G1 Heat Transfer in Pipe Flow

1 Flow Through Pipes, Critical Reynolds Number

Pipe flow is always laminar if the Reynolds number is less than Re = 2300, and is said to be turbulent at higher values. There is no doubt that turbulent flow sets in at Re > 10⁴. In the transition region of 2300 < Re < 10⁴, the type of flow is influenced by the nature of the inlet stream and the form of the pipe inlet.

2 Definition of Heat Transfer Coefficient

The average heat transfer coefficient α over a length l of a pipe is defined by

$$ \dot q = \alpha \;\rm \Delta T _{{\rm{LM}}} $$

The variable $\rm \Delta T _{{\rm{LM}}}$ is the logarithmic mean temperature difference and is given by

$$ \rm \Delta T _{{\rm{LM}}} = {{(T _{\rm{w}} - T _{\rm{i}} ) - (T _{\rm{w}} - T _{\rm{o}} )} \over {\ln {\displaystyle{T _{\rm{w}} - T _{\rm{i}} } \over {\displaystyle T _{\rm{w}} - T _{\rm{o}} }}}} $$

where $T _{\rm{i}}$ and $T _{\rm{o}}$ are the inlet and outlet temperatures of the flowing medium and $T _{\rm{w}}$is the constant...