Effect of the magnetic field and the temperature of the heated hollow mag-netizable cylinder on the heat and mass transfer at the cooling cylinder in the magnetic fluid

V. V. Gogosov¹ - M. Yu. Klimenko² - A. Ya. Simonovskii²

¹ Institute of Mechanics of the M.V. Lomonosov Moscow State University, 117192, Moscow, Russia
² Academy of Stavroplol, 355014 Stavroplol, Russia

Abstract
Experiments on the cooling of the hollow magnetizable cylinder in the magnetic fluid are described. Effect of the external magnetic field magnitude and direction and the initial temperature of the heated cylinder on the cooling rate of various points of the outer and inner surfaces of the cylinder and boiling modes of the magnetic fluid surrounding the cylinder both inside and outside are being investigated. The terms "poles of the cylinder" and "side surface of the cylinder" are introduced. The term "poles of the cylinder" and denotes the points situated at the ruling of the outer cylinder surface and characterized by the angle q between the position radius-vector and the external applied magnetic field vector far from the cylinder equals zero or 180°. The term "side elements of the cylinder" denotes the straight lines on the outer surface marked by the angle q = ± 90°; the term "side surfaces of the cylinder" denotes the outer surface patches situated in the vicinity of the "side elements of the cylinder". It is found that at the initial time the cooling of the inner surface of the hollow cylinder, heated up to 800 °C, without the magnetic field is of grater intensity than the cooling of the outer surface. This is caused by the rapid boiling of the magnetic fluid, penetrating into the inner cavity of the cylinder at its dipping into the fluid and formation of the strong vapour-liquid flux emerging from the upper hole of the hollow cylinder. The new amount of nonheated magnetic fluid penetrates in the cylinder cavity in place of the outward vapour-liquid flux through the lower cylinder hole and begins intensively to boil contacting with the wall. The new bubbles are generated, the new foam and vapour-liquid flux appear and so on. Rapid cooling of the inner surface of the cylinder in compared to the outer surface occurs due to its contact with new amount of the fluid entering into the cavity through the bottom hole of the cylinder. Cooling of the outer surface goes sequentially by way of the film, transient and bubble boiling modes. Realization of one kind or another mode can be determined in studies of the structure of the magnetic fluid precipitate on the cylinder surface. Processes of the boiling and cooling rate in the absence of the magnetic field are the same in all points of the inner surface and in all points of the outer surface - do not depend on the angle q, within the limits of the experimental error and various fluctuations. The cooling rate of the inner and outer surfaces of the hollow cylinder in the magnetic fluid with the presence of the external magnetic field differs and depends significantly on the angle q at the cooling of the outer surface. This dependence increases with the growth of the magnetic field magnitude. The time dependence of the cooling rate of the cylinder with the presence of the magnetic field is determined mostly by the initial temperature T0 of the heated cylinder wherein the cooling begins. In the case when T0 exceeds the Curie temperature TK of the wall substance of the cylinder, the wall is in the paramagnetic state and distorts weakly the external uniform magnetic field. Cooling of the cylinder at the initial time of the cooling occurs in the same manner as in the absence of the field. With decreasing temperature less than TK the substance of the cylinder wall transforms to the ferromagnetic state. The external applied uniform magnetic field in the vicinity of the cylinder becomes nonuniform and magnetic forces acting on the magnetic fluid arise. These magnetic forces deform variously the thickness of the vapour layer surrounded the outer cylinder surface. The vapour layer thickness and cooling rate of the various points of the outer cylinder surface, due to the vapour layer thickness, depend significantly on the angle q. Certainly, magnetic forces arise only when the cylinder transfers from the paramagnetic state to the ferromagnetic state and begins disturb the external uniform magnetic field. It is found that such transition occurs at the temperature which is significantly less than the Curie temperature of the cylinder wall substance. It is shown that after such transition the most intensive cooling occurs in the vicinity of the cylinder poles, where the magnetic forces press the fluid against the outer surface, displacing out the vapour layer to the regions of the side surfaces of the cylinder. In this case the vapour layer thickness between the cylinder and the fluid decreases and the heat transfer increases. The regions of the outer side of the cylinder surface, situated in the vicinity of the angles q = ±90°, are cooled less intensive: in these points the vapour layer thickness increases as a result of the magnetic forces action. The heat transfer at the inner surface of the cylinder is the weakest. This can be explained by exclusion of the magnetic fluid from the inner cylinder cavity by the magnetic forces. As a result the cooling of the inner surface are caused by its contact with vapour or vapour-liquid flux; this decreases the cooling rate. The cooling of the hollow ferromagnetic cylinder from its initial temperature T0 which is less the Curie temperature TK differs significantly from the cooling at T0 > > TK. Beginning with of the first fractions of the second, the cooling of the inner surface of the cylinder is of much weaker intensity than the cooling of the outer surface. The cooling rate is the same in all points of the inner surface of the hollow cylinder within the limits of the experimental errors. This can be also explained by exclusion of the magnetic fluid from the inner cavity by the magnetic forces. The cooling of the inner surface are caused by its contact with the vapour. The cooling rate of the outer surface of the cylinder in the presence of the magnetic field at T0 < TK depends significantly from the angle q. The most intensive cooling occurs in the vicinity of the poles where magnetic forces press the fluid against the surface of the cylinder and displace the vapour layer. The cooling rate of the side surfaces of the cylinder is less intensive significantly; in these regions the magnetic forces push the fluid out from the surface, - the vapour layer thickness increases and heat transfer decreases. Figs 10, Refs 17.