Poiseuille flow viscous dissipation

We consider viscous dissipation in Couette flow We consider the pressure gradient in Poiseuille flow Viscous dissipation acts as heat source in Couette flow For moderate flow, no heat source within Poiseuille flow. 

The consequences of the wetting ridge in the capillary penetration of a liquid into a small-diameter tube have been evaluated. Viscoelastic braking reduces the liquid flow rate when viscoelastic dissipation outweighs the viscous drag resulting from Poiseuille flow. 

The temperature contours for convectionless flow are shown in figure 2, which shows a hot region at the entrance of the capillary due to the combination of high viscous energy dissipation there and its distance from cool boundaries to which heat may be conducted. These isotherms are normalized on the maximum centerline temperature expected for Poiseuille flow in the capillary. 

K. C. Cheng, and R. S. Wu, Viscous Dissipation Effects on Convective Instability and Heat Transfer in Plane Poiseuille Flow Heated from Below, Appl. Set Res., (32), 327-346,1976. 

For a thermally fully developed laminar flow, for a fixed dynamic and thermal boundary condition and by neglecting the fluid axial conduction, (Pe oo), viscous dissipation (Br = 0), the flow work fi = 0), and electro-osmotic phenomena (Sl=f = 0), the Nusselt number depends on the cross-sectional geometiy (through the Poiseuille number e) only. 

In the intermediate case (ii) corresponding to classic dewetting on a solid substrate (Poiseuille flow), we find that viscous dissipation generally predominates. In contrast, for low-viscosity liquids, such as water, dewetting very hydrophobic surfaces (large angles 6 ), rapid inertial dewetting can be achieved... 

Electrical resistance leads to dissipation of electrical energy in the form of Joule heating. Similarly, hydraulic resistance leads to viscous dissipation of mechanical energy into heat by internal friction in the fluid. The role of viscous dissipation can be explained based on the schematic of transient flow behavior shown in Figure 2.9. Let an incompressible Poiseuille fluid flow takes place inside a channel at times t < 0. The constant Poiseuille-type velocity field is maintained by a constant over-pressure AP applied to the left end of the channel. The over-pressure AP is suddenly removed at time, t = 0. However, the fluid flow continues due to the inertia of the fluid. The internal viscous friction of the fluid gradually slows down the motion of the fluid, and eventually in the limit t - c the fluid comes to rest relative to the channel walls. As time passes, the kinetic energy of the fluid at t = 0 is gradually transformed into heat by the viscous friction. 

The surface, ds has been shown pictorially in Figure 2.10. The channel surface dS consists of three parts the solid side wall d5 an, the open inlet dSi, and the open outlet dS2- The contribution to the surface integral in equation (2.94) from is zero due to the no-slip boundary condition that ensures 0 = 0 on solid walls. The two contributions from dSi and dS2 exactly cancel each other due to the translation invariance of the Poiseuille flow problem. Therefore, the first term in right-hand side of equation (2.94) is equal to zero. The change in kinetic energy of the flow inside the channel is due to viscous dissipation only. 

Let s assume the Poiseuille flow v = u(y, je. The simplified viscous energy dissipation in a Poiseuille flow is therefore given by the volume integral... 

The second term in equation (2.100) is the viscous dissipation part. The result for the viscous dissipation of energy in steady-state Poiseuille flow can be written as... 

---