LDM ,

Do you mean that with everything else unchanged, a tube would run hotter with the fins (with a 2 cm valley bottom diameter), than a plain bare tube with a 2 cm diameter, notwithstanding the apparent extra surface area caused by the fins using the fin design used for the Lugano device?

For a bare tube the convective power can be calculated as :

Q = h x At x (Ts - Ta)

---------h--------Convective heat transfer coefficient

---------Q--------The power

---------At-------The area of the tube

---------Ts-------Temperature of the surface

---------Ta-------Ambient temperature

For the finned tube the power is calculated as :

Q = C x h x Af x (Ts - Ta)

---------C--------Convective heat transfer correction factor for the finned tube

---------h--------Convective heat transfer coefficient

---------Q--------The power

---------Af-------The area of the fins

---------Ts-------Temperature of the surface

---------Ta-------Ambient temperature

C, the correction factor has a value of .752

h is for both cases 13.28

At, the area of a bare tube of 20 mm diameter and 200 mm length is 0.0125 m^2

Af, the area of a finned tube is 0.0263 m^2

For the surface temperature we take 445 degree C

For the ambient temperature we take 21 degree C

The calculated powers for both cases are then

Qt-------------70.75 Watt for the bare tube

Qf------------111.36 Watt for the finned tube

Clearly with fins the dissipated power by convection is larger and thus the temperature lower.

As an additional comment : C x h = 9.99, the convective heat transfer coefficient I derived for the finned area.

Hope this explains it for you.