κ:=60;
ρ:=7800;
c:=440;
T0:=273.15;
T1:=373.15;
R:=0.3;
a:=(κ/(c*ρ));
(* Nmax to liczba uwzględnianych członów w szeregu *)
f[r_,t_,n_]:=((((-1))^(n+1))/n)*Exp[-((a*(n^2)*(π^2))/(R^2))t]*Sin[((n*π)/R)r];
sum[r_, t_, Nmax_]:=Sum[f[r,t,n],{n,1,Nmax}] 
T[r_,t_, Nmax_]:=T0+((2*(T1-T0)*R)/(π*r))*sum[r, t, Nmax];
(* Nmax = 1 *)
Plot3D[T[r,t, 1],{r,0,0.3},{t,0,2000},PlotTheme->"Detailed",AxesLabel->{"r","t", "T(r,t)"}]

(* Nmax = 10 *)
Plot3D[T[r,t, 10],{r,0,0.3},{t,0,2000},PlotTheme->"Detailed",AxesLabel->{"r","t", "T(r,t)"}]

(* Nmax = 100 *)
Plot3D[T[r,t, 100],{r,0,0.3},{t,0,2000},PlotTheme->"Detailed",AxesLabel->{"r","t", "T(r,t)"}]

(* Nmax = 1000 *)
Plot3D[T[r,t, 1000],{r,0,0.3},{t,0,2000},PlotTheme->"Detailed",AxesLabel->{"r","t", "T(r,t)"}]