Range = EWT – LWT
Approach = EWTHS - LWTCS
Where
• EWT = Entering Water Temperature (°F)
• LWT = Leaving Water Temperature (°F)
• EWTHS = Entering Water Temperature – Hot Side (°F)
• LWTCS = Leaving Water Temperature – Cold Side (°F)
Logarithmic Mean Temperature Difference – LMTD
In a heat transfer process, the temperature difference varies with position and time. The determination of the mean temperature difference in a heat transfer process depends upon the direction of fluid flow involved in the process. The primary and secondary fluid in a heat exchanger process may:
1) flow in the same direction - parallel flow/co-current flow
2) in the opposite direction - counter current flow
3) or perpendicular to each other - cross flow
When the secondary fluid passes over the heat transfer surface, the highest rate of heat transfer occurs at the inlet and progressively decays with higher secondary fluid temperature along its way to the outlet. The rise in secondary temperature is non-linear and is best represented by a logarithmic calculation. For this purpose the mean temperature difference chosen is termed the Logarithmic Mean Temperature Difference or LMTD and can be expressed as:
LMTD = (TD2 - TD1) / ln (TD2 / TD1)
Where
• LMTD = Logarithmic Mean Temperature Difference 0F
• TD1 = TP1 – TS2 - Entering primary fluid and leaving secondary fluid temperature difference °F
• TD2 = TP2 – TS1 - Leaving primary fluid and entering secondary fluid temperature difference °F
Arithmetic Mean Temperature Difference – AMTD An easier but less accurate way to calculate the mean temperature difference is to consider the Arithmetic Mean Temperature Difference or AMTD and can be expressed as:
AMTD = (TP1 + TP2 ) / 2 - (TS1 + TS2 ) / 2
Where
• AMTD = Arithmetic Mean Temperature Difference 0F
• TP1 = primary inlet temperature 0F
• TP2 = primary outlet temperature 0F
• TS1 = secondary inlet temperature 0F
• TS2 = secondary outlet temperature 0F
A linear increase in the secondary fluid temperature makes it easier to do manual calculations. AMTD will in general give a satisfactory approximation for the mean temperature difference. When heat is transferred as a result of a change of phase in condensation or evaporation heat exchangers, the temperature of the primary or secondary fluid remains constant. For example, with saturation of steam the primaryfluid temperature can be tak en as a constant because heat is
transferred as a result of a change of phase only. The equation can then be simplified by setting
TP1 = TP2 or TS1 = TS2 0F
Thus in the equation above, the temperature profile in the primary fluid is not dependent on the direction of flow.
