8
Internal Forced Convection
8.1 Velocity and Temperature Profiles in a Circular Tube
or between Parallel Plates
Internal forced convection is that flow moves through the internal surface of
a passage and forms an internal boundary layer on the surface. For example, fluid flowing through a circular tube or between two parallel plates is a
most common application. Figure 8.1 shows the hydrodynamic boundarylayer development (due to viscosity) for flow entering a circular tube
(or between two parallel plates). The boundary layer starts from the tube (or
plate) entrance and grows along the tube (or plate) length. The velocity profile
keeps changing in the entrance region of the tube (or plate). The flow becomes
a “hydrodynamic fully developed flow” when the boundary thickness is the
same as the tube radius (or half-spacing between the two plates). The velocity profile no longer changes after a fully developed flow. For a laminar flow,
the entrance length to tube diameter ratio is about 5% of Reynolds number
(based on the tube diameter). This implies that the entrance length increases
with increasing Reynolds number (because a thinner boundary layer requires
longer distance for the boundary layer to merge). Figure 8.1 also shows that
shear stress decreases from the entrance along the tube and becomes a constant value when the flow reaches the fully developed condition, and shear
stress increases with Reynolds number (because of a thinner boundary layer
from the entrance and the longer entrance length). For a turbulent flow, the
entrance length is harder to determine; the entrance length is around 10–20
tube diameter. It is hard to distinguish whether the turbulent flow is fully
developed or not from 10 to 20 tube diameter downstream [1–4].
Figure 8.2 shows the thermal boundary-layer development (due to thermal
conductivity and velocity) for flow entering a circular tube (or between two
parallel plates). The thermal boundary layer starts from the tube (or plate)
entrance and grows along the tube (or plate) length. The temperature profile
keeps changing from the entrance due to adding heat along the tube (or plate)
wall. The flow becomes “thermally fully developed flow” when the thermal
boundary thickness is the same as the tube radius (or half-spacing between the
two plates). The dimensionless temperature profile no longer changes after
being thermally fully developed (but the temperature still keeps increasing).
167
Internal Forced Convection
8.1 Velocity and Temperature Profiles in a Circular Tube
or between Parallel Plates
Internal forced convection is that flow moves through the internal surface of
a passage and forms an internal boundary layer on the surface. For example, fluid flowing through a circular tube or between two parallel plates is a
most common application. Figure 8.1 shows the hydrodynamic boundarylayer development (due to viscosity) for flow entering a circular tube
(or between two parallel plates). The boundary layer starts from the tube (or
plate) entrance and grows along the tube (or plate) length. The velocity profile
keeps changing in the entrance region of the tube (or plate). The flow becomes
a “hydrodynamic fully developed flow” when the boundary thickness is the
same as the tube radius (or half-spacing between the two plates). The velocity profile no longer changes after a fully developed flow. For a laminar flow,
the entrance length to tube diameter ratio is about 5% of Reynolds number
(based on the tube diameter). This implies that the entrance length increases
with increasing Reynolds number (because a thinner boundary layer requires
longer distance for the boundary layer to merge). Figure 8.1 also shows that
shear stress decreases from the entrance along the tube and becomes a constant value when the flow reaches the fully developed condition, and shear
stress increases with Reynolds number (because of a thinner boundary layer
from the entrance and the longer entrance length). For a turbulent flow, the
entrance length is harder to determine; the entrance length is around 10–20
tube diameter. It is hard to distinguish whether the turbulent flow is fully
developed or not from 10 to 20 tube diameter downstream [1–4].
Figure 8.2 shows the thermal boundary-layer development (due to thermal
conductivity and velocity) for flow entering a circular tube (or between two
parallel plates). The thermal boundary layer starts from the tube (or plate)
entrance and grows along the tube (or plate) length. The temperature profile
keeps changing from the entrance due to adding heat along the tube (or plate)
wall. The flow becomes “thermally fully developed flow” when the thermal
boundary thickness is the same as the tube radius (or half-spacing between the
two plates). The dimensionless temperature profile no longer changes after
being thermally fully developed (but the temperature still keeps increasing).
167