निम्नलिखित में से कौन सा ऊष्मा विनिमायक ठंडे और गर्म तरल पदार्थों दोनों के लिए समानांतर और रैखिक तापमान प्रोफ़ाइल देता है?

Explanation:

Concept: 

• In a parallel flow heat exchanger, both the cold and hot fluid enters the heat exchanger from the same end and the flow direction is also the same.
• In the counter-flow heat exchanger, both the cold and hot fluid enters the heat exchanger from the opposite end and the flow direction is also opposite.

Solution:

• The above-given temperature profile is possible when the heat capacity of both cold and hot fluid is not equal.
• For equal heat capacities of both cold and hot fluids:

\(\Delta\)T₁ = \(\Delta\)T₂

Where, \(\Delta\)T₁ = temperature difference of inlet hot fluid and outlet cold fluid, and \(\Delta\)T₂ = temperature difference of outlet hot fluid and inlet cold fluid.

Then, the log means temperature difference (LMTD) is:

\(\Delta\)T_LMTD = \(\frac{0}{0}\), which is an indeterminate form.

Applying L' Hospital's rule, log mean temperature difference is:

\(\Delta\)T_LMTD = \(\Delta\)T₁ = \(\Delta\)T₂

The temperature profile is parallel and linear and it is possible only for counter-flow heat exchangers this type of heat exchanger is known as a balanced counter flow heat exchanger. 

Thus, option (2) is the correct answer.