the Prandtl number Pr, the conduction-radiation parameter R d , and the surface temperature parameter θ w , are discussed in terms of amplitude and phase of the rate of heat transfer for fluid having the Prandtl number equal to 0.1. Also the effects of these parameters on the amplitude of oscillation of the transient skin-friction and transient heat transfer have been investigated.
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