The effectiveness (ϵ) of a heat exchanger is defined as the ratio of the actual heat transfer to the maximum possible heat transfer
Effectiveness, ε:
Effectiveness of a heat exchanger is defined as ratio of actual heat transferred to maximum possible heat that can be transferred.
In physical terms, the heat exchanger effectiveness can be defined as the ratio of actual heat transferred to the theoretically maximum possible heat transfer between the two sides of heat exchanger. The number of transfer units (NTU) technique is a well-documented method of characterizing the performance of a heat exchanger.
The simplified mathematical model based on the NTU technique is:
effectiveness = 1 – EXP(-NTU)
Where NTU is the ratio of the product of overall heat transfer coefficient (U) and the contact surface area to the heat capacity rate of the transfer fluid.
Therefore: NTU = (U.A)/(m_min*cp) = (U.A)/(C_min)
Note: C_min is the minimum heat capacity rate of the two fluids
In most heat exchangers utilizing PCM, at first glance, it appears that the value of Cmin is for the PCM as its in general in its liquid or solid state has lower heat capacity than other working fluids such as water. This is actually wrong and i saw it as a A COMMON MISTAKE IN MANY PAPERS.
The right mathematical and physical term to do it is: since the PCM undergoes no temperature change during latent heat exchange, it has infinite heat capacity (per unit temperature) at that time and the minimum heat capacity rate should be that of the working fluid. Therefore, you should use of the specific heat of the heat transfer fluid (could be water) to get an estimate of effectiveness of a thermal energy storage heat exchanger.