In the general transport equation of problem 8.6, consider that the property (r, v, t) is the

In the general transport equation of problem 8.6, consider that the property χ(r, v, t) is the random momentum flux, that is, m_αC_αjC_αk· Show that, in this case,

where the summation convention on repeated indices is being used. Plug these results in the general transport equation to derive the following equation, known as the viscous stress equation:

Data from Problem 8.6

Derive the following general transport equation, similar to (2.13), for the case when the quantity χ depends on r, v, and t,

Equation 2.13

Transcribed Image Text:

Ә дхi Ә at (na a) = -(na < Xvi >a) = na a=0 Әx Ət Za Pajk Ət ә дxi -(Qaijk + Uai Pajk) диак Paij ахi tk Juaj - Paik axi - >a=Pma