This means that complementary of the fillers enhances

hysteresis loss, even though the formation and collapsing of aggregate (filler-filler accumulation) which leads to frictional energy is possible [35].

During excitation, when the ramping rates are 10, 5, 1, 0.5, and 0.1 A/s, the turn-to-turn losses are 5557.3, 5354.5, 4079.5, 3069.5, and 957.2 J, and the

hysteresis losses are 636.5, 618.3, 378.8, 209.7, and 101.1 J.

Symbols Meanings [k.sub.h]

Hysteresis loss coefficient [k.sub.e] Eddy loss coefficient [k.sub.ex] Extra loss coefficient f Actual flux frequency of the core [B.sub.m] Maximal magnetic flux density F Force applied on the bearing d Diameter of bearing v Peripheral speed of center of ball in the bearing t Time [K.sub.x] Heat conductivity along x direction, [K.sub.x] = [K.sub.y] [K.sub.y] Heat conductivity along y direction [v.sub.x] Heat transfer rate along x direction [v.sub.y] Heat transfer rate along y direction [beta] Convective heat transfer coefficient on the boundary [S.sub.3] n Unit normal vector with positive orientation away from the boundary surface [K.sub.n] Heat conductivity along vector n Table 1.

Therefore, it is possible to ignore the eddy current loss in magnetite nanoparticles in contrast to the

hysteresis loss.

The experimental output responses evaluated included the cell nucleation density, bulk density of the foam, compression

hysteresis loss, tensile strength, and Shore A hardness.

Hysteresis losses of the stator core can be calculated as:

Magnetic

hysteresis loss of unit mass is expressed as Eq.

The electrical losses of a PM AC machine include, i.e., eddy current and

hysteresis losses in the stator and rotor cores, eddy current and

hysteresis loss in the permanent magnet and copper loss of the stator winding.

Loss separation breaks the total core loss into static

hysteresis loss, classical eddy current loss, and excess loss [7].

Hysteresis loss is defined as the loss of energy of the specimen when deformed during a given loading-unloading cycle.

As the current reverses direction, the

hysteresis loss at specific frequencies changes significantly under strain.

Further, in certain of the enhanced elastic modulus embodiments, the rubber compositions containing the metal carboxylate also have decreased

hysteresis loss.

Evans, "Pyroelectric energy conversion:

hysteresis loss and temperature sensitivity of a ferroelectric material," Journal of Applied Physics, vol.

This kind of heat dissipation has been termed "

hysteresis loss." Briefly, the heat dissipation from nanoparticles with unit weight during unit time, also called specific loss power Ph, abruptly increases from zero to 4[[mu].sub.0][mu][H.sub.K] x f x [w.sup.-1] (= 4[[mu].sub.0][M.sub.s][H.sub.K] x f x [[rho].sup.-1]) when [H.sub.ac] becomes higher than [H.sub.K], where w and [[rho].sup.-1] are the weight and density of the magnetic core of the nanoparticles, respectively.

If the principle components for these losses are accounted (e.g., static

hysteresis loss, classical eddy current loss, and excess loss for [P.sub.mc] [10]; joint action of eddy and proximity effects for [P.sub.w]) they can be presented