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This equation will often depend on temperature, so a heat transfer equation is required or the postulate that heat transfer can be neglected. Next, notice that only 10 of the original 14 equations are independent, because the continuity equation T a b ; b = 0 {\displaystyle T^{ab}{}_{;b}=0} is a consequence of Einstein's equations.
Derivation from linearized MHD equations [1] [2] [3]. In an ideal electrically conducting fluid with a homogeneous magnetic field B, the closed set of MHD equations consisting of the equation of motion, continuity equation, equation of state, and ideal induction equation (see Magnetohydrodynamics § Equations) linearized about a stationary equilibrium where the pressure p and density ρ are ...
H {\displaystyle H} is the magnitude of the applied magnetic field (A/m), T {\displaystyle T} is absolute temperature (K), C {\displaystyle C} is a material-specific Curie constant (K). Pierre Curie discovered this relation, now known as Curie's law, by fitting data from experiment. It only holds for high temperatures and weak magnetic fields.
In physics and materials science, the Curie temperature (T C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism is lost at a critical temperature. [1]
The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is [6] = +, ˙, where q is heat flux vector, −ρc p (∂T/∂t) is temporal change of internal energy (ρ is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and ˙ is the energy conversion to and from thermal ...
The thermodynamic limit is essentially a consequence of the central limit theorem of probability theory. The internal energy of a gas of N molecules is the sum of order N contributions, each of which is approximately independent, and so the central limit theorem predicts that the ratio of the size of the fluctuations to the mean is of order 1/N 1/2.
Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "Alfvén's theorem" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the Magnetic Reynolds Number is very large: this makes the convective term in the induction equation dominate in such regions.
Schematic view of the different current systems which shape the Earth's magnetosphere. In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed current sheets. [10] These can divide the fluid into magnetic domains, inside of which the currents are relatively weak.