The BUET librarian who assisted me in purchasing all research papers from abroad referred to this thesis. In vogue, suggestions have been made that the movement of the sea may also cause disturbances in the earth's magnetic field. In the case where the conductor is either liquid or gas, electromagnetic forces will be created which can be of the same order of magnitude as the dynamic and inertial forces of the liquid.
For ionization to take effect, the gas must be very hot • at temperatures in excess of 5000' K or so.. some of the stars are of this type of liquid with high conductivity and possess a strong magnetic field. The authors also provided an alternative proof of the well-known theorem developed by Prim [11] and Kapur [12] for the flow of a gas, for which the velocity magnitude is cons1ani along a streamline. Laier, Colwell and Talbot 114] obtained some exact solutions of the basic equations in Cartesian coordinate systems for unsteady plane-unsteady gas flow.
In their investigations, Colwell and ThIbot [141 removed the hypothesis, taken from Kingston and Rogers [13], thai the streamlines were steady and the gas flow was irrotational. The present study explores some exact solutions of the basic equations, developed in Chapter 2, in the Carlesian coordinate system for the irrotational, plane, and nns1 flow of a non-healing electrically conducting fluid in the presence of a transverse magnetic field. but in the absence of other external forces. In this analysis, it is assumed that the flow variables such as density, velocity, pressure and entropy are separable and the magnetic field is normal to the plane of flow.
The exact description of the phenomena occurring in the flow of a gas requires a continuous investigation of the collision phenomena.
Electromagnetic Field Equations
Medium at Rest 6
Equation (2.4) describes how the magnetic field H depends on the conduction current density J and on the displacement current given by (€/41r)8E/Bt due to change of displacement vector D in the dielectric medium. In the next section we are going to change the above equations medium into motion. We now assume that the dielectric medium is a moving fluid, such as an ionized gas.
As in the development of the theory of gas dynamics, we assume that the medium is continuous and has isotropic properties at all points". Such an assumption is reasonable if the mean free paths of the particles are much smaller than the typical lengths associated with the system under consideration. Furthermore, for this moving medium to change the form of Ohm's law represented by equation (2.5).
Momentum equation
Therefore, the conductive component J effectively contributes to the magnetic body force, but not the convective part qq. If5S is the normal section of the fluid whose length 58 is in the J direction.
Energy Equation
This represents the sum of the heat energy H and the kinetic energy of fluid per unit mass. This shows that the time rate of change of the stagnation enthalpy with heat addition. For adiabatic flow, the added heat is zero, that is, dQ = 0, and this leads to equation (2.21).
The Proposed Problem
Consider the length s measured along the flow line, and n is the normal vector perpendicular to the tangent plane at point P (shown in Figure 1). If T is the tangent vector, n is the normal vector to the length, and 0 is the angle that T makes with the x-axis, then we have. Assuming that the flow variables H, q, E, J, e, and 8 are the product of functions of time (t) and functions of spatial coordinates (x, y), we can write
These equations were obtained by Colwell and Talbot [14) investigating the inviscid, planar, and unsteady gas flow in the absence of a magnetic field. Finally, equations (3.29) to (3.31) govern the unsteady irrotational plane flow of a gas in the presence of a magnetic field in the internal coordinate system. In the following chapter, the detailed method of solving the equations governing the flow is presented.
Therefore, the case in the present analysis is not responsible. which after differentiation with respect to t and some manupulation turns. 4.23) Finally, the above equation gives The same equation was obtained by Colwell and Talbot [14] for the planar irrotational unsteady flow of a gas in the absence of the magnetic field... where C is the integration constant and g' is function depending on space alone. 4.48). Now we must derive the appropriate form for the pressure distribution of the gas flow.
From the velocity distribution above, we can conclude that the flow will be rectilinear at all times. In this section we will find explicit expressions for stream variables. Once we know the function !, except for the constant, we can determine all the flow variables, i.e. pressure, velocity, magnetic field and energy.
If we now collect the relations between Cartesian and intrinsic coordinates (3.4 ) and (3.5), which are introduced into equation (4.84), we get For the geometry of the streamlines, consider a point (x, y) on the transverse line corresponding to the equation as given below: 4.95) In the above equation we substitute (J = Pot + f and after Httle manipulation we have. Collecting the value of t from the equation and inserting into the above equation, we get the following expression for the velocity field: 4.105) From the above connection we can conclude that the velocity field must satisfy the constraint taat.
In the present analysis, an irrotationally unstable phne magnetogasdY;:Iamic flow with infinite electrical conductivity is investigated using the method of invariant transformations. For two values of ,8, namely f3=,8(t) and j3 =13o, are the solutions of the equations representing the flow variables, such as velocity, energy, density, pressure, magnetic field, current density and the streamlines. obtained in closed form. From which the conclusion can be drawn that the streamlines are parallel straight lines. ii) The above fact results in the flow variables vanishing in the flow field. i) the streamlines are concentric circles centered at the point (a, b) and with radius Co. ii) the pressure field p' decreases when the magnetic field H' /[(2) is negative.
Olle dimensional unsteady motion of an ideal compressible fluid, PJiJI :J Ustinov, M.D., Transiormation and some solutions of the equation of motion of an ideal gas, Izvestiya Academi "Nauk SSSR, ~lekhanika Zhid.
