Question

Steam in a heating system flows through tubes whose outer diameter is D₁ =3 cm and whose walls are maintained at a temperature of 120^oC. Circular aluminum fins (k = 180 W/m.^oC) of outer diameters D₂ = 6 cm and constant  thickness t = 2mm are attached to the tubes.  The space between the fins is 3 mm. Heat is transferred to the surrounding air at T_∞  = 25 ^oC, with a convection heat transfer coefficient of h = 60 W/m².^oC.

Determine the number of fins per metre length

r2 = 3 cm Hr. = 1.5 cm t = 2 mm S = 3 mm

Answer 1

Assumptions used while solving of the question :

1. Steady State.

2. Thermal conductivity (k) is a constant.

3. Heat transfer byRadiation is negligible

4. Convective heat transfer coefficient (h) is uniform over the entire fin surfaces.

Here - I will be finding

1. Number of Fins

2. Efficiency of Fins

3. Effectiveness of fins

Given, k = 180 W/m °C & h = 60 W/m^2 °C

To = 120°C

To = 25c

Since it is given that spacing between the fins is 3mm and and each fin is 2mm thick.

Number of fins per metre (i.e..1000mm) length = 200

Now to find : The increase in heat transfer from the tube per meter of its length as a result of adding fins

In the case of no fins, heat transfer from the tube per meter of its length is determined from Newton’s law of cooling.

QNoFin = hАNoFin To -T)

AnoFin = DiL = (0.03)(1) = 0.0942 m2

QNoFin = (60) 0.0942(120-25)

QNoFin = 537 W

Noting that

L=(D2 – Di) = 5(0.06 – 0.03) = 0.015 m

in this case, we have

r2 + 0.03+0.002 -= 2.07 0.015

(2+39V6 – (0,015 +0.02) 150 20 ore = 1207

Efficiency :

nin= 2.07 – 0.207 2.07 -= 0.95

Afin = 27 (ri - r) + 2arzt = 0.00462 m2

Q Fin = nfin hAfin (T. -T.)

QFin= 0.95 (60) (0.00462) (120 – 25) = 25 W

Heat transfer from the unfinned portion of the tube is

Aun fin = 7 D S = (0.03) (0.003) = 0.000283 m

Qunfin = 7D1S = h Aun fin (T. -T.)

Qunfin = (60) 0.000283) (120 – 25) = 1.60 W

Noting that there are 200 fins and thus 200 inter-finspacings per meter length of the tube, the total heat transfer from the finned tube becomes

QTotal Fin = 200 (Qun fin + Qrin) = 200 (25.0+ 1.6) = 5320 W

Therefore, the increase in heat transfer from the tube per meter of its length as a result of the addition of fins is

Qincrease = Qtotal fin - Qnofin

(Per m of tube length)

Qincrease = 5320 - 537 = 4783 W

The overall effectiveness of the finned tube is

efin

Qrin On Fin

efin

5320 = 9.9 337

That is, the rate of heat transfer from the steam tube increases by a factor of almost 10 as a result of adding fins. This explains the widespread use of finned surfaces.