## Mean temperature difference

**Introduction:**

For accurate design of condenser, one has to consider the de-superheating, condensation and subcooling regions separately and evaluate the area required for each region, and finally find the total area.

**Description:**

- In a refrigerant condenser, the mean temperature difference ΔTm, between the refrigerant and the external fluid varies continuously along the length as shown in Fig.

- However, the heat transfer coefficient on the refrigerant side, hr is small during de-superheating (2-3) in vapour phase but temperature difference between refrigerant and coolant ΔT is large, while during condensation (3-3’) the heat transfer coefficient on refrigerant side is large and the temperature difference is small.

- As a result, the product hrΔT is approximately same in both the regions; hence as an approximation one may design the condenser by assuming that condensation occurs throughout the condenser.

- This implies that the refrigerant temperature is assumed to remain constant at condensing temperature throughout the length of the condenser.

- As mentioned, this is an approximation, and is considered to be adequate for rough estimation of condenser area.

- However, for accurate design of condenser, one has to consider the de-superheating, condensation and subcooling regions separately and evaluate the area required for each region, and finally find the total area.

If we assume condensation throughout the length of the condenser and also assume the pressure drop to be negligible, then the mean temperature difference is given by the Log Mean Temperature Difference (LMTD):

In the above equation are the inlet and outlet temperatures of the external fluid, and Tc is the condensing temperature.