Mercury is to be evaporated at 317°C in a furnace. The mercury flows through a 25.4 mm BWG No. 18 gauge 304 stainless-steel tube, that is placed in the center of the furnace. The furnace cross section, perpendicular to the tube axis, is a square 20 cm by 20 cm. The furnace is made of brick having an emissivity of 0.85, and its walls maintained uniformly at 977°C. If the convection heat transfer coefficient on the inside of the tube is 2.8 kW/(m2 K) and the emittance of the outer surface of the tube is 0.60, calculate the rate of heat transfer per meter of tube, neglecting convection within the furnace.
GIVEN
Mercury flow through a tube in the center of a furnace
Mercury temperature (Tm) = 317°C = 590 K
Tube specification: 25.4 mm BWG no 18 gauge stainless steel
Furnace cross section is 20 cm x 20 cm = 0.2 m x 0.2 m
Furnace emissivity (Tube specification: 25.4 mm BWG no 18 gauge stainless steel
Furnace wall temperature (T2) = 977°C = 1250 K
Tube interior heat transfer coefficient (hci) = 2800 W/(m2 K)
Tube exterior emissivity (?1) = 0.602) = 0.85
FIND
The rate of heat transfer per meter of tube
ASSUMPTIONS
Steady state
Convection within the furnace is negligible
SKETCH
the Stephan-Boltzmann constant
for 25.4 mm 18 BWG tubes
Inside diameter (Di) = 22.9 mm= 0.0229 m
Outside diameter (Do) = 25.4 mm = 0.0254 m
for type 304 stainless steel,the thermal conductivity (ks) = 14.4 W/(m K)
The tube and furnace can be thought of as two infinitely long concentric gray cylinders. The rate of radiative heat transfer is
The thermal circuit for this problem is shown below
where
Rci = Convective thermal resistance inside the tube
Rk = Conductive thermal resistance of the tube wall
Rr = Radiative thermal resistance
qc = Convective heat transfer to the tube wall interior
qk = Conductive heat transfer through the tube wall
q1–2 = Radiative heat transfer
For steady state, these three heat transfer rates must be equal
Solving for Tw1 from the first part of the equation
Substituting this into the second part of the equation to solve for T1 yields
Checking the units, then eliminating them for clarity
By trial and error
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