The document discusses forced convection in internal flow, emphasizing the confined nature of fluids in tubes compared to external flow, which allows the boundary layer to grow indefinitely. It details the temperature and velocity profiles in different flow regimes, including laminar and turbulent flows, and explains the importance of hydraulic diameter in optimizing heat transfer. Additionally, it outlines the steps for convection calculations, including determining the appropriate Nu-number equations and assessing flow characteristics.

1. Force Convection
Internal Flow
Hanim Z. Amanah

2. Forced convection
internal flows
In external flow, the fluid has
a free surface, and thus the
boundary layer over the
surface is free to grow
indefinitely. In internal flow,
however, the fluid is
completely confined by the
inner surfaces of the tube,
and thus there is a limit on
how much the boundary layer
can grow.
For a fixed surface area, the circular tube gives the most heat
transfer for the least pressure drop, which explains the
overwhelming popularity of circular tubes in heat transfer
equipment.

3. Velocity profile & temperature profile

4. Laminar and turbulent flows in tubes
• Hydraulic diameter
• D: Hydraulic diameter
• A: Cross section area
• P: Perimeter

5. Entrance region
velocity & temperature

6. Entrance region
velocity & temperature
Note that the temperature profile in the
thermally fully developed region may vary
with x in the flow direction. That is, unlike
the velocity profile, the temperature profile
can be different at different cross sections
of the tube in the developed region, and it
usually is. However, the dimensionless
temperature profile defined above remains
unchanged in the thermally developed
region when the temperature or heat flux at
the tube surface remains constant.

7. Variation of the heat transfer coefficient
in the entrance region

8. General thermal analysis

9. Constant surface heat flux

10. Temperature profile
In fully developed flow in a tube subjected to constant
surface heat flux, the temperature gradient is independent of
x and thus the shape of the temperature profile does not
change along the tube.

11. Constant surface temperature
Arithmetic mean temperature difference
Logarithmic mean temperature difference

12. Number of transfer units
For NTU > 5, the exit
temperature of the fluid becomes
almost equal to the surface
temperature, Te ≈ Ts. Noting that
the fluid temperature can
approach the surface
temperature but cannot cross it,
an NTU of about 5 indicates that
the limit is reached for heat
transfer, and the heat transfer will
not increase no matter how much
we extend the length of the tube.

13. Example 19-6

14. Nu for circular tube
(laminar flow)

15. Average Nu
Internal flows

16. Nu for internal flows
(turbulent flow)
N=0.4 for heating & 0.3 for cooling
The Dittus-Boelter equation(1930) (error up to 25%)
Gnielinski (1976)

17. Outline for convection calculations
• Draw the geometry of the system (tube, plate, internal flow, external flow)
• Calculate the bulk temperature
• Calculate velocity and pressure loss
• Calculate Reynolds number and decide if it is laminar or turbulent flow
• Choose the right Nu –number equation
• Calculate Nu-number and heat transfer coefficient.
• Calculate the heat transfer or heat tranfer area