Question

A concentric tube heat exchanger is comprised of a stainless steel (k_s = 40 W/mK) inner pipe, NPS 2- nominal schedule 40 size (corresponding to an inner diameter of 52.5 mm and an outer diameter of 60.3 mm), and an outer stainless steel pipe of NPS 3-nominal schedule 40 (ID = 77.9 mm, OD = 88.9 mm). The heat exchanger has an effective length of 35 m.

The inner pipe fluid is ammonia (v_a = 0.3 · 10^-6m²/s, c_pa = 5000 J/kgK, p_a = 700 kg/m³ , Pr_a = 1.5) which enters the pipe at -50^oC and has a volume flow rate of m'_a = 25 L/s.

The outer fluid is water (v_w = 1 · 10^-6 m²/s, c_pw = 4200 J/kgK, p_w = 1000 kg/m³ , Pr_w = 6), which enters the pipe at 50^oC and has a volume flow rate of m'_w = 12L/s.

Phase change is negligible, and the properties of the fluids are constant as given. The heat exchanger operates at steady state. Assume heat loss through the outer surface of the exchanger is negligible.

Determine the outlet temperature of the water and the ammonia.

Outside the outer pipe is air at T_infinity = 20^oC which is not originally moving. Determine if the assumption of negligible heat loss through the outer wall is justified compared to the rate of heat exchanged between the water and ammonia (ie, q_loss < 0.05q_exchanged).

v_air = 15 · 10^-6 m²/s, Pr_air = 0.7, k_air = 0.03 W/mK.

Answer 1