Liquid mercury at a temperature of 315°C flows at a velocity of 10 cm/s over a staggered bank of 5/8-in. 16 BWG stainless steel tubes, arranged in an equilateral triangular array with a pitch-to-diameter ratio of 1.375. If water at 2 atm pressure is being evaporated inside the tubes, estimate the average rate of heat transfer to the water per meter length of the bank, if the bank is 10 rows deep and contains 60 tubes. The boiling heat transfer coefficient is 20,000 W/(m2 K).

Question

GIVEN

Liquid mercury flow over an equilaterally staggered tube bank

Inlet mercury temperature (Tm,in) = 315°C

Mercury velocity (Us) = 10 cm/s = 0.1 m/s

Tubes are 5/8 in., 26 BWG stainless steel

Pitch to diameter ratio (S/D) = 1.375

Water at 2 atm pressure is being evaporated within the tubes

Number of rows of tubes (N) = 10

Number of tubes (Nt) = 60

boiling heat transfer coefficient (bh) = 20,000 W/(m2 K)

FIND

The average rate of heat transfer per meter length of the bank (q/L)

ASSUMPTIONS

Steady state

Tubes are type 304 stainless steel

Temperature change of the mercury across the tube bank is negligible

SKETCH



PROPERTIES AND CONSTANTS



the saturation temperature of water at 2 atm (2.02 x 105 Pa) is Tw = 120°C

Outside diameter (Do) 5/8 in. = 0.0159 m

Inside diameter (Di) = 0.495 in. = 0.0126 m

the thermal conductivity of type 304 stainless steel (ks) = 14.4 W/(m K) at 20°C

Answer 1

Therefore, the minimum free flow area is between adjacent tubes in a row, and the maximum air

velocity is



The Reynolds number is



Applying the correlation



The thermal circuit for the problem is shown below



where

Rcw = Thermal resistance of the boiling water



Rk = Conductive resistance of the tube wall



Rcm = Convective resistance of the mercury side



The rate of heat transfer to the steam is



COMMENT

Note that the thermal resistance of the tube wall is 99% of the total resistance.