Thermal characteristics of fin-tubes. Refer to the Journal of Heat Transfer study of the straight-line relationship between heat transfer enhancement (y) and unflooded area ratio (x), Exercise. Construct a 95% confidence interval for β1, the slope of the line. Interpret the result.
Exercise
Thermal characteristics of fin-tubes. A study was conducted to model the thermal performance of integral-fin tubes used in the refrigeration and process industries (Journal of Heat Transfer, August 1990). Twenty-four specially manufactured integral-fin tubes with rectangular fins made of copper were used in the experiment. Vapor was released downward into each tube and the vapor-side heat transfer coefficient (based on the outside surface area of the tube) was measured.
The dependent variable for the study is the heat transfer enhancement ratio, y, defined as the ratio of the vapor-side coefficient of the fin tube to the vapor-side coefficient of a smooth tube evaluated at the same temperature. Theoretically, heat transfer will be related to the area at the top of the tube that is ‘‘unflooded'' by condensation of the vapor. The data in the table are the unflooded area ratio (x) and heat transfer enhancement (y) values recorded for the 24 integral-fin tubes.
(a) Fit a least squares line to the data.
(b) Plot the data and graph the least squares line as a check on your calculations.
(c) Calculate SSE and s2.
(d) Calculate s and interpret its value.
| Unflooded Area Ratio, x |
Heat Transfer Enhancement, y |
| 1.93 |
4.4 |
| 1.95 |
5.3 |
| 1.78 |
4.5 |
| 1.64 |
4.5 |
| 1.54 |
3.7 |
| 1.32 |
2.8 |
| 2.12 |
6.1 |
| 1.88 |
4.9 |
| 1.7 |
4.9 |
| 1.58 |
4.1 |
| 2.47 |
7 |
| 2.37 |
6.7 |
| 2 |
5.2 |
| 1.77 |
4.7 |
| 1.62 |
4.2 |
| 2.77 |
6 |
| 2.47 |
5.8 |
| 2.24 |
5.2 |
| 1.32 |
3.5 |
| 1.26 |
3.2 |
| 1.21 |
2.9 |
| 2.26 |
5.3 |
| 2.04 |
5.1 |
| 1.88 |
4.6 |