Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];
Needs["VectorAnalysis`"]
SetCoordinates[Cartesian[x,y,z]];

U=230*0.9;
Tin=5;
Tout=50;
ρ=1000;
mm=0.001;
cm=10mm;
m=40cm;
d=5mm;
c=4186.;
msteckou=0.2;
Vsteckou=(msteckou/ρ);
vx=(Vsteckou/(m*d));
Print["vx= ",vx," m/s"]

dataMB={{20,(1/70.)},{75,(1/30)}};
dataPha={{10,(1/35.)},{50,(1/10.)}};
gammaMB[T_]=Fit[dataMB,{1,T},T]
gammaPha[T_]=Fit[dataPha,{1,T},T]

rce={T'[x]==((gammaMB[T[x]])/(vx*ρ*c))*((((U/d)))^2),T[0]==Tin};
res=DSolve[rce,T[x],x][[1]]//Simplify
vysteplota=T[x]/.res
delka=x/.FindRoot[vysteplota==Tout,{x,0.1}];
Plot[vysteplota,{x,0,1}];

rce={T'[x]==((gammaPha[T[x]])/(vx*ρ*c))*((((U/d)))^2),T[0]==Tin};
resPha=DSolve[rce,T[x],x][[1]]//Simplify
vysteplotaPha=T[x]/.resPha
delkaPha=x/.FindRoot[vysteplotaPha==Tout,{x,0.1}]
Plot[{vysteplota,vysteplotaPha},{x,0,0.7}]

ClearAll[delka]
Rth=(1/(2*Pi*λ*delka))*Log[(r2/r1)]+(1/(2*Pi*α*r2*delka));
0==D[Rth,r2]//Solve[#,r2]&

Plot[Rth/.{λ->0.3,α->10,r1->1mm,delka->1},{r2,1mm,80mm}]

(λ/α)/.{λ->0.3,α->10}

(λ/α)/.{λ->0.01,α->15}

dos={r1->10cm,r2->10.1cm,delka->1,ϵ->0.01,T1->45,λ->400,σ->5.67*(10^(-8)),α->4,To->20};
Rth=(1/(2*Pi*λ*delka))*Log[(r2/r1)];
S=2*Pi*r2*delka;
Qk=α*S*(Tp-To);
Qr=ϵ*σ*S*((((Tp+273))^4)-(((To+273))^4));
rce=((T1-Tp)/Rth)==Qk+Qr/.dos;
Select[Solve[rce],(Im[#[[1,2]]]==0)&&(Re[#[[1,2]]]>0)&][[1]]
Qk+Qr/.%/.dos

((#)^2)&[5]

Quiet@Remove["Global`*"];
$HistoryLength=2;

alfas={2,10,30,100,1000};
σ=5.67*(10^(-8));
sol[α_]:=T1-270/.FindRoot[α*(T1-293)==σ*((T1^4)-(293^4)),{T1,2000}];
sol/@alfas

sol[α_]:=T1-270/.Solve[α*(T1-293)==σ*((T1^4)-(293^4)),T1];
sol[2]

Needs["VectorAnalysis`"]
SetCoordinates[Cartesian[x,y,z]];
Div[λ[T[x]]*Grad[T[x]]]

cm=0.01;
a=1;
b=1.5;
c=2;
Tpec=1200;
λPlastizol=0.4;
Tokoli=20;
λSibral=0.15;
dPlastizol=5cm;
RthPlastizol=dPlastizol/(λPlastizol*2*((a+dPlastizol)*(b+dPlastizol)+(a+dPlastizol)*(c+dPlastizol)+(b+dPlastizol)*(c+dPlastizol)));
RthSibral=dSibral/(λSibral*2*((a+2dPlastizol+dSibral)*(b+2dPlastizol+dSibral)+(a+2dPlastizol+dSibral)*(c+2dPlastizol+dSibral)+(b+2dPlastizol+dSibral)*(c+2dPlastizol+dSibral)));
Spec=2*((a+2dPlastizol+2dSibral)*(b+2dPlastizol+2dSibral)+(a+2dPlastizol+2dSibral)*(c+2dPlastizol+2dSibral)+(b+2dPlastizol+2dSibral)*(c+2dPlastizol+2dSibral));
α=5;
Qk=α*Spec*(Tpovrch-Tokoli);
ϵ=0.9;
Qr=ϵ*σ*Spec*((((Tpovrch+273))^4)-(((Tokoli+273))^4));

rce[dSibrall_]:=Qk+Qr/.FindRoot[((Tpec-Tpovrch)/(RthPlastizol+RthSibral))==Qk+Qr/.dSibral->dSibrall,{Tpovrch,320}]/.dSibral->dSibrall;
rce[0.20]