Univerzalne metode u istraživanju nestacionarnog ravanskog laminarnog strujanja nestišljivog provodnog fluida, u spregnutim MHD, dinamičkim, toplotnim i difuzionim graničnim slojevima

Abstract

In this dissertation a detailed research was conducted into the unsteady flow in a plane, dynamic, temperature and diffusion MHD boundary layer of an incompressible electrically conducting fluid in the presence of source/sink of heat, radiation heat, chemical reactions, suction/blowing of fluid through the porous contour, and the effect of buoyancy force and transverse homogeneous magnetic field in the model of non inductive approximation. The outer flow velocity, temperature and concentration on the body, as well as velocity of suction/blowing, are arbitrary, differentiable functions of the longitudinal coordinate and time. To study the movement of a conductive fluid around the body of arbitrary shape, a system of basic partial differential equations was derived, as well as a system of equations for dynamic, temperature and diffusion MHD boundary layers. The derived system of equations is of general nature, because these equations contain a number of different influences. Thus, dynamic equations include the impact of nonstationary force, pressure force, Lorentz force and buoyancy forces, which are the result of differences in temperature and concentration as well as the influence of porosity of the surface. Energy and diffusion equations contain the impact of the heat which is the result of the viscous friction, fluid expansion, Joule heat, brought or taken heat by the source/sink of heat, radiation heat, and the impact of source/sink impurities, resulting from a homogeneous first order chemical reaction. Furthermore, corresponding integral equations are derived for the dynamic, temperature and diffusion boundary layer, which also have a general character, since they are reduced, by rejecting certain individual members, to a series of simpler physical tasks. Based on the presentation and analysis of the papers in which MHD flow boundary layers are studied, the universal parametric method of generalized similarities of Professor Loitsianskii L.G. was used for the resolution of the obtained system of MHD equations derived in this dissertation. Following the introduction of the similarity variables for the transverse coordinate, for the stream function, for temperature and concentration, and a series of infinite sets of similarity parameters, dynamic and magnetic, suction/blowing, temperature and diffusion, buoyancy force of temperature and diffusion, chemical reaction parameters and the parameters of source/sink of heat, a system of universal MHD equations was derived. This system of equations represents a generalized system of MHD boundary layer equations, which, with the rejection of certain members, becomes like many previously known systems. The universal system of MHD equations, after the formulation of the initial boundary conditions, defining the functions FS and TS, was numerically solved in a two-parameter, repeatedly localized approximation. With the implementation of finite difference method, iteration and linearization of non-linear coefficient, the resulting algebraic system of finite difference equations addressed the gathering points of indirect network integration, using the tridiagonal method. The obtained universal results provide an analysis of the impact of introduced parameters on the development of dimensionless quantities of velocity, temperature, concentration, and on the development of integral and differential characteristics of the considered MHD boundary layers, that is, the ability to manage the boundary layers was demonstrated. By applying the results of universal equations and solving the momentum equation, the effects of heat and mass transfer in MHD boundary layers were discussed in the example of convection flow horizontal circular cylinder at a constant velocity values of sucking / blowing, and for several values of the parameters introduced and the number of similarities r P , c E and c S . At the end of the dissertation, the initial system of equations of MHD dynamic, temperature and diffusion boundary layer was solved using a new approach, which can, to some extent, be divided into new methods for solving MHD boundary layer equations. Thus obtained system of equations, which also has the characteristic of universal approach, was applied to consider the effects of mass and heat transfer in mixed convection task, and the convection flow past a horizontal circular cylinder. Flow analysis was performed via the introduced dimensionless quantity for the class of deceleration and acceleration flow. The results of typical values of boundary layers, as well as the dimensionless function of the ratio of velocity, temperature and concentration, are shown graphically and confirm the conclusions on the expected tendencies of changes of these values in relation to the presence of different influences.