Solution Tbave = (Tb1 + Tb2)/2 = 37.5 °C
Water properties – Table A-9: cp = 4174 J/kg-°C, ρ = 993 kg/m3, μ = 6.82 x 10-4 kg/m-s,
k = 0.630 W/m-°C, Pr = 4.53
Reynolds number Red = ρumd/μ
mdot = 0.8 kg/s = ρAum = (993 kg/m3)*(π/4)*(0.025 m)2*um gives um = 1.641 m/s
Red = (993 kg/m3)*(1.641 m/s)*(0.025 m)/(6.82 x 10-4 kg/m-s) = 59741.4 (turbulent)
Using Eqn. (6-4c) good for 1.5 < Pr < 500, 3000 < Re < 106
Nu = hd/k = 0.012*(Red0.87 – 280)*Pr0.4 = 0.012*(59741.40.87 – 280)*4.530.4 = 307.9
h = 307.9k/d = (307.9)*(0.630)/(0.025) = 7758.8 W/m2-°C
q = mdot*cp*∆Tb = hA*(Tw – Tb)ave
Computing q1 = mdot*cp*∆Tb = (0.8 kg/s)*(4714 J/kg-°C)*(40 – 35) °C = 18856 W
so 18856 W = hπdL*(Tw – Tb)ave = (7758.8 W/m2-°C)*π*(0.025 m)*L*(90 – 37.5) °C
gives L = 0.589 m.