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What is the Thermal Entry Region?
The Entry Region exists for internal flow (in a pipe). It is the region where the velocity and/or the temperature profiles are NOT fully developed (Fun fact – this is usually at the entrance to the tube :O). Velocity and temperature depend on both the x position (how far in it is) and the r position (on the radius). For fully developed flow, the profiles only depend on the r position.There are two scenarios:
1. “Thermal entry length problem” – Fully developed velocity profile, but developing temperature profile.
2. “Combined entry length problem” – Temperature and velocity profiles developing simultaneously
This graph shows the Nusselt number NuD and shows that at the start (x = 0) NuD is effectively infinite. With increasing x (distance from the end), the NuD values decrease to an asymptote (the fully developed values).
Another way of representing the entry region is to use the equation:
· For Gz < 20, the flow is fully developed
· For Gz > 20, the flow is NOT fully developed; it is in the entrance region
This is the Graetz number, and it represents the ratio of the [time taken for heat to radially diffuse into a fluid by conduction] to the [time taken for the fluid to reach distance x]. (For the curious, more information can be found here:http://thermopedia.com/content/820/.)
Entry Region and the Nusselt Number
It is useful to know the average Nusselt number to solve any entry region questions.
· For “Thermal entry length”:
(or combined entry length with Pr > 5)
**Note the extra zero in the equation is correct – not as written in the lecture slides!**
· For “Combined entry length”:
Pr > 0.1
This second equation is horrific, but fortunately, only the first one is examinable...
Further Resources
Here is a useful video that explains the general concepts of the thermal entrance region.
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