Calculate thermal flow for air flowing through a tube, with fins

Question

I have the same problem as described in this question:
How to calculate the resulting temperature for a stream of air through a hot tube?, but I want to increase the transferred heat by adding fins onto the inner side of the tube, parallel to the flowing air. Is that useful? If yes, how does the formula mentioned in the answer (https://engineering.stackexchange.com/a/5536/2844) change?
Furthermore, how do I get from the temperature difference to the transferred heat power?

Answer 1

Internally finned tubes are not that common because of the high cost of manufacture. There aren't many sources for this kind of heat transfer.

This paper provides a detailed description of numerical methods used to calculate heat transfer in a finned tube with fully developed laminar flow.

It evaluates fins with the following measurement limits:

Number of Fins:$$8\le M\le32$$ Fin Length (ft):$$0.2\le\ell\le0.9$$ Fin angle:$$1.5°\le\beta\le3°$$

If you do have laminar flow, you can use the following chart to estimate the Nusselt number for a certain fin design:

Use the Nusselt number to calculate the heat transfer coefficient, h:

$$Nu= \frac {hd}{k}$$

Optimally, you would use the hydraulic diameter rather than the nominal tube diameter. This uses a method of determining hydraulic diameter of an internally finned tube using the ratio of cross sectional area of flow to the wetted perimeter. This area would be irritating to calculate for fins and I don't think it would affect the result any more than the other assumptions we have made.

Also of course, use the thermal conductivity, k, value for your fluid.

Lastly use this equation to get your heat transfer:

$$Q=hA_s\theta_{lmtd}=mC_p\Delta{T}$$

This paper analyzes T shaped internal fins and gives a good analysis on how fins affect friction factor and a comparison of smooth tube vs finned.