ro=2400;
Cp=1011;
Tout=5+273;
ToutS=-5+273;
Tin=20+273;
sigma=5.775*(10^(-8));
epsilon=0.93;
alfa=15;
lambda=0.3;
tloustka=0.3;
tMax=200000;

rce=ro*Cp*D[T[x,t],t]==lambda*D[D[T[x,t],x],x];
pocPodminka=T[x,0]==Tout;
okrVlevo=T[0,t]==Tin*Tanh[t]+Tout*(1-Tanh[t]);
okrVpravo=-lambda*D[T[x,t],x]==(alfa*(T[x,t]-Tout)+sigma*epsilon*((((T[x,t]))^4)-(((ToutS))^4)))*(t/(t+1))/.x->tloustka;

res=NDSolve[{rce,pocPodminka,okrVlevo,okrVpravo},T[x,t],{x,0,tloustka},{t,0,tMax}]

Plot3D[T[x,t]-273/.res,{x,0,tloustka},{t,0,tMax}]