The Heat-Flux Vector in Steady-State Shear and Elongational Flows

7 The Heat-flux Vector in Steady-state Shear and Elongational Flows 

For any kind of flow we may write the polymer contribution to the heat-flux vector as  

The tensorial coefficient p, in this expression is not the thermal conductvity tensor, since it is not a generalization of the thermal conductivity (scalar) in Eq. (16.33). The two tensors appearing in Eq. (16.34) are, however, a convenient representation for the fluid response m a system with velocity gradients as well as temperature and concentration gradients. 

For steady shear flow with i = yy, Vy = 0, and = 0, these tensors can be displayed explicitly by usmg Eqs. (13.22) and (13.23) to give us directly  

Several comments can be made about these results  

---