Question

If a heat exchanger has effectiveness = 1, it means:

• A. No heat transfer
• B. Maximum possible heat transfer occurs
• C. Temperature difference becomes zero
• D. Both fluids exit at same temperature

Hint:

Effectiveness is a efficiency-like term for heat exchangers.
An effectiveness of 1.0 (or $100\%$) represents the perfect, ideal thermodynamic limit where the maximum achievable heat transfer takes place.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question explores the thermodynamic meaning of a heat exchanger operating at an effectiveness (\(\epsilon\)) equal to \(1\).

Step 2: Key Formula or Approach:
The effectiveness \(\epsilon\) of a heat exchanger is defined using the ratio of actual heat transfer rate to the maximum possible thermodynamic heat transfer rate:
\[ \epsilon = \frac{q_{\text{actual}}}{q_{\text{max}}} \]

Step 3: Detailed Explanation:

• The maximum possible heat transfer rate \(q_{\text{max}}\) is a theoretical limit that would occur in an infinitely long counter-flow heat exchanger.

• It is calculated based on the fluid with the minimum heat capacity rate (\(C_{\text{min}}\)) undergoing the maximum possible temperature difference present in the system:
\[ q_{\text{max}} = C_{\text{min}} (T_{\text{h,in}} - T_{\text{c,in}}) \]
where \(T_{\text{h,in}}\) is the inlet temperature of the hot fluid, and \(T_{\text{c,in}}\) is the inlet temperature of the cold fluid.

• Substituting \(\epsilon = 1\) into the effectiveness definition gives:
\[ 1 = \frac{q_{\text{actual}}}{q_{\text{max}}} \implies q_{\text{actual}} = q_{\text{max}} \]

• This means the actual rate of heat transfer achieved by the heat exchanger is equal to the absolute physical maximum rate allowed by the laws of thermodynamics.

• Achieving an effectiveness of 1 is practically impossible because it requires an infinitely large heat transfer surface area.

Step 4: Final Answer:
An effectiveness equal to 1 signifies that the maximum possible heat transfer occurs.