No abstract

No abstract

An analytical study is accomplished by using the Finite Hankel Transform Technique for the variation of the temperature and the velocity profile with several nondimensional parameters. In this problem, an electrically conducting fluid has been considered in the vertical concentric annulus, with a perpendicular radial magnetic field. Furthermore, a closed and exact type of expression for the velocity and the temperature are received in the form of Bessel functions of both kinds (first and second). The impact of emerging parameters in this model, such as time, Hartmann number, Prandtl number, and the annular gap between the cylinders, is discussed through graphs, whereas the numerical values of the skin friction, mass flux, and the Nusselt number are given in the tabular form. As a consequence of this, it is detected that the velocity and temperature distributions are increasing continuously with an enhanced time scale. Eventually, it gains its steady state very quickly. Moreover, the impact of the Prandtl number and the Hartmann number leads to a decrease in the velocity profiles.

No abstract

We investigate in this paper the dynamics of tornadoes by considering that the real inflow radial velocity depends on both the radial and vertical coordinates. The formulation is based on the model for the radial velocity that has been deduced from an experimentally verified model of azimuthal velocity. We present an analytical model for steady, incompressible, and viscous fluids and try for exact solutions. Although all the three components depend on radial and axial coordinates, viscosity affects merely the azimuthal velocity and the pressure. It is observed that the magnitude of the radial velocity increases to the maximum at the core but reverses the trend beyond and vanishes as it reaches the centerline. The magnitude reduces linearly with axial distance as per the supposition. At the core, the larger the Reynolds number, the lower is the velocity for moderate Reynolds numbers. Insignificant impact is observed for very large Reynolds number. However, inside and outside the core, the trends are reversed. Radial pressure distributions for different axial positions are similar to theoretical, numerical, and experimental observations. As we move outward from the axis, pressure increases. The difference between the pressures at the axis and that in outward regions increases with height. Pressure falls with rising Reynolds number uniformly for all radial distances. This is an indication that quantitative difference in pressure is large between viscous and inviscid flows.