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Heat exchanger problem

  1. Mar 8, 2013 #1
    Okay, I'm having trouble with a heat transfer HW problem. We are designing a tube-in-shell steam condenser.

    We are given:
    [itex]\dot{m}[/itex]steam = 4.38kg/s
    Tsteam = 378K
    the steam is saturated 90%
    Tc of cooling water = 293.15K
    Th of cooling water = 296.5K

    For the tubes in the bundle:
    Inner diameter = 2.16cm
    Outer diameter = 2.67cm
    Remax = 10,000

    The problem I'm having is in calculating the necessary number of tubes in the bundle to keep the Re low enough

    I started by calculating the heat duty for the condensing steam:
    hf = 438 kJ/kg
    hfg = 2245 kJ/kg
    h1 = 438 + (0.90 * 2245) = 2458 kJ/kg
    h2 = 438 kJ/kg
    Δh = 2458 - 438 = 2020 kJ/kg
    Q = 4.38 * 2020 kJ/kg ≈ 8850 kJ/s = 8850 kW

    Next, I calculated the necessary mass flow of the cooling water:
    Tc = 293.15K
    Th = 296.5K
    ΔT = (296.5-293.15) = 3.35K
    Cp = 4.18 kJ/(kg*K)
    8850 kJ/s = m * Cp * ΔT
    8850 kJ/s = m * 4.18 kJ/(kg*K) * 3.35K
    [itex]\dot{m}[/itex]water = 632kg/s

    After I found [itex]\dot{m}[/itex]water I tried to calculate the maximum velocity in one tube based on the maximum reynolds number. This is where I think I went wrong. This is what I did.
    Remax = 10,000
    L = Inner diameter = 2.16cm = 0.0216m
    μwater = 1.002 * 10-3 kg/m*s
    ρwater = 998kg/m3
    vwater = (Re * μ)/(ρ * L)
    vwater = (10,000 * 1.002*10-3) / ( 998kg/m3 * 0.0216m)
    vwater = 0.46m/s

    I thought that the velocity seemed pretty low, but I went even further to calculate the necessary number of tubes in the bundle:
    [itex]\dot{m}[/itex]water = 632kg/s
    vwater = 0.46m/s
    ρwater = 998kg/m3
    Arequired = [itex]\dot{m}[/itex]water/[ρwater * vwater]
    Arequired = 632kg/s / [998kg/m * 0.46m/s]
    Arequired ≈ 1.38m2 = 13,800cm

    Aone tube = (pi/4)*(2.16cm)2 = 3.66cm2

    So the required number of tubes Nt would be
    Nt = (13,800cm2)/(3.662) ≈ 3770

    This number that I'm getting is way beyond the number of tubes were are allowed to use, which supposed to be in the hundreds. I feel like my mistake is somewhere in my calculation of the velocity, but I've double and triple checked and can't find my mistake. Help would be greatly appreciated!!!
     
  2. jcsd
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