Validity of the Effectiveness Equation for Heat Exchangers

Introduction:
The effectiveness equation is a widely used equation in heat exchanger analysis. It relates the heat transfer rate to the maximum possible heat transfer rate in a heat exchanger. In this article, we will discuss the validity of the effectiveness equation for different types of heat exchangers.

Validity of the Effectiveness Equation:
The effectiveness equation ε = 1 − e−NTU is valid for heat exchangers that satisfy the following conditions:

(a) Boiler and Condenser for Parallel Flow:
The effectiveness equation is valid for heat exchangers that have parallel flow of the hot and cold fluids. In a parallel flow heat exchanger, both the hot and cold fluids enter the heat exchanger from the same end and flow in the same direction. The effectiveness equation is valid for both boilers and condensers that have parallel flow.

(b) Boiler and Condenser for Counter Flow:
The effectiveness equation is also valid for heat exchangers that have counter flow of the hot and cold fluids. In a counter flow heat exchanger, the hot and cold fluids enter the heat exchanger from opposite ends and flow in opposite directions. The effectiveness equation is valid for both boilers and condensers that have counter flow.

(c) Both Parallel Flow and Counter Flow:
The effectiveness equation is valid for heat exchangers that have both parallel and counter flow of the hot and cold fluids. In such heat exchangers, the hot and cold fluids enter the heat exchanger from opposite ends and flow in opposite directions for some portion of the heat exchanger, and then flow in the same direction for the remaining portion. The effectiveness equation is valid for both boilers and condensers that have both parallel and counter flow.

(d) Gas Turbine for Both Parallel Flow and Counter Flow:
The effectiveness equation is also valid for gas turbine heat exchangers that have both parallel and counter flow of the hot and cold fluids. In such heat exchangers, the hot and cold fluids enter the heat exchanger from opposite ends and flow in opposite directions for some portion of the heat exchanger, and then flow in the same direction for the remaining portion.

Conclusion:
In conclusion, the effectiveness equation is a valid equation for different types of heat exchangers including boilers, condensers, and gas turbine heat exchangers that have either parallel, counter, or both parallel and counter flow of the hot and cold fluids.