I.T.Selezov, A.V.Radionov, S.A.Savchenko Transient temperature field under a heating of ferrofluid seal |
Applied hydromechanics, Vol. 17 (89) ¹ 4, (2015) |
| This paper presents a solution of the problem of a transient thermal regime for a ferrofluid seal on the basis of ferrohydrodynamics equations which are reduced to a dimensionless form with the introduction of similarity criteria of Reynolds, Prandtl and Brinkman assumed in further to be frozen. Approximate analytical analysis performed in this paper is achieved at the cost of strong restrictions but gives you the opportunity to obtain new results on the thermal fields. Define The function of heating is found on the basis of the problem of fluid motion in the annular region following Loitsanski and calculating the heat source, which is proportional to the square of the strain rate tensor following Landau. A problem of the propagation of heat in radial direction in three regions is considered: in the bottom (shaft), internal (fluid) and external (body). A statement of the corresponding initial boundary value problem in the case of entering the step-type function of heating source (the Heaviside function) with a coefficient taking into account all the parameters of heating. The Laplace transform in time is applied and analytical solutions are constructed from the analysis of the Riemann-Mellin inverse in the complex plane. It is found that the dominant contribution comes from a single residual. Using the Duhamel integral and its computation in parts, the solution in a closed form is obtained for arbitrary functions of heating time increasing from zero On this basis the calculations for some real scenarios are carried out. The results can be useful in calculating the real seals allowing to consider different similarity criteria, which include the specific parameters: viscosity, heat capacity etc. |
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KEY WORDS: ferrofluid seal, nonstationary temperature field, Laplace transform, Duhamel integral |
| TEXT LANGUAGE: Russian |