Question

Statement(I): Fins are equally effective irrespective of whether they are on the hot-side or cold-side of the fluid.

Statement (II): The temperature along the fins varies and hence the rate of heat transfer varies along the elements of fins.

1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true
5.

Answer 1

Correct Answer - Option 4 : Statement (I) is false but Statement (II) is true

Explanation: 

Effectiveness (ϵ)

Effectiveness is defined as the ratio of heat transfer rate with a fin to heat transfer rate without fin.

\(\epsilon = \frac{{{{\dot Q}_{with\;fin}}\;}}{{{{\dot Q}_{without\;fin}}}}\)

For a long fin

\(\epsilon = \frac{{{{\dot Q}_{with\;fin}}\;}}{{{{\dot Q}_{without\;fin}}}} = \sqrt {\frac{{KP}}{{h{A_c}}}} \)

where K = thermal conductivity of fin, P = perimeter of fin

h = heat transfer coefficient, Ac = cross-section area of fin

From the above formula, we can conclude:

Fins are more effective when they have lesser heat transfer coefficients (h), therefore statement 1 is false.

Temperature distribution:

In all the cases of the fin, the temperature distribution along the fin varies.

And so the rate of heat transfer varies along with the element of fins.

Because Rate of heat transfer ∝ Temperature gradient;

∴ statement 2 is true