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Heat Transfer during Mixing (Just need confirmation!)

  1. Apr 10, 2012 #1
    Hi Everybody!

    This is my first post on this forum! Anyways... I have a problem where I think I have the correct answer, however I would like some confirmation.

    Problem

    I have TWO inlet streams (m1, m2) that connect to each other into ONE outlet stream (m3). I need to solve m1 and m2 (See below for known parameters)

    Therefore the equations that I am using are: m1 + m2 = m3 and Q1 + Q2 = Q3

    Known Parameters
    T1, T2, T3 and m3 (the total outlet flow)

    I need to determine the mass flow of the inlet streams (i.e. m1 and m2).

    My Solution

    Q1 + Q2 = Q3
    m1cp(Tr - T1) + m2cp(Tr - T2) = m3cp(T3-Tr)
    *Tr is the reference point where the two inlet streams meet and mix together*
    Since no heat is being generated, only mixed, I can assume Tr will just be a weighted average of m1 and m2 therefore:

    Tr = (m1T1 + m2T2) / m3

    Since I only need a ballpark figure and the temperature differences aren't too far apart, I assume the specific heat values (cp) to be equal so I can cancel them out.

    What I'm left with is

    m1(Tr-T1) + (m3-m1)(Tr-T2) = m3cp(T3-Tr)

    All I have to do is plug in the equation for Tr and eventually I'll get

    m1 = m3(T3-T2) / (T1-T2)

    Final Statements

    I can do the last steps myself so to save your time, I only need confirmation on:
    1) Is my Q1 + Q2 = Q3 equation correct?
    2) Is my Tr equation correct?

    Thank You!

    Remember: You're all f**king awesome, dont let nobody tell you otherwise!
     
  2. jcsd
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