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  Basically I’m trying to op...

Colin6919 5
March 20 2012

 

Basically I’m trying to optimize a heat exchanger with N fin of zero thickness and an outer diameter of Do. I'm just trying to pull the maximum point off the 3d graph but I can't seem to get that to work. I suppose I could use lagrange multipliers but figured there was probably an easier way.

 

Thanks for any help!

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restart
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NULL
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Q := Cmin*(Th-Tc)*(1-exp(-NTU*(1-Cmin/Cmax)))/(1-Cmin*exp(-NTU*(1-Cmin/Cmax))/Cmax);

Cmin*(Th-Tc)*(1-exp(-NTU*(1-Cmin/Cmax)))/(1-Cmin*exp(-NTU*(1-Cmin/Cmax))/Cmax)

 (1)
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NTU := UA/Cmin;

UA/Cmin

 (2)
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Cmax := (1/4)*rho[1]*Pi*Di*U[1]*Cp[1];

(1/4)*rho[1]*Pi*Di*U[1]*Cp[1]

 (3)
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Cmin := rho[2]*Ac*N*U[2]*Cp[2];

rho[2]*Ac*N*U[2]*Cp[2]

 (4)
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UA := 1/(1/(h[2]*Atotal)+1/(h[1]*Di*Pi*L));

1/(1/(h[2]*Atotal)+1/(h[1]*Di*Pi*L))

 (5)
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Afin := 2*N*flengthc*L;

2*N*flengthc*L

 (6)
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Abase := (Pi*Di-t*N)*L;

(Pi*Di-t*N)*L

 (7)
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Atotal := Afin+Abase;

2*N*flengthc*L+(Pi*Di-t*N)*L

 (8)
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flength := (Do-Di)*(1/2);

(1/2)*Do-(1/2)*Di

 (9)
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flengthc := flength+Pi*Do/(2*N)

(1/2)*Do-(1/2)*Di+(1/2)*Pi*Do/N

 (10)
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eq[1] := dp[1] = (4*f[1]*L/Dh[1]*(1/2))*rho[1]*U[1]^2;

dp[1] = 2*f[1]*L*rho[1]*U[1]^2/Dh[1]

 (11)
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eq[2] := dp[2] = (4*f[2]*L/Dh[2]*(1/2))*rho[2]*U[2]^2;

dp[2] = 2*f[2]*L*rho[2]*U[2]^2/Dh[2]

 (12)
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f[1] := 0.79e-1/(rho[1]*U[1]*Dh[1]/mu[1])^(1/4);

0.79e-1/(rho[1]*U[1]*Dh[1]/mu[1])^(1/4)

 (13)
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U[1] := (dp[1]*(rho[1]*Dh[1]/mu[1])^(1/4)*Dh[1]/(.158*L*rho[1]))^(1/1.75);

2.870187284*(dp[1]*(rho[1]*Dh[1]/mu[1])^(1/4)*Dh[1]/(L*rho[1]))^.5714285714

 (14)
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f[2] := 0.79e-1/(rho[2]*U[2]*Dh[2]/mu[2])^(1/4);

0.79e-1/(rho[2]*U[2]*Dh[2]/mu[2])^(1/4)

 (15)
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U[2] := (dp[2]*(rho[2]*Dh[2]/mu[2])^(1/4)*Dh[2]/(.158*L*rho[2]))^(1/1.75);

2.870187284*(dp[2]*(rho[2]*Dh[2]/mu[2])^(1/4)*Dh[2]/(L*rho[2]))^.5714285714

 (16)
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h[1] := 0.23e-1*(rho[1]*U[1]*Dh[1]/mu[1])^(4/5)*Pr[1]^(1/3)*k[1]/Dh[1];

0.5346333238e-1*(rho[1]*(dp[1]*(rho[1]*Dh[1]/mu[1])^(1/4)*Dh[1]/(L*rho[1]))^.5714285714*Dh[1]/mu[1])^(4/5)*Pr[1]^(1/3)*k[1]/Dh[1]

 (17)
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h[2] := 0.23e-1*(rho[2]*U[2]*Dh[2]/mu[2])^(4/5)*Pr[2]^(1/3)*k[2]/Dh[2];

0.5346333238e-1*(rho[2]*(dp[2]*(rho[2]*Dh[2]/mu[2])^(1/4)*Dh[2]/(L*rho[2]))^.5714285714*Dh[2]/mu[2])^(4/5)*Pr[2]^(1/3)*k[2]/Dh[2]

 (18)
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Dh[1] := Di;

Di

 (19)
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Dh[2] := 4*Ac/P;

4*Ac/P

 (20)
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Ac := Pi*(Do^2-Di^2)/(4*N)-t*flength;

(1/4)*Pi*(Do^2-Di^2)/N-t*((1/2)*Do-(1/2)*Di)

 (21)
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P := Pi*(Do-Di)/N+2*flength-2*t;

Pi*(Do-Di)/N+Do-Di-2*t

 (22)
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Qnum := evalf(subs(dp[1] = 750, dp[2] = 250, rho[1] = 1000, rho[2] = 1.2, mu[1] = 0.1e-2, mu[2] = 0.1846e-4, Pr[1] = 3.15, Pr[2] = .7, L = 4*V/(Pi*Do^2), V = 0.5e-1, k[1] = .645, k[2] = 0.263e-1, Cp[1] = 4130, Cp[2] = 1004, Di = 0.5e-1, Tc = 25, Th = 95, t = 0, kc = 52, Q)):
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plot3d(Qnum(Do,N),Do=0.05..0.5,N=1..800,axes=boxed, labels = ['Do','N', 'Q'], view = [0.05 .. 0.5,1..800, 0..25000]);

 
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plottools[getdata(plot3d(Qnum(Do, N), Do = 0.5e-1 .. .5, N = 1 .. 400)[3])]

Error, index must evaluate to a name when indexing a module

  
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