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Chapter 8: Problem 13

How is the thermal entry length defined for flow in a tube? In what region is the flow in a tube fully developed?

Short Answer

Expert verified
Answer: The relationship between thermal entry length and fully developed flow in a tube is that thermal entry length determines the point at which the temperature profile fully develops in the flow. When the flow reaches the thermal entry length, the temperature profile will no longer change and remain constant along the tube's length, corresponding to the fully developed flow in the tube.

Step by step solution

01

Definition of Thermal Entry Length

The thermal entry length is defined as the distance from the tube entrance where the temperature profile reaches a steady state or fully developed the condition. Specifically, it is the distance required for the temperature profile to remain unchanged in the axial direction, which means the axial heat conduction becomes negligible.
02

Fully Developed Flow in a Tube

In a fluid flowing through a tube, fully developed flow refers to a state where both the velocity and the temperature profiles have reached their steady states. For a fully developed flow in a tube, the fluid motion is entirely parallel to the tube walls and exhibits the following characteristics: 1. No variation in velocity profile across the axial direction of the tube (axial velocity gradient is zero). 2. No acceleration or deceleration of fluid particles as they move along the tube (radial velocity gradient is zero). 3. Constant temperature profile throughout the entire length of the tube (no axial temperature gradient).
03

Connection between Thermal Entry Length and Fully Developed Flow

The thermal entry length is related to the fully developed flow because it determines the point at which the temperature profile fully develops in the flow. When the flow reaches the thermal entry length, the temperature profile will no longer change and remain constant along the tube's length. This corresponds to the fully developed flow in the tube.

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Most popular questions from this chapter

How is the friction factor for flow in a tube related to the pressure drop? How is the pressure drop related to the pumping power requirement for a given mass flow rate?

How is the hydrodynamic entry length defined for flow in a tube? Is the entry length longer in laminar or turbulent flow?

Consider laminar flow in a circular tube. Will the friction factor be higher near the inlet of the tube or near the exit? Why? What would your response be if the flow were turbulent?

Consider the flow of oil in a tube. How will the hydrodynamic and thermal entry lengths compare if the flow is laminar? How would they compare if the flow were turbulent?

Someone claims that in fully developed turbulent flow in a tube, the shear stress is a maximum at the tube surface. Do you agree with this claim? Explain.
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