Contents
dati1=[1084.62 100 0
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1082.88 99.7069 0.29315
1080.51 99.3211 0.678928
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341.218 3.56116 96.4388
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dati8=[226.842 0.0058372 99.9942
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107.437 39.0686 60.9314
115.937 39.0686 60.9314
132.937 39.0686 60.9314
166.937 39.0686 60.9314
183.937 39.0686 60.9314
186.062 39.0686 60.9314
187.125 39.0686 60.9314
187.391 39.0686 60.9314
187.523 39.0686 60.9314
187.523 39.0686 60.9314];
dati82=[100 0.000257679 99.9997
100 0.000257679 99.9997];
plot(dati1(:,1),dati1(:,2),dati2(:,1),dati2(:,2),dati3(:,1),dati3(:,2),dati4(:,1),dati4(:,2),dati5(:,1),dati5(:,2),dati6(:,1),dati6(:,2),dati7(:,1),dati7(:,2),dati8(:,1),dati8(:,2),dati9(:,1),dati9(:,2),dati10(:,1),dati10(:,2));
hold;
plot(dati11(:,1),dati11(:,2),dati12(:,1),dati12(:,2),dati13(:,1),dati13(:,2),dati14(:,1),dati14(:,2),dati15(:,1),dati15(:,2),dati16(:,1),dati16(:,2),dati17(:,1),dati17(:,2),dati18(:,1),dati18(:,2),dati19(:,1),dati19(:,2),dati20(:,1),dati20(:,2));
plot(dati21(:,1),dati21(:,2),dati22(:,1),dati22(:,2),dati23(:,1),dati23(:,2),dati24(:,1),dati24(:,2),dati25(:,1),dati25(:,2),dati26(:,1),dati26(:,2),dati27(:,1),dati27(:,2),dati28(:,1),dati28(:,2),dati29(:,1),dati29(:,2),dati30(:,1),dati30(:,2));
plot(dati31(:,1),dati31(:,2),dati32(:,1),dati32(:,2),dati33(:,1),dati33(:,2),dati34(:,1),dati34(:,2),dati35(:,1),dati35(:,2),dati36(:,1),dati36(:,2),dati37(:,1),dati37(:,2),dati38(:,1),dati38(:,2),dati39(:,1),dati39(:,2),dati40(:,1),dati40(:,2));
plot(dati41(:,1),dati41(:,2),dati42(:,1),dati42(:,2),dati43(:,1),dati43(:,2),dati44(:,1),dati44(:,2),dati45(:,1),dati45(:,2),dati46(:,1),dati46(:,2),dati47(:,1),dati47(:,2),dati48(:,1),dati48(:,2),dati49(:,1),dati49(:,2),dati50(:,1),dati50(:,2));
plot(dati51(:,1),dati51(:,2),dati52(:,1),dati52(:,2),dati53(:,1),dati53(:,2),dati54(:,1),dati54(:,2),dati55(:,1),dati55(:,2),dati56(:,1),dati56(:,2),dati57(:,1),dati57(:,2),dati58(:,1),dati58(:,2),dati59(:,1),dati59(:,2),dati60(:,1),dati60(:,2));
plot(dati61(:,1),dati61(:,2),dati62(:,1),dati62(:,2),dati63(:,1),dati63(:,2),dati64(:,1),dati64(:,2),dati65(:,1),dati65(:,2),dati66(:,1),dati66(:,2),dati67(:,1),dati67(:,2),dati68(:,1),dati68(:,2),dati69(:,1),dati69(:,2),dati70(:,1),dati70(:,2));
plot(dati71(:,1),dati71(:,2),dati72(:,1),dati72(:,2),dati73(:,1),dati73(:,2),dati74(:,1),dati74(:,2),dati75(:,1),dati75(:,2),dati76(:,1),dati76(:,2),dati77(:,1),dati77(:,2),dati78(:,1),dati78(:,2),dati79(:,1),dati79(:,2),dati80(:,1),dati80(:,2));
plot(dati81(:,1),dati81(:,2));
hold;
grid on
xlabel('Temperatura [ºC]')
ylabel('% Cu')
plot(100-dati1(:,2), dati1(:,1));
plot(100 - dati55(:,2), dati55(:,1));
plot(100- dati1(:,2),dati1(:,1),100- dati55(:,2),dati55(:,1));
plot(dati1(:,1),dati1(:,2),dati55(:,1),dati55(:,2));
T=[800:1:1086];
c0=88;
cl=0.0000731*T.^2-0.04648*T+64.08;
cs=-0.000168*T.^2+0.3649*T-98.19;
fl=(c0-cs)./(cl-cs);
fs=(cl-c0)./(cl-cs);
plot(T,cl,'--',T,cs,'--')
hold on
plot(dati1(:,1),dati1(:,2),dati55(:,1),dati55(:,2));
xlabel('Temperatura [ºC]')
ylabel('% Cu')
legend('approx liquidus','approx solidus','liquidus','solidus')
f=fs+fl;
plot(T,fl,T,fs,T,f,'--');
grid on
legend('f_l','f_s','f_l+f_s')
xlabel('Temperatura [ºC]')
axis([800 1086 -5 5])
plot(T,fl,T,fs);
grid on
legend('f_l','f_s')
xlabel('Temperatura [ºC]')
axis([820 972 0 1])
Current plot held
Current plot released
Calcolo della densità
a_cu=7552.21;
b_cu=1.061386;
c_cu=-0.000668;
a_sn=2.73;
b_sn=0.006429;
c_sn=0;
d_sn=-1.307482;
e_sn=0.023920;
CL=12;
T=[800:1:1086];
densita_l=a_cu+b_cu*T+c_cu*T.^2+(a_sn+b_sn*T+c_sn*T.^2+d_sn*CL+e_sn*CL^2)*CL;
figure(9)
plot(T,densita_l)
xlabel('Temperatura [ºC]')
ylabel('Densità [kg/m^3]')
title('Densità della fase liquida [kg/m^3] in funzione della temperatura')
Tif=[820:1:972];
densita_lc=a_cu+b_cu*Tif+c_cu*Tif.^2+(a_sn+b_sn*Tif+c_sn*Tif.^2+d_sn*CL+e_sn*CL^2)*CL;
a_cu=8945.62;
b_cu=-0.460976;
c_cu=-0.0000614;
a_sn=-1.46;
b_sn=-0.005569;
c_sn=0.000010;
d_sn=0.121010;
Ts=[600:1:972];
densita_s=a_cu+b_cu*Ts+c_cu*Ts.^2+(a_sn+b_sn*Ts+c_sn*Ts.^2+d_sn*CL)*CL;
figure(10)
plot(Ts,densita_s)
xlabel('Temperatura [ºC]')
ylabel('Densità [kg/m^3]')
title('Densità della fase solida [kg/m^3] in funzione della temperatura')
Tif=[820:1:972];
densita_sc=a_cu+b_cu*Tif+c_cu*Tif.^2+(a_sn+b_sn*Tif+c_sn*Tif.^2+d_sn*CL)*CL;
Tif=[820:1:972];
cl=0.0000731*Tif.^2-0.04648*Tif+64.08;
cs=-0.000168*Tif.^2+0.3649*Tif-98.19;
fl=(c0-cs)./(cl-cs);
fs=(cl-c0)./(cl-cs);
densita=1./((fl./densita_lc)+((1-fl)./densita_sc));
figure(11)
plot(Tif,densita)
xlabel('Temperatura [ºC]')
ylabel('Densità [kg/m^3]')
title('Densità complessiva [kg/m^3] fra temperature di inizio e fine solidificazione')
figure(12)
plot(T(1,172:1:286),densita_l(1,172:1:286),Tif,densita,Ts(1,1:1:220),densita_s(1,1:1:220))
grid on
xlabel('Temperatura [ºC]')
ylabel('Densità [kg/m^3]')
title('Densità della fase liquida e solida e complessiva [kg/m^3] in funzione della temperatura')
legend('Fase liquida','Fase L+FCC','Fase solida')
Calcolo della conducibilità
a_cu=134,407;
b_cu=0.026743;
c_cu=0;
a_sn=-2.474;
b_sn=0;
c_sn=0;
d_sn=-14.779;
n_sn=0.04;
k_l=a_cu+b_cu*T+c_cu*T.^2+(a_sn+b_sn*T+c_sn*T.^2)*CL+d_sn*CL*10^-(n_sn*CL);
figure(13)
plot(T,k_l)
grid on
xlabel('Temperatura [ºC]')
ylabel('Conducibilità termica [W/K·m]')
title('Conducibilità termica della fase liquida [W/K·m] in funzione della temperatura')
k_lc=a_cu+b_cu*Tif+c_cu*Tif.^2+(a_sn+b_sn*Tif+c_sn*Tif.^2)*CL+d_sn*CL*10^-(n_sn*CL);
a_cu=398.61;
b_cu=-0.042062;
c_cu=-0.0000205;
a_sn=-15.61;
b_sn=0;
c_sn=0;
d_sn=-126.177;
e_sn=0.125745;
n_sn=0.08;
CS=12;
k_s=a_cu+b_cu*Ts+c_cu*Ts.^2+(a_sn+b_sn*Ts+c_sn*Ts.^2)*CS+(d_sn+e_sn*Ts)*CS*10^-(n_sn*CS);
figure(14)
plot(Ts,k_s)
grid on
xlabel('Temperatura [ºC]')
ylabel('Conducibilità termica [W/K·m]')
title('Conducibilità termica della fase solida [W/K·m] in funzione della temperatura')
k_sc=a_cu+b_cu*Tif+c_cu*Tif.^2+(a_sn+b_sn*Tif+c_sn*Tif.^2)*CS+(d_sn+e_sn*Tif)*CS*10^-(n_sn*CS);
A=1;
k=(1-fl).*k_sc+A*fl.*k_lc;
figure(15)
plot(T(1,172:1:286),k_l(1,172:1:286),Tif,k,Ts(1,1:1:220),k_s(1,1:1:220))
grid on
xlabel('Temperatura [ºC]')
ylabel('Conducibilità termica [W/K·m]')
title('Conducibilità termica della fase liquida e solida e complessiva [W/K·m] in funzione della temperatura')
legend('Fase liquida','Fase L+FCC','Fase solida')
a_cu =
134
Viscosità
a_cu=7552.21;
b_cu=1.061386;
c_cu=-0.000668;
a_sn=2.73;
b_sn=0.006429;
c_sn=0;
d_sn=-1.307482;
e_sn=0.023920;
T=[972:1:1184];
Tk=[1245:1:1457];
CL=12;
densita_l=a_cu+b_cu*Tk+c_cu*Tk.^2+(a_sn+b_sn*Tk+c_sn*Tk.^2+d_sn*CL+e_sn*CL^2)*CL;
h=6.626e-34;
N=6.022e23;
R=8.3145;
M_cu=63.54;
M_sn=118.69;
X_cu=0.932;
X_sn=0.068;
M=X_cu*M_cu+(1-X_cu)*M_sn;
a_cu=22153;
b_cu=20.878;
deltaG_cu=a_cu+b_cu*Tk;
a_sn=5516;
b_sn=25.437;
deltaG_sn=a_sn+b_sn*Tk;
c=0.5;
L=(-9003-5.838*Tk)+(-20100+3.637*Tk)*(1-2*X_sn)+(-10528)*(1-2*X_sn)^2;
Ge=(1-X_sn)*X_sn*L;
deltaG=X_cu*deltaG_cu+X_sn*deltaG_sn+c*(X_cu*R*Tk*log(X_cu)+X_sn*R*Tk*log(X_sn)+Ge);
eta=1000*((h*N*densita_l)./M).*exp(deltaG./(R.*Tk));
figure(16)
plot(T,eta)
xlabel('Temperatura [ºC]')
ylabel('Viscosità [Pa·s]')
title('Viscosità della fase liquida secondo elaborazione di Miettinen')
A=0.00115;
E=14750;
Tk=[1245:1:1457];
R=8.134;
eta2=A*exp(E./(R*Tk));
T=[972:1:1184];
figure(17)
plot(T,eta2)
xlabel('Temperatura [ºC]')
ylabel('Viscosità [Pa·s]')
title('Viscosità della fase liquida secondo equazione di Arrhenius')
figure(18)
plot(Tk,eta,Tk,eta2)
xlabel('Temperatura [ºC]')
ylabel('Viscosità [Pa·s]')
title('Miettinen vs Arrhenius')
Legend('\eta Miettinen','\eta Arrhenius')
errore=((eta2-eta)./eta2)*100;
figure(18)
plot(T,errore)