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

Universal methods in research of unsteady plane laminar flow of an incompressible conducting fluid in composite mhd, dynamic, thermal and diffusion boundary layer

##### Author

Boričić, Aleksandar Z.##### Mentor

Nikodijević, Dragiša##### Committee members

Savić, SlobodanJovanović, Miloš

Ilić, Gradimir

Živković, Dragan

##### Metadata

Show full item record##### 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, dynami...c 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.

##### Faculty:

Универзитет у Нишу, Машински факултет##### Date:

30-05-2014##### Projects:

- The revitalization of existing and designing of new micro and mini hydro power plants (from 100 up to 1000 kW) on the territory of south and southeastern Serbia (RS-33040)
- Research of MHD flows around the bodies, in the tip clearances and the channels and application in the MHD pumps development (RS-35016)