Temperature behaviour of vortices of a 3D thermoconducting viscous fluid

The Navier–Stokes–Fourier model for a 3D thermoconducting viscous fluid, where the evolution equation for the temperature T contains a term proportional to the rate of energy dissipation, is investigated analytically at the light of the rotational invariance property. Two cases are considered: the Couette flow and a flow with a radial velocity between two rotating impermeable and porous coaxial cylinders, respectively. In both cases, we show the existence of a maximum value of T, Tmax, when the difference of temperature ΔT=T2−T1 on the surfaces of the cylinders is assigned. The role of Tmax is discussed in the context of different physical situations.