The logarithmic mean temperature difference ($${{\text{t}}_{\text{m}}}$$) is given by (where $$\Delta {{\text{t}}_1}$$ and $$\Delta {{\text{t}}_2}$$ are temperature differences between the hot and cold fluids at entrance and exit)

The logarithmic mean temperature difference ($${{\text{t}}_{\text{m}}}$$) is given by $${{\text{t}}_{\text{m}}} = \frac{{\Delta {{\text{t}}_1} - \Delta {{\text{t}}_2}}}{{{{\log }_{\text{e}}}\left( {\frac{{\Delta {{\text{t}}_1}}}{{\Delta {{\text{t}}_2}}}} \right)}}$$
Where $$\Delta {{\text{t}}_1}$$ and $$\Delta {{\text{t}}_2}$$ are temperature differences between the hot and cold fluids at entrance and exit.