KINETIC-MODEL FOR UNIFORM SHEAR-FLOW

The so-called ellipsoidal statistical (ES) kinetic model is used to st udy the uniform shear flow problem in a dilute gas. This model is an e xtension of the well-known BCE-I kinetic to account for the correct Pr andtl number. The velocity moments and the velocity distribution funct ion are obtained in terms of the shear rate and a parameter Pr which p lays the role of the Prandtl number. It is shown that, independently o f the numerical value of Pr, the expressions of the second-degree velo city moments (which are related to the pressure tensor) coincide with the ones derived from the Boltzmann equation for Maxwell molecules. A comparison with previous results obtained from the Boltzmann equation for the fourth-degree velocity moments and for the velocity distributi on function is carried out. Surprisingly enough, the comparison shows a superiority of the BGK model (Pr=1) over the ES model (Pr=2/3) in th is problem. If one chooses values of Pr larger than one, the ES predic tions are improved significantly.