Needs["VectorAnalysis`"]

SetCoordinates[Cartesian[x,y,z]];

koefRozt=14*(10^(-6));
ΔT=1320.;
delka0=1;
Δdelka=koefRozt*ΔT*delka0;
Print["prodlouzeni je ",100Δdelka," cm"]

d=0.2;
P=2000;
S=2*(0.25*0.25+2*0.25*0.3);
λ=0.155;
ρ=600;
cp=1000;
To=20;
α=14;
ϵ=0.7;
σ=5.67*(10^(-8));

rce=ρ*cp*D[T[x,t],t]==Div[λ*Grad[T[x,t]]]

poc=T[x,0]==20;

qx=-(P/S)*(t/(t+10));
Tnastavena=1100;
okrUvnitr=qx*(1-Tanh[((T[x,t]-Tnastavena)/20)])*0.5==-λ*Derivative[1,0][T][x,t]/.x->d

Plot[(1-Tanh[((T-Tnastavena)/20)])*0.5,{T,1000,1200}];

qVen=α*(T[x,t]-To)+ϵ*σ*((((T[x,t]+273))^4)-(((To+273))^4))/.x->0;
okrVenku=-λ*Derivative[1,0][T][x,t]==-qVen/.x->0

Plot[(t/(t+10)),{t,0,100}];

hodina=3600;
tmax=15*hodina;
res=NDSolve[{rce,poc,okrUvnitr,okrVenku},T[x,t],{x,0,d},{t,0,tmax}][[1]]
Plot3D[T[x,t]/.res,{x,0,d},{t,0,tmax},AxesLabel->{"x[m]","t[s]","T[°C]     "}]

{rce,poc,okrUvnitr,okrVenku}