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52 Chapter 3 includes the work done by the pressure, the macroscopic energy flux, and the transport of heat by conduction s = s Ts . The thermal conductivity of the species is denoted by s , which is given in SI units [5] by s = 3.2 e ne2TeV , (3.5-29) m where TeV in this equation is in electron volts (eV). The right-hand side of Eq. (3.5-28) accounts for the work done by other forces as well for the generation/loss of heat as a result of collisions with other particles. The term Rs represents the mean change in the momentum of particles “s” as a result of collisions with all other particles: Rs Rsn = nsms sn (vs vn ). (3.5-30) nn The heat-exchange terms are Qs , which is the heat generated/lost in the particles of species “s” as a result of elastic collisions with all other species, and s , the energy loss by species “s” as a result of inelastic collision processes such as ionization and excitation. It is often useful to eliminate the kinetic energy from Eq. (3.5-28) to obtain a more applicable form of the energy conservation law. The left-hand side of Eq. (3.5-28) is expanded as nmv Dvs+msvs2Dns+nm vs2 v +3 ps+ 5pv + sssDt 2Dtss2 s2 t 2sss =qsnsE vs +Rs vs +Qs s. The continuity equation for the charged species is in the form D n s = n s + v s n s = n ̇ n s v s . Dt t Combining these two equations with the momentum equation dotted with vs gives n s m s v s D v s = n s q s v s E v s p s + v s R s n ̇ m s v s 2 . ( 3 . 5 - 3 3 ) Dt The energy equation can now be written as (3.5-31) ( 3 . 5 - 3 2 )PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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