G7 Heat Transfer in Cross-flow Around Single Rows of Tubes and Through Tube Bundles

The average coefficient of heat transfer $$\alpha $$ at the surface of a row of tubes and in a tube bundle is defined by $$\dot q = \alpha \;\rm \Delta {T _{{\rm{L}}\,{\rm{M}}}}$$ The variable $$\rm \Delta {T _{{\rm{LM}}}}$$ is the logarithmic mean temperature difference and is given for a constant wall temperature boundary condition by $$\rm \Delta {T _{{\rm{L}}\,{\rm{M}}}} = {{({T _{\rm{w}}} - {T _{{\rm{in}}}}) - ({T _{\rm{w}}} - {T _{{\rm{out}}}})} \over {\ln {{{(T _{\rm{w}}} - {T _{{\rm{in}}}}_{_{\rm{i}}}}) \mathord{\left/ ({\vphantom {{{T _{\rm{w}}} - {T _{{\rm{in}}}}_{_{\rm{i}}}} {{T _{\rm{w}}} - {T _{{\rm{out}}}}}}} \right.} {{T _{\rm{w}}} - {T _{{\rm{out}}})}}}}},$$ where $${T _{{\rm{in}}}}$$ and $${T _{{\rm{out}}}}$$ are the inlet and outlet temperatures, respectively, of the flowing medium, and $${T _{\rm{w}}}$$ is the wall temperature.