Needs["VectorAnalysis`"]

ClearAll[x,T,d,T0,Td]
SetCoordinates[Cartesian[x,y,z]];
Div[Grad[T[x]]]
resT=DSolve[{T''[x]==0,T[0]==T0,T[d]==Td},T[x],x][[1]]
teplota=T[x]/.resT
qx=(-λ*Grad[teplota])[[1]]
Q=qx*S/.{d->0.6,S->1,λ->0.8,T0->15,Td->0}

dCihla=0.60;
dPolystyren=0.1;
xmax=dCihla+dPolystyren;
λCihla=0.8;
λPolystyren=0.04;
vyr[x_]:=a+b*x;
res=Solve[{vyr[-1]==λCihla,vyr[1]==λPolystyren}][[1]];
kStrmost=500;
λx=vyr[Tanh[kStrmost*(x-dCihla)]]/.res;
Plot[λx,{x,0,xmax},PlotRange->All,PlotStyle->Thick,AxesLabel->{"x[m]","λx[W.(m^(-1)).(K^(-1))]"},AxesOrigin->{0,0}];

rce=Div[λx*Grad[T[x]]]==0;
resT=DSolve[{rce,T[0]==T0,T[d]==Td},T[x],x][[1]];
teplx=(T[x]/.resT)/.{T0->15,Td->0,d->xmax};

resStrelba[derT_]:=T[x]/.NDSolve[{rce,T[0]==15,T'[0]==derT},T,{x,0,xmax},MaxStepSize->(10^(-3))xmax][[1]]
resStrelba[-5]

Manipulate[
tisk=resStrelba[der0];
Plot[{tisk,0},{x,0,xmax},PlotRange->All,PlotStyle->Thick,AxesLabel->{"x[m]","T[°C]"},AxesOrigin->{0,0}]
,{der0,-0.1,-20}]

derλx=D[λx,x]
Plot[derλx,{x,0,xmax},PlotRange->All,PlotStyle->Thick,AxesLabel->{"x[m]","λx'"},AxesOrigin->{0,0}]

tisk=resStrelba[-5.88];
Plot[{tisk,0},{x,0,xmax},PlotRange->All,PlotStyle->Thick,AxesLabel->{"x[m]","T[°C]"},AxesOrigin->{0,0}]

RthPred=(1/(αin*S))+(1/(αext*S))+(d1/(λ1*S));
RthPo=(1/(αin*S))+(1/(αext*S))+(d1/(λ1*S))+(d2/(λ2*S));
αin=6;
αext=15;
d1=0.45;
λ1=0.8;
λ2=0.04;
Solve[(RthPo/RthPred)==3,d2];
Tin=25;
Texter=-15;
Q=((Tin-Texter)/RthPred)
ΔTkonvekce=Q*(1/(αin*S));
Tstena=Tin-ΔTkonvekce
TstenaPo=Tin-(1/3)ΔTkonvekce