Effectiveness of infinitely long heat exchanger

Article by: 
Chandresh Kr. Mahajan (Founder @exergic.in, AIR-37 ME GATE14, Ex-IOCL)

Estimated reading time: 3 minutes.

Note: This article is not to be treated as the explanation of Effectiveness of Heat Exchanger. It primarily deals with the special case of effectiveness of infinitely long heat exchanger and it assumes that you are already aware of basics of effectiveness of heat exchanger.

Effectiveness of a heat exchanger is the ratio of heat actually transferred to the maximum heat transfer possible (theoretically).

To determine the maximum possible heat transfer for a heat exchanger, maximum possible temperature difference present in the heat exchanger is (T_h1 – T_c1) and the fluid which might undergo this temperature difference is the fluid with lower heat capacity. How? Since the value of heat exchange is same, so lesser the C, more the ΔT.

So, Q_max = (mc)_min (T_{h, i} – T_{c, i})

As we already know, the expression for effectiveness of heat exchanger has two different expressions:

Expression 1:  When (mc)_h > (mc)_c
ε =  (T_{c, o}  – T_{c, i}) / (T_{h, i} – T_{c, i})

Expression 2: When (mc)_{h <} (mc)_c
ε =  (T_{h, i} – T_{h, o}) / (T_{h, i} – T_{c, i})

Let use find effectiveness for both of these cases.

Case 1: When (mc)_h >(mc)_c, as there is prolonged time for heat exchange between hot and cold fluids, so T_c,o almost reaches T_h,i. Putting in Expression 1 of this case above, we get ε ≈ 1.

Case 2: When (mc)_h <(mc)_c, as there is prolonged time for heat exchange between hot and cold fluids, so T_h,o almost reaches T_c,i. Putting in Expression 2 of this case above, we get ε ≈ 1.

In both the cases effectiveness tends to 1.