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The first term in Equation 5.15 represents this energy source. d3⃗⃗2me3 dt 2nekBTe =j·E− ne M kmiNi2kB (Te −Ti)− neklNl∆εl (5.15) iil The second term of (5.15) represents energy loss from elastic collisions while the last term is energy loss from inelastic collisions. Here Mi is the mass of the heavy collisional partner, Ti is the heavy gas temperature, kB is Boltzmann’s constant, and ∆εl is the required energy for the excitation process to occur [4,96]. A similar differential equation can be constructed for Tg using energy balance principles: d(NcT)=n2mek N3k (T−T)+nkN∆ε dtpg eMmii2Be i ejjj iij −∆Hj − κ (Tj −Tw)− d 1MwNvx2 (5.16) Unlike the electron energy equation, elastic and inelastic collisions are contributing sources for the gas temperature equation, represented by the first two terms. Energy losses appear in the last three terms. First, ∆Hj is the heat of reaction for process j. The next term represents conduction loss to the wall, where κ is the mixture averaged thermal conductivity, Λ is the diffusion coefficient, and Tw is the wall temperature. The last term accounts for energy loss as the gas expands and flow velocity, vx, increases, where Mw is the mixture averaged molecular weight [4,96]. Each of these differential equations outlined above requires the input of a reaction rate coefficient, which are dependent upon the EEDFs generated by the external Boltzmann solver. The Boltzmann module solves Boltzmann’s equation (5.17) to determine the EEDF [61]. j Λ2 dt2 ∂f F ∂f ∂t+v·∇rf+m·∇rf= ∂t 102 (5.17) collisionPDF Image | CO2 Conversion in a Microwave Plasma Catalyst System
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