Define the computational domain, and write the full system of governing equations and boundary conditions for the following situations. In each of them, consider a long straight duct with smooth walls and uniformly distributed circular pipes crossing the duct in the direction perpendicular to the duct axis and parallel to one set of walls (see Figure 2.7).

a) There is a flow of air along the duct. Air can be assumed incompressible and having constant temperature equal to the temperature of the duct walls and pipes.

b) The same as in (a), but now temperature varies. The cylinders are maintained at constant temperature \(T_{c}\), which is significantly higher than the air temperature \(T_{i}\) at the duct inlet. Air is still assumed incompressible.

c) The duct is now filled with a solid material of density \(ho\), specific heat \(C\), and conductivity \(\kappa\). Temperature of the cylinders is \(T_{c}\), and the temperature of the walls is \(T_{w}\).

Transcribed Image Text:

Figure 2.7 Schematic for Problem 2.8.9.