Numerical Investigation of Flow and Heat Transfer From a Rotating Sphere with Constant Angular Velocity Around Vertical Axis Floating in Stationary Fluid

Convective heat transfer for a rotating sphere around a vertical axis floating in stationary fluid is studied numerically using the model of volume of fluid (VOF). The effects of the immersion angle and rotating velocity on the streamlines, isotherm and volume fraction contours, mean and local Nusselt numbers, volumetric flow rate, and water film thickness are investigated for the angular rotational velocity, 1500 ≤ Ω ≤ 3500 and the immersion angle, 30° ≤ θi 60°. The results show that the sphere's rotation causes the liquid to be sucked from the lower pole of the sphere, which is thrown out after stopping in the equator. Due to the strong jet flow in the equatorial zone, heat is transferred by forced convection, but diffusion is dominant for heat transfer in other zones. At low rotational velocities, the liquid film is thrown out of the equator in the form of large droplets, but as the rotational velocity increases, its shape changes to a jet. Also, it is found that there is a direct relation between the Reynolds number and mean Nusselt number at different immersion angles so that an average of 27.5% increase for the mean Nusselt number is achieved by increasing the immersion angle from θi = 30° to θi = 60°. In addition, at a constant rotational velocity, the volumetric flow rate increases with increasing immersion angle.

Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres

We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions.

Mixed convection stagnation point flow of the blood based hybrid nanofluid around a rotating sphere

In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time-dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, $${\text{TiO}}_{2} \,\,{\text{and}}\,\,{\text{Ag}}$$ TiO 2 and Ag as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Optimal Homotopy Analysis Method is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. Detailed research is also performed to investigate the influences of relevant constraints on the rates, momentum and heat transport for both $${\text{TiO}}_{2} + {\text{Ag}} + Blood$$ TiO 2 + Ag + B l o o d and $${\text{TiO}}_{2} + Blood$$ TiO 2 + B l o o d . One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in the case of the hybrid nanofluid enhances the thermal conductivity from 5.8 to 11.947% and for the same value of the nanoparticle volume fraction in the case of nanofluid enhance the thermal conductivity from 2.576 to 5.197%.