Internal Flow
Chapter 8
Internal fluid flow is fluid flow that occurs within a pipe or other container.
If the flow is laminar (ie. in the fully developed region) the velocity profile is parabolic. See entry-region for how to calculate the distance at which the fully developed region starts.
When dealing with turbulent flow it becomes extremely difficult to find the temperature gradient so instead we use the mean temperature (or mixed bulk temperature).
For internal flow the characteristic length is known has hydraulic diameter.
Mass Flow Rate (Equation 8.5):
Where
See Chapter 8 and ME3304 S24 Lecture Note (3) Convection for more info.
Energy Balance
Section 8.3
As the flow in completely enclosed, an energy balance can be used to find the mean temperature.
Equation (8.34):
See 7C - 1st Class.
Constant Surface Heat Flux
Covered in Section 8.3.2, analyzing internal flow with constant heat flux is greatly simplified as heat flux becomes independent of location. Equation 8.38 gives convection heat transfer rate:
As shown in 7C - 1st Class and section 8.3.2 we can derive an expression for temperature as a function of location (Equation 8.49):
Idk what Figure 8.7 is, its just "very important" or smth
Constant Surface Temperature
Covered in Section 8.3.3, another simplification we can take advantage of is when there is a constant surface temperature.
Equation 8.41b:
Equation 8.42:
Where
Equation 8.45:
See 7C - 1st Class.