<< Calculus`VectorAnalysis`
SetCoordinates[Cartesian[x, y, z]];

resT = DSolve[{T''[x] == 0, T[0] == T1, 
              T[d] == T2}, T[x], 
            x][[1]];
teplota = T[x] /. resT;
qx = -λ*Grad[teplota][[1]] // Simplify

zed = {λ -> 0.8, d -> 0.3, T1 -> 15, 
          T2 -> 0};
qx /. zed

dosabPha = Solve[{a*10 + b == (1/35), 
            a*50 + b == (1. /10)}][[1]]

dosabMB = Solve[{a*20 + b == (1/72), 
            a*75 + b == (1. /30)}][[1]]

T[t] /. resT

FindRoot[(T[t] /. resT) == 100, {t, 10000}]

Ecko = (230/0.1);
ρ = 1000;
cp = 4186;
γ = a*T[t] + b /. dosabPha;
resT = DSolve[{T[0] == 
              10, ρ*cp*T'[t] == γ*(Ecko^2)}, T[t], 
          t][[1]]
tmax = 
        t /. FindRoot[(T[t] /. resT) == 100, {t, 
              1000}];
Plot[T[t] /. resT, {t, 0, tmax}, 
      PlotStyle -> {Hue[0.63], Thickness[0.008]}, 
      AxesLabel -> {"t[s]", "T[°C]"}]
Print["t= ", (tmax/60), " min"]

T1 = 4;
T2 = 45;
msteckou = 0.3;
cp = 4186;
Print["vykon= ", ((msteckou*cp*(T2 - T1))/1000), " \
kW"]

cm = 0.01;
mm = 0.1  cm;
d = 3  mm;
Ecko = (230/d);
ρ = 1000;
cp = 4186;
γ = a*T[x] + b /. dosabPha;
ρ = 1000;
Vsteckou = (msteckou/ρ);
m = 15  cm;
vx = (Vsteckou/(m*d));
resT = DSolve[{T[0] == 
                T1, ρ*cp*vx*T'[x] == γ*(Ecko^2)}, T[x], 
            x][[1]];
teplota = T[x] /. resT;
delka = 
        x /. FindRoot[
            teplota == T2, {x, 0.5}];
Plot[teplota, {x, 0, delka}, 
      PlotStyle -> {Hue[0.63], Thickness[0.008]}, 
      AxesLabel -> {"x[m]", "T[°C]"}]

cm = 0.01;
mm = 0.1  cm;
d = 3  mm;
Ecko = (230/d);
ρ = 1000;
cp = 4186;
γ = a*T[x] + b /. dosabMB;
ρ = 1000;
Vsteckou = (msteckou/ρ);
m = 15  cm;
vx = (Vsteckou/(m*d));
resT = DSolve[{T[0] == 
                T1, ρ*cp*vx*T'[x] == γ*(Ecko^2)}, T[x], 
            x][[1]];
teplota = 
        T[x] /. resT;
  
Plot[teplota, {x, 0, delka}, 
      PlotStyle -> {Hue[0.63], Thickness[0.008]}, 
      AxesLabel -> {"x[m]", "T[°C]"}]

λ = 0.8;
d = 0.45;
Tin = 25;
Texter = -18;
S = 1;
αin = 5;
αext = 23;
Solve[{Q == αin*S*(Tin - T1), 
        Q == αext*S*(T2 - Texter), 
        Q == ((T1 - T2)/((d/(λ*S))))}]

R1 = (1/(αin*S));
R2 = (1/(αext*S));
R3 = (d/(λ*S));
R4 = (diz/(λiz*S));
Rsum = R1 + R2 + R3 + R4;
Q = ((Tin - Texter)/Rsum);
λiz = 0.04;
Solve[Q == ((Tin - 18)/R1)]
resdiz = Solve[
          Rsum == 3*(Rsum - R4)][[1]]

(R4/R3) /. resdiz

Plot[{10  Log[ξ], (ξ^2) - 1},{ξ, 1, 10},AxesLabel->{"(r2/r1)","odpor,cena"},PlotStyle -> {{Hue[0], Thickness[0.008]}, {Hue[0.63], 
              Thickness[0.008]}}]

Rsum = 
      (1/(λ*2*Pi*delka))*Log[(r2/r1)] + 
        (1/(2  Pi*α*r2*delka))

D[Rsum, r2] == 0 // Solve[#, r2] &

dostepiz = {λ -> 0.04, α -> 
            15};
doseliz = {λ -> 0.4, α -> 15};

(λ/α) /. dostepiz
(λ/α) /. doseliz

Off[
      General::"spell1"]

<< Miscellaneous`PhysicalConstants`

γ = 57*(10^6);
mm = 0.001;
α = 10;
ϵ = 0.8;
Tmax = 60;
Tok = 20;
Tor = 15;
delka = 1;
prurez = 1  (mm^2);
polomer = 
        r /. Solve [
              prurez == Pi*(r^2)][[2]];
povrch = 2*Pi*polomer*delka;
Qk = α*povrch*(Tmax - Tok);
Print["Qk= ", Qk, "  W"]

σ = StefanConstant[[1]];

Qr = 
        povrch*ϵ*σ*((((Tmax + 273.15))^4) - (((Tor + 273.15))^4));
Print["Qr= ", Qr, "  W"]

odpor = delka/prurez/γ;
Print["R= ", odpor, "  Ω"]

Solve[odpor*(proud^2) == Qk + Qr];
Print["max proud= ", proud /. %[[2]], "  A"]

U = 400. ;
kW = 1000;
P = 30  kW;
cosfi = 1;
fi = -ArcCos[cosfi];
tanfi = ((-(Sqrt[1 - (cosfi^2)]))/cosfi);
(P/(U^2)) (1 - I*Tan[fi])
(P/(U^2)) (1 - I*tanfi)

46.9 - (125/(Sqrt[3])) + (187.5/(Sqrt[3]))

-93.8 + (62.5/(Sqrt[3])) - (187.5/(Sqrt[3]))

(125/(Sqrt[3])) - (62.5/(Sqrt[3]))

a = 0.6;
b = 0.5;
c = 0.5;
Tpec = 1200;
Tpl = 50;
Tor = 15;
Tok = 30;
cm = 0.01;
d1 = 3  cm;

    
datλPl = {{1100, 0.4}, {1000, 0.36}} // 
          Union;

      
λ1 = 
        Fit[datλPl, {1, T}, T] /. 
          T -> Tpec;
\(Print["λ1= ", λ1, \*"" W.(m^(-1)).(K^(-1))""]\)

ϵ = 0.95;
σ = 5.67*(10^(-8));
αr = ϵ*σ*
              Simplify[(((T1^4) - (T2^4))/(T1 - T2))] /. {T1 -> 
                Tpec + 273, T2 -> Tpec + 273} // 
          Simplify;
\(Print["αr= ", αr, \*"" W.(m^(-2)).(K^(-1))""]\)

S1 = 
        2*((a + d1)*(b + d1) + (c + d1)*(b + d1) + (a + 
                    d1)*(c + d1));
\(\(Print["S1= ", 
        S1, \*"" \!\(m\^2\)""];\)\)
Rt1 = (d1/(λ1*S1));
λ2 = 0.162;
S2 = 
        2*((a + 2  d1 + d2)*(b + 2  d1 + d2) + (c + 2  d1 + 
                      d2)*(b + 2  d1 + d2) + (a + 2  d1 + 
                      d2)*(c + 2  d1 + d2)) // 
          Simplify;
\(\(Print["S2= ", 
        S2, \*"" \!\(m\^2\)""];\)\)
Rt2 = (d2/(λ2*S2));
S3 = 
        2*((a + 2  d1 + 2  d2)*(b + 2  d1 + 2  d2) + (c + 2  d1 + 
                      2  d2)*(b + 2  d1 + 2  d2) + (a + 2  d1 + 
                      2  d2)*(c + 2  d1 + 2  d2)) // 
          Simplify;
\(\(Print["S3= ", S3, \*"" \!\(m\^2\)""];\)\)

α = 5;
Qk = S3*α*(Tpl - Tok);
Qr = ϵ*σ*
          S3*((((Tpl + 273))^4) - (((Tor + 273))^4));

resd2 = 
        Solve[((Tpec - Tpl)/(Rt1 + Rt2)) == Qr + Qk] // 
          Last;
Print["d2= ", 
        d2 /. resd2, " m"];
ztraty = Qk + Qr /. resd2;
Print["ztraty= ",  ztraty, " W"]

nabeh = (t/(t + 1));
Plot[nabeh, {t, 0, 100}]

ClearAll[vyr];
vyr[x_] = 
        (1/Pi)*(ArcTan[((-x + 1200)/0.1)] + 
              (Pi/2));
Plot[vyr[x], {x, 1200 - 50, 1200 + 50}]

ϵ = 0.95;
σ = 
        5.67*(10^(-8));
α = 
        5;
Tor = 
        15;
Tok = 
        30;
λ = 
        0.162;
ρ = 
        130;
cp = 
        969;
qd = 
        3000;
d = 
        d2 /. resd2;
qk = α*(T[d, t] - 
              Tok);
qr = ϵ*σ*((((T[d, t] + 273))^4) - (((Tor + 273))^4));
rce = ρ*cp*D[T[x, t], t] == λ*
            D[T[x, t], {x, 2}];
poc = 
        T[x, 0] == Tok;
okrLeft=qd*nabeh*vyr[T[x, t]]==-λ*D[T[x, t], x]/.x -> 0;
okrRight=(qk + qr)*nabeh==-λ*D[T[x, t], x]/.x -> d;
hodina = 
        3600;
tmax = 
        2*hodina;
resT=NDSolve[{rce, poc, okrLeft, okrRight},T[x, t],{x, 0, d},{t, 0, tmax},MaxStepSize->{d/100, tmax/10000},MaxSteps -> (10^6)][[1]];
teplota = 
        T[x, t] /. resT;
Plot3D[
        teplota, {x, 0, d}, {t, 0, tmax}, 
        AxesLabel -> {"x[m]", "    t[s]", "T[°C]   \
"}, PlotRange -> All];
teplotavlevo = 
        teplota /. x -> 0;
Plot[
        teplotavlevo, {t, 0, tmax}, 
        AxesLabel -> {"t[s]", "T[°C]"}, 
        PlotRange -> All];

Pzadany = 5000;
U = 230. ;
R = 
        r /. Solve[
              Pzadany == ((U^2)/r)][[1]];
Print["R= ", R, " Ω"]

ClearAll[s]
Tmax = 1350;
ϵ = 0.9;
σ = 5.67*(10^(-8));
Tpec = 1200;
Solve[
          Pzadany == 
            S*ϵ*σ*((((Tmax + 273))^4) - (((Tpec + 273))^4))][[1]];
\(Print["S= ", \(10\^4\) 
          S /. %, \*"" \!\(cm\^2\)""]\)
\(Print[\*""((cm^2)/Ω)= "", \(\(10\^4\) S /. %%\)\/R, \*"" ((cm^2)/Ω)""]\)

ohmnametr = 0.8205;
Print["l= ", (R/ohmnametr) " m"]