THE STATIONARY PROBLEM OF THE BOUNDARY LAYER FORMED BY THE JOINT ROTATION OF A POROUS CIRCULAR PLATE AND THE SUROUNDING CONDUCTIVE FLUID TAKING INTO ACCOUNT THE MAGNETIC FIELD AND HEAT TRANSFER IN THE CASE OF VARIABLE SUCTION VELOSITY
DOI:
https://doi.org/10.52340/building.2024.01.69.03Keywords:
Conductivity, injection velocity, flow, heat transfer, magnetic field, porosityAbstract
In the paper, the stationary problem of the boundary layer formed by the
joint rotation of a porous circular plate and the surrounding conductive fluid is studied by the Shvetz method (method of successive approximation), taking into account the magnetic field and heat transfer, when the suction velocity changes according to the linear law.
In order to solve the problem, the Navier-Stokes differential equations of fluid motion in a magnetic field and energy nonlinear differential equations in partial derivatives by using generalized Karman transformations are reduced to ordinary nonlinear differential equations, the solutions of which are sought in the form of infinite series. The first two approximations have been clearly calculated, which determine the distribution of fluid velocity, temperature and pressure in the dynamic and thermal boundary layers formed on the circular plate.
In order to calculate the thicknesses of the dynamic and thermal boundary layers, the appropriate equations are obtained and the exact solutions of these equations are recorded. In a particular case, the relationship between the thicknesses of the dynamic and thermal boundary layers is determined. The moment of resistance to rotation of the plate and the heat transfer coefficient are also calculated.
Downloads
References
Prantl L., Verh. Der. III Intern. Math. Kongr. In Heidelberg, 1904, Leipzig, 1905.
Karman T. Laminare und turbulente reibung. ZAAM, 1921, №1, p. 233-252.
Cochran W.G. The flow to a rotating disk. Proc. Cambridge Phyl. Soc., 1934, №30, p. 365-375 (in English).
Stuart J.T. On the effects of uniform suction on the steady flow due to a rotating disk. Quart. J. Mech. and Appl. Math., 1954, 7, p. 446-449 (in English).
L. Jikidze. Approximate method of the nonstationary rotation problem of the porous plate in the weak conductive fluid. Proceedings of Tbilisi University, 1995 (320), pp. 65-77 (in Russian).
L. Jikidze, V. Tsutskiridze. Unsteady simultaneous rotation problem of the infinite porous plate and surrounding fluidaccount of magnetic field and heat transfer in case of variable eleqtric conductivity and injection velocity, Georgian Technical University, works, 2015, №3 (497), pp.194-202 (in English).
L. Jikidze, V. Tsutskiridze, E. Elerdashvili. Stationary task of the boundary layer generated by the rotation of a porous circular plate in an electrically conductive fluid with respect to a weak magnetic field and heat transfer at variable suction velocity, Georgian Technical University, works, 2022, №3(525), pp.157-165 (in Georgian).
Shvets M. Ye. Approximate solution of certain problems of the hydrodynamics of the boundary layer. Applied mathematics and mechanics. 13, №3. 1949, 257-266 pp. (in Russian).
Slezkin N.A., Targ S. M. The generalized equations of Reynolds. Reports of Academy of Sciences of the USSR. 54, №3. 1946, 205-208 pp. (in Russian).
Dorfman L. A. Pressure drop and heattransfer of rotating bodies. Fizmatgiz. Moscow. 1960. (in Russian).
Schlichting G. Theory of the boundary layer. Publishing house "Science". Moscow. 1974. (in Russian).
Lomov S.A. Lomov I.S. Fundamentals of the mathematical theory of the boundary layer. Publishing house of MSU. 2011. (in Russian).
