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MINIMUM OF GAMMA FUNCTION

## This string finds the minimum of the Gamma function
## integral(x^(alpha-1)*exp(-x))dx) (x=[0,infinity])
## in the interval 0<alpha<4.
dx=1E-2; ## Increment in x
x=0:dx:100; ## x array
Gamma=[]; ## Empty Gamma function
alpha=0.00:dx:4.00; ## The independent variable of Gamma function
for i=1:length(alpha)
## Call the trapezoid function to
## calculate all entries of Gamma function
## corresponding to entries of alpha
f=x.^(alpha(i)-1).*exp(-x); ## integrand of Gamma function
Gamma(i)=trapezoid(x,f);
endfor
plot(alpha,Gamma);
title('Gamma values vs alpha');
legend('Gamma(alpha)');
xlabel('alpha');
ylabel('Gamma');
## The following 'for loop' finds the minimum value of Gamma
## and the corresponding alpha value.
minimum=Gamma(1);
for n=1:length(Gamma)
if(minimum>Gamma(n))
minimum=Gamma(n);
n; ## The array index where the minimum of Gamma is.
m=alpha(n); ## The alpha value corresponding to the min of Gamma
endif
endfor;
printf('Minimum of the Gamma Function in the interval 0<alpha<4 is %f\n for the alpha=%f\n' ,minimum,m)
print('-dpsc',MINGAMMA.ps');
save -text MINGAMMA.dat

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NEWTON-RAPSON METHOD FOR HEAT FLOW

##Constants and initializations
a=5.67E-8; ## Stefan-Boltzman constant[Watt/meter^2Kelvin^4]
e=0.8; ## Rod surface emissivity [Dimensionless]
h=20; ## Heat transfer coefficient of air flow [W/m^2-K]
Tinf=Ts=25; ## Temperature of air and the walls of the close[Celcius]
D=0.1; ## Diameter of the rod[meter]
I2R=100; ## Electric power dissipated in rod (Ohmic Heat)[W]
T=[]; ## Temperature of the rod[*C]
T(1)=25; ## Initial guess of the temperature of the rod[*C]
Q=[]; ## Heat function [W]
Qp=[]; ## First derivative of Q wrt T [W/C*].
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Q(i)=pi*D*(h*(T(i)-Tinf)+e*a*(T(i)^4-Ts^4))-I2R;
Qp(i)=pi*D*(h+4*e*a*T(i)^3);
T(i+1)=T(i)-Q(i)/Qp(i); ## Newton-Rapson Method
endfor
printf('The steady state temperature is %f\n',T(i+1))
save -text HeatFlowTemp.dat
## The plot
t=1:100; ##temperature
for n=1:100
H(n)=pi*D*(h*(t(n)-Tinf)+e*a*(t(n)^4-Ts^4))-I2R;
endfor
plot(t,H)
xlabel('T(Celcius)');
ylabel('Q(Watt)');
legend('Q(T)');
title('Heat flow vs Temperatu…