A double-pipe heat exchanger is used to condense steam at 7370 N/m². Water at an average bulk temperature of 10????C flows at 3.0 m/s through the inner pipe, which is made of copper and has a 2.54-cm ID and a 3.05-cm OD. Steam at its saturation temperature flows in the annulus formed between the outer surface of the inner pipe and an outer pipe of 5.08-cm-ID. The average heat transfer coefficient of the condensing steam is 5700 W/(m² K), and the thermal resistance of a surface scale on the outer surface of the copper pipe is 0.000118 (m² K)/W. 

(a) Determine the overall heat transfer coefficient between the steam and the water based on the outer area of the copper pipe and sketch the thermal circuit. 

(b) Evaluate the temperature at the inner surface of the pipe. 

(c) Estimate the length required to condense 45 gm/s of steam. 

(d) Determine the water inlet and outlet temperatures. 

GIVEN

• Double-pipe heat exchanger, steam in annulus, and water in inner pipe.
• Steam is condensing at a pressure of 7370 N/m².
• Average bulk water temperature, T_b = 10^oC, and water velocity, V = 3.0 m/s.
• Copper inner pipe
• Inside diameter, D_p,i = 0.0254 m
• Outside diameter, D_p,o = 0.0305 m.
• Outer pipe inside diameter, D_o = 0.0508 m
• Heat transfer coefficient of condensing steam, h_c,s = 5700 W/(m² K)
• Thermal resistance of scale on outside of copper pipe, (AR_k,s) = 0.000118 (m² K)/W

ASSUMPTIONS

• Steady-state.
• Constant steam temperature during condensation.
• The flow is fully developed, and copper tube is made of pure copper.

Steam p-7370 Pa Water T-10C V-3 m/s D.- 5.08 cm Copper Plpe Da-2.64 cm, Dpo -3.05 cm