Question

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

#Answer# Thermal entry length is defined as the distance along a tube where the temperature profile between the flowing fluid and the tube wall reaches a steady state, remaining constant thereafter. The region of fully developed flow in a tube occurs beyond the hydrodynamic and thermal entry lengths, where both the velocity and temperature profiles in the fluid no longer change along the tube length.

Step-by-step solution

Definition of Thermal Entry Length

The thermal entry length is the distance along the length of a tube where the temperature profile between the flowing fluid and the tube wall reaches a steady state, meaning that it remains constant thereafter. It is denoted as Lth and is an important parameter in analyzing the heating and cooling processes in fluid flow through tubes.

Region of Fully Developed Flow

In tube flow, the flow is considered fully developed when both the velocity and temperature profiles in the fluid do not change any further along the tube length. This occurs beyond the hydrodynamic and the thermal entry lengths. In this region, the velocity profile has reached a constant shape, and the temperature profile has become independent of the axial distance. It is crucial in predicting fluid flow behavior and related heat transfer phenomena inside tubes.