<<BlackBodyRadiation`

Off[General::obspkg]

BlackBodyProfile[4000 Kelvin,5000 Kelvin,6000 Kelvin,PlotRange->{{0,2.0×(10^(-6))},{0,1.1×(10^14)}}]

λ=ElementData["Copper","ThermalConductivity"];
ρ=ElementData["Copper","Density"];
cp=ElementData["Copper","SpecificHeat"];

σ=5.67*(10^(-8));

Needs["VectorAnalysis`"]
SetCoordinates[Cartesian[x,y,z]];

Icurr=5000;
Tamb=20;
Tfirst=10;
xmax=50mm;
mm=0.001;
d=3mm;
S=((Pi*(d^2))/4);
αR=3.9*(10^(-3));
γ20=57*(10^6);
ρel=((1+αR*(T[x,t]-20))/(γ20));
J=(Icurr/S);
QV1=ρel*(J^2);
Ssurf=Pi*d*dx;
α=5;
ϵ=0.6;
Psurf=Ssurf*(α*(T[x,t]-Tamb)+ϵ*σ*((((T[x,t]+273))^4)-(((Tamb+273))^4)));
QV2=(Psurf/(S*dx));
QV=QV1-QV2;
tmax=1;
eqn=ρ*cp*D[T[x,t],t]==Div[λ*Grad[T[x,t]]]+QV;
initialCond=T[x,0]==Tfirst;
bound1=T[0,t]==Tamb;
bound2=T[xmax,t]==Tamb;
sol=NDSolve[{eqn,initialCond,bound1,bound2},T[x,t],{x,0,xmax},{t,0,tmax}][[1]]
Plot3D[T[x,t]/.sol,{x,0,xmax},{t,0,tmax}]