Consider fully developed flow inside the annulus shown in Figure P13.27. Both velocity and temperature profiles are fully developed. The heat fluxes in from the two walls are different but are constant along the length of the annulus.

a. Determine the velocity profile inside the annulus for a constant pressure drop \((\Delta P / L)\) and fluid of viscosity, \(\mu\).

b. Using the velocity profile from part (a), solve the energy equation using boundary conditions based on the heat flux and surface temperature of the inner cylinder. Repeat using the heat flux and surface temperature for the outer cylinder.

c. Following the procedure outlined in Section 13.5.1, determine a general expression for the Nusselt number and a particular value when \(q_{o}^{\prime \prime}=q_{i}^{\prime \prime}\) and \(r_{i}=r_{o} / 2\).

Transcribed Image Text:

FIGURE P13.27 % T m " To(z) T(z)