Thermomechanical coupling in a circular Couette flow

The circular Couette flow between concentric cylinders is in the 0-direction only, and satisfies vr = vz = 0, ve = Vfl(r), and T = T(r). The inner cylinder is stationary while the outer cylinder rotates with an angular velocity w. Assuming a steady and laminar flow without end effects, the velocity distribution is 

With surface temperatures of T0 and T for the outer and inner cylinders, respectively, the temperature profile is given by 

Substituting Eqs. (4.32) and (4.35) into Eq. (4.30), we can determine the rate of entropy production for the tangential annular flow. 

The first terms of Eqs. (4.23) and (4.30) show the entropy production due to the heat transfer prod A7, while the second terms show the entropy production due to the fluid friction Spr0(j,ap hence, the rate of entropy production expression has the following basic form  

An increase in Be indicates a competition between the irreversibilities caused by heat transfer and friction. At high Reynolds numbers, the distribution of Be is relatively more uniform than at lower Re. For a circular Couette device, the Reynolds number (Re = wr2lv) at the transition from laminar to turbulent flow is strongly dependent on the ratio of the gap to the radius of the outer cylinder, 1 — n. The critical Re reaches a value 50,000 at 1 n 0.05. We may control the distribution of the irreversibility by manipulating various operational conditions such as the gap of the Couette device, the Brinkman number, and the boundary conditions. 

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Example 4.4 Thermomechanical coupling in a circular Couette flow For a circular Couette flow (Figure 4.5), the entropy production rate for an incompressible Newtonian fluid held between two coaxial cylinders is... 

Example 4.4 Thermomechanical coupling in a Circular Couette flow... 

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