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//Variable declaration:
po = 53*16.0185 //Density of oil (kg/m^3)
co = 0.46*4186.7 //Heat capacity of oil (J/kg. C)
pi = %pi
muo = 150/1000 //Dynamic viscosity of oil (kg/m.s)
ko = 0.11*1.7303 //Thermal conductivity of oil (W/m. C)
qo = 28830*4.381*10**-8 //Volumetric flowrate of oil (m^3/s)
pw = 964 //Density of water (kg/m^3)
cw = 4204 //Heat capacity of water (J/kg. C)
muw = 0.7/3600*1.4881 //Dynamic viscosity of water (kg/m.s)
kw = 0.678 //Thermal conductivity of water (W/m. C)
qw = 8406*4.381*10**-8 //Volumetric flowrate of water (m^3/s)
t1 = 23.5 //Initial temperature of oil ( C)
t2 = 27 //Final temperature of oil ( C)
T1 = 93 //Water heating temperature of water ( C)
syms T2 //Minimum temperature of heating water ( C)
syms A //Heat transfer area (m^2)
Uc = 35.4 //Clean heat transfer coefficient (W/m^2.K)
Rf = 0.0007 //Thermal resistance (m^2.K/W)
D = 6*0.0254 //Inside diameter of pipe (m)
//Calculation:
vo = muo/po //Kinematic viscosity of oil (m^2/s)
mo = po*qo //Mass flowrate of oil (kg/s)
vw = muw/pw //Kinematic viscosity of (m^2/s)
mw = pw*qw //Masss flow rate of water (kg/s)
Q1 = mo*co*(t2-t1) //Duty of exchanger of oil (W)
T2m = t1 //Lowest possible temperature of the water ( C) (part 1)
Qmw = mw*cw*(T1-T2m) //Maximum duty of exchanger of water (W) (part 2)
Q2 = mw*cw*(T1-T2) //Duty of exchanger of water in terms of T2 (W)
x = eval(solve(Q1-Q2,T2)) //Solving value for T2 ( C)
T3 = x; //Minimum temperature of heating water ( C)
DT1 = T3-t1 //Inlet temperature difference ( C)
DT2 = T1-t2 //Outlet temperature difference ( C)
DTlm = (DT1-DT2)/log(DT1/DT2) //Log mean temperature difference ( C)
Ud1 = 1/Uc+Rf //Dirty heat transfer coefficient (W/m^2.K) (part 3)
Ud2 = 34.6 //Dirty heat transfer coefficient (W/m^2. C)
Q3 = Ud2*A*DTlm //Duty of exchanger (W) (part 4)
y = eval(solve(Q1-Q3,A)) //Heat transfer area (m^2)
A1 = y //Required heat transfer area (m^2)
L = A1/(pi*D) //Required heat transfer length (m)
Qmo = mo*co*(T1-t1) //Maximum duty of exchanger of oil (W) (part 5)
Qm = Qmw //Maximum duty of exchanger (W)
E = Q1/Qm*100 //Effectiveness (%)
NTU = Ud2*A1/(mw*cw) //Number of transfer units
//Result:
disp("1. The lowest possible temperature of the water is :")
disp(T2m)
disp(" C .")
disp("2. The log mean temperature difference is : ")
disp (DTlm)
disp(" C .")
disp("3. The overall heat transfer coefficient for the new clean exchanger is : ")
disp (Ud2)
disp ("W/m^2. C .")
disp("4. The length of the double pipe heat exchanger is : ")
disp(L)
disp (" m .")
disp("5. The effectiveness of the exchanger is : ")
disp(E)
disp("%")
disp("The NTU of the exchanger is : ")
disp(NTU)
// Answers are correct. Please calculate manually.
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