In[]:=
Clear["Global`*"]​​T0=303;Tinf=373;ρ=2200;Cp=700;α=k/(ρ*Cp);​​ pde=D[T[z,t],t]==α*D[T[z,t],{z,2}];​​ cond={D[T[0,t],z]==0,T[z,0]==T0,T[0,t]==Tinf};​​sol=DSolve[{pde,cond},T[z,t],{z,t}]//FullSimplify​​​​
DSolve
:Equation or list of equations expected instead of True in the first argument 
(0,1)
T
[z,t]
k
(2,0)
T
[z,t]
1540000
,{True,T[z,0]303,T[0,t]373}.
Out[]=
DSolve1540000
(0,1)
T
[z,t]k
(2,0)
T
[z,t],{True,T[z,0]303,T[0,t]373},T[z,t],{z,t}