I am trying to design a control system for a simple heating system (I am not en expert in this area) and I want to set the mass flow on both sides of the counter-flow heat exchanger at a given moment (in a simplified way for now). The cold water stream has temperature T[sub]1[/sub] and the mass flow is m[sub]1[/sub]. I want to heat it to T[sub]final[/sub] temperature. The warm water stream has a temperature T[sub]2[/sub]>T[sub]final[/sub] and the question is what should be the mass flow of the warm stream m[sub]2[/sub]? I want to assume (for now) an ideal exchanger, which means that the overall heat transfer coeffisient OHTC can be as big as I want. For now, I used a simple equation:
m[sub]1[/sub]*cp_water*(T[sub]final[/sub]-T[sub]1[/sub]) = m[sub]2[/sub]*cp_water*(T[sub]2[/sub]-T[sub]x[/sub])
I have two unknowns: m[sub]2[/sub] and T[sub]x[/sub]. I assumed that T[sub]x[/sub] can go down to T[sub]1[/sub], hence I can estimate (T[sub]x_min[/sub] = T[sub]1[/sub]) that:
m1*(T[sub]final[/sub] - T[sub]1[/sub])<= m[sub]2[/sub](T[sub]2[/sub]-T[sub]1[/sub])
hence:
m[sub]2[/sub] >= m[sub]1[/sub]*(T[sub]final[/sub]-T[sub]1[/sub])/(T[sub]2[/sub]-T[sub]1[/sub])
However, this is only an estimate (and I don't know if it is corrent)and does not take into account the flows in the exchanger.
Could someone help me (give me the right equation) or point me to a source that would allow me to correctly calculate m[sub]2[/sub]?
m[sub]1[/sub]*cp_water*(T[sub]final[/sub]-T[sub]1[/sub]) = m[sub]2[/sub]*cp_water*(T[sub]2[/sub]-T[sub]x[/sub])
I have two unknowns: m[sub]2[/sub] and T[sub]x[/sub]. I assumed that T[sub]x[/sub] can go down to T[sub]1[/sub], hence I can estimate (T[sub]x_min[/sub] = T[sub]1[/sub]) that:
m1*(T[sub]final[/sub] - T[sub]1[/sub])<= m[sub]2[/sub](T[sub]2[/sub]-T[sub]1[/sub])
hence:
m[sub]2[/sub] >= m[sub]1[/sub]*(T[sub]final[/sub]-T[sub]1[/sub])/(T[sub]2[/sub]-T[sub]1[/sub])
However, this is only an estimate (and I don't know if it is corrent)and does not take into account the flows in the exchanger.
Could someone help me (give me the right equation) or point me to a source that would allow me to correctly calculate m[sub]2[/sub]?