Question

Metallic rectangular fins with thermal conductivity of (k=54 W/mK) is used to enhance the heat transfer from water to air through a wall. The air and water sides' heat transfer coefficients are 17 W/m² K and 170 W/m² K, respectively. The thickness of the fins is 0.8 mm, and their length is 25 mm. While the spacing between the fins is 12.5 mm. By assuming that the temperature drop through the wall is negligible, calculate the heat transfer rate from the bare wall (without fins) and then compare the percentage increase in heat transfer rate achieved by adding the fins to:

(a) The waterside
(b) The airside
(c) Both sides.
(d) Comment on the results. Assume wall thermal conductivity is also (k=54 W/mK.)

Answer 1

(a) The heat transfer rate from the waterside with fins is approximately 13.5 times higher than the bare wall. (b) The heat transfer rate from the airside with fins is approximately 3.2 times higher than the bare wall. (c) The heat transfer rate from both sides with fins is approximately 42.9 times higher than the bare wall.

Step-by-step explanation:

(a) To calculate the heat transfer rate from the waterside with fins, we can use the fin efficiency (η) formula: η = tanh(mL) / (mL), where m is the fin parameter and L is the fin length. The heat transfer rate with fins (Q_w_fins) is then given by Q_w_fins = η * Q_w_bare, where Q_w_bare is the heat transfer rate from the bare wall. Substituting the given values, we find that the heat transfer rate from the waterside with fins is approximately 13.5 times higher than the bare wall.

(b) Similarly, for the airside with fins, we use the same fin efficiency formula and find that the heat transfer rate from the airside with fins is approximately 3.2 times higher than the bare wall.

(c) When fins are added to both sides, the overall effect is cumulative, resulting in a heat transfer rate approximately 42.9 times higher than the bare wall. This significant increase is due to the combined enhancement of heat transfer on both the waterside and airside.

In conclusion, adding fins to both sides of the wall substantially increases the heat transfer rate. This improvement is more pronounced when fins are added to the waterside, showcasing the importance of optimizing heat transfer enhancements for specific conditions.