Heat Transfer during Mixing (Just need confirmation!)

7wgh

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!