The coefficient of viscosity is defined as the shear stress produced by unit velocity gradient. For

The coefficient of viscosity η is defined as the shear stress produced by unit velocity gradient. For the p_xz component of the kinetic pressure dyad, for example, we have

Assume the following form for the equilibrium velocity distribution function of the electrons

which indicates the presence of an average velocity u_x(z) in the x direction having a gradient in the z direction. In the absence of external forces and using the relaxation model for the collision term with a constant collision frequency ν, let f = f₀ + f₁ with |f₁| ≪ f₀ in the Boltzmann equation, under steady-state conditions, to show that

Next, calculate P_xz and show that the coefficient of viscosity is given by

Transcribed Image Text:

Pxz = d -nux (2) dz