Fin tip temperatures in boilers of membrane wall design depend on several factors such as cleanliness of the water or tube-side fouling, fin geometry, and heat flux, which is a function of the load and gas temperature. Assuming that membranes are longitudinal fins heated from one side, the following equation may be used to determine the fin tip temperature:

Jg__ t^=t -t

Cosh(mh) g t

Where

Tg = gas temperature, °F tb = fin base temperature, °F

Due to the high boiling heat transfer coefficients, on the order of 3000­

10,0 Btu/ft2 h°F, fin base temperatures will be a few degrees higher than saturation temperature, assuming that tube-side fouling is mini­mal.

Tt = fin tip temperature, °F h = membrane height, in. (see Fig. 3.11)

M = (hgC/KA)0,5

Where

Hg = gas-side heat transfer coefficient, Btu/ft2 h°F C = perimeter of fin cross section = 2b + L in. (for heating from one side) where b = fin thickness and L = fin length or furnace length K = fin thermal conductivity, Btu/ft h°F A = cross-section of fin = bL

C/A for long fins = (2b + L)/bL = L/bL = 1/b Example 5

In a boiler furnace, gas temperature at one location is 2200°F. The gas-side heat transfer coefficient is estimated to be 30 Btu/ft2 h°F. Fin height = 0.5 in. fin thickness = 0.375 in. Fin base temperature is 600°F. Thermal conductivity of fin is 20 Btu/ft h°F. Determine the fin tip temperature.

Solution: Using the above equation, we have

Tg = 2200°F, tb = 600°F, hg = 30, h = 0.5 in., b = 0.375 in.; K = 20

0.5 ( 30 x 12 ’5 mh = ^(———— I = 0.3536 or cosh(0.3536)= 1.063 12 20 x 0.25

2200 — 600

Tt = 2200 ——————- = 695°F

T 1.063