Energy of stratified magnetic fluid on a porous basis in the environment

. Stratified magnetic fluid on a porous basis leads to energy savings of the human economy associated with the environment, which goes beyond the usual biospheric transformations.


Introduction
The environment is penetrated with magnetic energy due to the Earth, which has a magnetic field. A device with a two-layer magnetic fluid on a porous basis helps save energy related to the environment. So, cooling lubricants with a magnetic fluid serve as an excellent pressure sealer in seals. Like the coil, inside of which there is a magnetic fluid that converts the energy of the oscillatory motion into electrical.
In mechanical engineering, for example, magnetic fluids are used as a lubricant having properties controlled by a magnetic field. To study the operation of bearings on magnetic lubricant, it is necessary to investigate the magnetic waves arising in this case, since they affect the movement of the liquid in a porous medium. Quite often, a variety of liquids are used in technology to transfer power or energy. For example, the bucket of a small excavator is driven by the pressure of the oil entering the hydraulic cylinders. You can also adjust the flow of liquid in the pipeline pre-installed on a given section of the pipe electromagnet and entering a small amount of magnetic fluid.
Magnetic fluid based on engine oils or cooling lubricants serves as an excellent sealer in various seals, bearings and complex assemblies of machines. Also, magnetic fluids are used in the technology of studying the interaction of Saccharomyces cerevisiae brewing yeast cells [1]. The problem of propagation of surface waves in a layer of magnetic fluid on a porous basis is considered in [5].

Materials and methods
The propagation of gravitational waves in a non-conductive magnetizing two-layer liquid located on a solid impermeable base is considered.
The coordinate system is chosen so that the z axis is directed vertically upwards, the plane z = 0 coincides with the surface of the section of the lower layer of the stratified liquid -an impermeable wall. Further, all values relating to the lower and upper layers of the magnetic fluid with different densities (ρ1 > ρ2) are denoted by numbers 1, 2, respectively ( Fig. 1). The values relating to the atmosphere are indicated by a low index of 3. The equations of motion of the magnetizing liquid at a constant magnetic permeability in the i-th layer (i=1,2) have the form [7]: In the layers of the lower and upper magnetic fluids, velocity potentials φ1, φ2 ( 1 ⃗⃗⃗⃗ = ∇ 1 ( , , , ), 2 ⃗⃗⃗⃗ = ∇ 2 ( , , , )) satisfy the Laplace equations ∆ = 0 (i=1,2). The magnetic field potential in the i-th region (i=1,2) is found from the equations: so far as The equation for the scalar potential in region 3 has the form: The magnetic permeabilities μ1, μ2, μ3 in regions 1,2,3 are further assumed to be constant.
The force in a magnetized medium has the form [3,10]: Where H =| ⃗ ⃗ |, = ( , , ) -is the magnetic permeability of the magnetic field, His the magnetic field strength, ρ -is the density, and T -is the temperature.
Thus, considering the linear approximation at the interface of two layers of a stratified magnetic fluid, we have: The seventh boundary condition takes into account: Further we have: In the seventh, eleventh boundary conditions for pressure, it is taken into account that the definite integral has the form: 2 ); 1 = 10 + 1 ; 2 = 20 + 2 .
In the initial boundary conditions, it is necessary to take into account that for the unperturbed state, the boundary conditions have the form: where ω -is the vibration frequency of the wave, 1 , 2 are real wave numbers characterizing wave propagation along the x, y axis, respectively.
We consider the case when ≥ 0, since there is no fluid for the equation < 0. Thus, the frequency value is found from the dispersion equation by the formula:

Results of the study
The results of the calculations are shown in the graphs of the dependence of the frequency of the wave oscillations on the wave number k, the dimensionless quantities ϰ=h2/h1 and σ=h2/λ, where λ is the wavelength (λ=2π/k). Figure 2 shows the curves calculated for the following values of the thickness of the lower layer of the magnetic fluid: h1 = 20; 150; 300; 600; 1000 cm, respectively. The thickness of the upper layer of the magnetic fluid is fixed h2 = 100 cm. At the same time, the values characterizing the magnetic field have the following values: magnetic permeability in the corresponding liquid layer μ1 = 1.25; μ2 = 1.5; The value of the unperturbed magnetic field in the atmosphere is H03z = 300 Oe.    Figure 4 depicts the dependence of the frequency of the wave oscillations on the dimensionless quantity ϰ=h2/h1 at k=1•10 -3 ; 1,5•10 -3 ; 2•10 -3 cm -1 . In this case, the values characterizing the magnetic field have the following values: the magnetic permeability in the corresponding liquid layer is μ1 = 1.25; μ2 = 1.5 and μ3 = 1. The value of the unperturbed magnetic field in the atmosphere is H03z = 300 Oe. In Figure 4, the thickness of the lower layer of the magnetic fluid is 50 cm -fixed, and h2=ϰh1.   Figure 6 shows the dependence of the oscillation frequency of the wave on H03z, for different values of h2 = 100; 150; 200 cm. In this case, h1 = 100cm; μ1 = 1,2; μ2 = 1.5 and μ3 = 1; k = 0.002 cm -1 -are fixed. Figure 6 Captions should be typed in 9-point Times. They should be centred above the tables and flush left beneath the figures.

Discussion and conclusions
From the graphs shown in Figure 2 it follows that when the wave number increases, if the thickness of the lower layer of the magnetic fluid is fixed, the oscillation frequency increases. For a fixed value of the wave number and an increase in the thickness of the lower layer of the magnetic fluid, the frequency also increases, i.e. shorter waves decay faster than the longer ones. From the graphs presented in Figure 3 it follows that for a fixed value of h1 and an increase in σ, the frequency ω increases. If we fix σ and increase the thickness of the lower liquid layer, then the frequency of the wave oscillations also increases. Thus, for fixed parameters characterizing a magnetic fluid, the dependence of the frequency ω on the dimensionless quantity ϭ remains qualitatively the same as for the case when the magnetic field is absent [7]. Figure 4 shows that as the dimensionless quantity ϰ and the fixed wave number increase, the frequency increases. Conversely, for a fixed value of ϰ and an increase in the wave number k, the slower the frequency decrease, the greater k.
A decrease in the frequency for fixed values of the wave number k and an increase in μ1 are shown in Figure 5. And also from this graph it follows that for a fixed value of μ1 and increasing the wave number k, the frequency increases.
It can be seen in Figure 6 that the frequency depends weakly on H03z for a fixed value of the thickness of the upper layer of the magnetic fluid. If we fix H03z, then the frequency ω decreases with increasing h2.
Thus, technological devices that use stratified magnetic fluid on a porous basis help supply energy to various devices, which help to save the energy of the environment.