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

resT = 
      DSolve[{T''[x] == 0, T[0] == T1, T[d] == T2}, 
        T[x], x]

teplota = T[x] /. resT[[1]]

qvect = -λ*Grad[teplota]

qx = qvect[[1]]

zed = {λ -> 0.8, d -> 0.45, 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] /. DSolve[{rce, T[0] == 10}, T[t], t][[1]] /. 
      t -> 0

ρ = 1000;
cp = 4186;
Ecko = (230/0.1);
rce = ρ*cp*T'[t] == (a*T[t] + b)*(Ecko^2) /. 
          dosabPha;
dosT = DSolve[{rce, T[0] == 10}, T[t], 
            t][[1]];
tmax = 
        t /. FindRoot[(T[t] /. dosT) == 100, {t, 
              1000}];
Print["t100= ", (tmax/60), " min"]
Plot[T[t] /. dosT, {t, 0, tmax}, 
      PlotStyle -> {Hue[0.63], Thickness[0.008]}]

QV = (a*T[t] + b)*(Ecko^2) /. dosabPha /. 
          dosT;
el = 0.1;
V = (el^3);
P = QV*V;
Plot[P, {t, 0, tmax}, 
      PlotStyle -> {Hue[0.63], 
          Thickness[0.008]}]
Plot[P/230, {t, 0, tmax}, 
      PlotStyle -> {Hue[0.63], Thickness[0.008]}]

msteckou = 0.5;
T1 = 4;
cp = 4186;
T2 = 40;
cm = 0.01;
mm = 0.1  cm;
vykon = msteckou*cp*(T2 - T1);
Print["P= ", (vykon/1000), "   kW"]

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

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

λ = 0.8;
d = 0.45;
Tin = 21;
Texter = -13;
αin = 5;
αext = 23;
S = 1;
Solve[{Q == ((λ*S)/d)*(T1 - T2), 
        Q == αin*S*(Tin - T1), 
        Q == αext*S*(T2 - Texter)}]

Rt1 = (d/(λ*S));
Rt2 = (1/(αin*S));
Rt3 = (1/(αext*S));
Rt4 = (diz/(λiz*S));
Q = ((Tin - Texter)/(Rt1 + Rt2 + Rt3 + Rt4));
λiz = 0.04;
Solve[Tin - Rt2*Q == 18][[1]]
Rt4 /. %

Rt1

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

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

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

dosizolace = {λ -> 0.04, α -> 
            15};
doselektroizolace = {λ -> 0.4, α -> 
            10};

(λ/α) /. dosizolace

(λ/α) /. doselektroizolace

f[x_] := (x^2);
f[2]

\(\(g := #\^2 &;\)\)
g[2]

Pi // N[#, 20] &

N[Pi, 20]

<< Miscellaneous`PhysicalConstants`;
mm = 0.001;
prurez = 1  (mm^2);
polomer = 
        r /. Solve[
              prurez == 
                Pi*(r^2)][[2]];
delka = 1;
povrch = 2*Pi*polomer*delka;
Tok = 20;
Tor = 15;
Tmax = 60;
α = 10;
ϵ = 0.8;
Qkonvekce = α*
          povrch*(Tmax - Tok);
Print["Qk= ",  Qkonvekce, "  W"]
σ = StefanConstant[[1]];
Qsalani = ϵ*σ*
          povrch*((((Tmax + 273))^4) - (((Tor + 273))^4));
Print["Qr= ",  Qsalani, "  W"]
γ = 57*(10^6);
odpor = (delka/(prurez*γ));
Print["R= ", 
      odpor, "  Ω"]
Solve[
        odpor*(proud^2) == 
          Qkonvekce + Qsalani];
Print["max proud= ", proud /. %[[2]], "  A"]

U = 400;
kW = 1000. ;
P = 30  kW;
Y = (P/(U^2))
cosfi = 0.8;
fi = -ArcCos[cosfi]
(P/(U^2)) (1 - I*Tan[fi])

-0.14 + (0.0625/(Sqrt[3])) - (0.125/(Sqrt[3]))

ϵ*σ*
        Simplify[(((T1^4) - (T2^4))/(T1 - T2))] //. {T1 -> T, 
        T2 -> T, T -> 1200 + 273}

a = 0.5;
b = 0.6;
c = 0.7;
Tpec = 1200;
Tpl = 50;
Tor = 15;
Tok = 30;
σ = 5.67*(10^(-8));
ϵ = 0.95;
cm = 0.01;
d1 = 3  cm;
S1 = 
        2*((a + d1)*(b + d1) + (c + d1)*(b + d1) + (a + 
                    d1)*(c + d1));
\(Print["S1= ", S1, \*""  \!\(m\^2\)""]\)

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

      
λ1 = 
        Fit[datλPla, {1, T}, T] /. 
          T -> Tpec;
\(Print["λ1= ", λ1, \*"" W.(m^(-1)).(K^(-1))""]\)
λ2 = 0.16;
\(Print["λ2= ", λ2, \*"" W.(m^(-1)).(K^(-1))""]\)

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, \*""  \!\(m\^2\)""]\)

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 = 
        S3*ϵ*σ*((((Tpl + 273))^4) - (((Tor + 273))^4));
rce = ((Tpec + Tpl)/((d1/(λ1*S1)) + (d2/(λ2*S2)))) == Qk + Qr;
dosd2 = Solve[rce] // Last;
Print["d2= ", d2 /. dosd2, "  m"]

ztraty = Qk + Qr /. dosd2;
Print["Pz= ", ztraty "  W"]

Tor = 15;
Tok = 30;
α = 5;
σ = 5.67*(10^(-8));
ϵ = 0.95;
cm = 0.01;

ClearAll[T];
qk = α*(T[x, t] - Tok);
qr = ϵ*σ*((((T[x, t] + 273))^4) - (((Tor + 273))^4));

nabeh = (t/(t + 1));

    Plot[nabeh, {t, 0, 10}]

x0 = 1200;
jakrychle = 0.1;
pom[
        x_] = (1 + 
          Tanh[-((x - x0)/jakrychle)])
Plot[pom[x]*0.5, {x, x0 - 10, x0 + 10}]

okrLeft

ρ = 250;
cp = 
        969;
λ = 
        0.16;
d = 
        0.33;
hodina = 
        3600;
tmax = 
        45*hodina;
qdop = 
        (ztraty/S2) /. 
          dosd2;
rce = ρ*cp*
            D[T[x, t], t] == λ*
            D[T[x, t], {x, 2}];
poc = 
        T[x, 0] == Tok;
okrLeft=pom[T[x, t]]*qdop*nabeh==-λ*D[T[x, t], x]/.x -> 0;
okrRigth=(qk + qr)*nabeh==-λ*D[T[x, t], x]/.x -> d;
res=NDSolve[{rce, poc, okrLeft, okrRigth},T[x, t],{x, 0, d},{t, 0, tmax},MaxStepSize->{d/100, tmax/10000},MaxSteps -> (10^6)][[1]];
teplota = 
        T[x, t] /. res;
Plot3D[
      teplota, {x, 0, d}, {t, 0, tmax}, 
      AxesLabel -> {"x[m]", "    t[s]", "T[°C]   "}, 
      PlotRange -> All]

teplpovrch = teplota /. x -> 0;

Plot[teplpovrch, {t, 0, tmax}, 
      AxesLabel -> {"t[s]", "T[°C]   "}, 
      PlotRange -> All]

Topne clanky

P1cl = 50000;
Tmax = 1350;
U = 230. ;
R = 
        r /. Solve[
              P1cl == ((U^2)/r)][[1]];
Print["R= ", R, "  Ω"]

Scl = 
        plochaclanku /. (P1cl == ϵ*σ*
                    plochaclanku*((((Tmax + 273))^4) - (((Tpec + 273))^4)) // Solve)[[1]];

\(Print["Scl= ", Scl*1000, \*""  \!\(cm\^2\)""]\)

\(Print[\*""((cm^2)/Ω)= "", \(Scl*1000\)\/R, \*""  (cm^2)/Ω""]\)