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TOTAL ISING ENERGY


function E=Ising_Energy(lattice,i,j,rneigh)
H=2; ## applied magnetic field times permeability[joule]
E=0; ## initial configuration energy[joule]
J0=1 ## coupling constant of function J, normaly in joule.
alpha=2 ## exponential constant of function J.
L=length(lattice); ## number of particles or spins in lattice
for r=1:rneigh
NN1=mod(j+r,L); NN1+=(NN1==0)*L;
NN2=mod(j-r,L); NN2+=(NN2==0)*L;
NN3=mod(i+r,L); NN3+=(NN3==0)*L;
NN4=mod(i-r,L); NN4+=(NN4==0)*L;
J=coupling(rneigh,J0,alpha);
dE=J*(lattice(i,NN1)+lattice(i,NN2)+
lattice(NN3,j)+lattice(NN4,j))-H*(sum((rand(L)>0.5)*2-1));
E+=-1*dE
endfor
endfunction

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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*].
for i=1:100
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…