Přirozená konvekce

T1=120;
T2=20;
Tdef=0.5*(T1+T2);
g=9.81;
Print["Tdef= ",Tdef," K"]
β=(1/(Tdef+273));
cm=0.01;
Dchar=5cm;

datν={{50,1.79*(10^(-5))},{100,2.3*(10^(-5))}};
ν=Fit[datν,{1,T},T]/.T->Tdef;

Gr=((β*Abs[T1-T2]*g*(Dchar^3))/(ν^2));
Pr=0.7;
Print["Gr= ",Gr,"  -"]
Print["Gr*Pr= ",Gr*Pr,"  -"]

Nu0=0.36;
odmocninaZNu=(Sqrt[Nu0])+((((((Gr*Pr)/300)/(((1+((((0.5/Pr)))^(9/16))))^(16/9)))))^(1/6));
Nu1=(odmocninaZNu^2);
Print["Nu z 1. vzorce= ",Nu1]
Nu2=0.54*(((Gr*Pr))^(1/4));
Print["Nu z 1. vzorce= ",Nu2]

λ=2.46*(10^(-2))*(4186/3600);
α1=Nu1*(λ/Dchar);
Print["α1= ",α1," W.(m^(-2)).(K^(-1))"]
α2=Nu2*(λ/Dchar);
Print["α2= ",α2," W.(m^(-2)).(K^(-1))"]

S=1*Pi*Dchar;
Vykon1=α1*S*Abs[T1-T2];
Vykon2=α2*S*Abs[T1-T2];
Print["P1= ",Vykon1," W"]
Print["P2= ",Vykon2," W"]

Vynucená konvekce

prutok=5*(10^(-3));
prurez=((Pi*(Dchar^2))/4);
rychlost=(prutok/prurez);
Print["v= ",rychlost," m.(s^(-1))"]
νVoda=0.413*(10^(-6));
PrVoda=2.56;
Rey=((rychlost*Dchar)/(νVoda));
Print["Re= ",Rey]
Nu=0.023*(Rey^0.8)*(PrVoda^0.4);
Print["Nu= ",Nu]
λVoda=0.574*1.16;
αVoda=((Nu*λVoda)/Dchar);
Print["αVoda= ",αVoda," W.(m^(-2)).(K^(-1))"]

Tcl1=37;
Tcl2=20;
Tdefcl=0.5*(Tcl1+Tcl2);
Print["Tdefcl= ",Tdefcl," °C"]
βcl=(1/(Tdefcl+273));
ν30cl=16.61*(10^(-6));
Prcl=0.7;
vyskacl=1.9;
Grcl=((βcl*Abs[Tcl1-Tcl2]*g*(vyskacl^3))/((ν30cl)^2));
Print["Grcl= ",Grcl,"  -"]
Print["Grcl*Prcl= ",Grcl*Prcl,"  -"]
Nucl=0.135*(((Grcl*Prcl))^(1/3));
λ30cl=1.16*2.22*(10^(-2));
αcl=Nucl*((λ30cl)/vyskacl);
Print["αcl= ",αcl," W.(m^(-2)).(K^(-1))"];
Scl=vyskacl*1;
Vykoncl=αcl*Scl*Abs[Tcl1-Tcl2];
Print["Clovek= ",Vykoncl," W"];

rychlostcl=10;
sirkacl=0.4;
Recl=((rychlostcl*sirkacl)/(ν30cl));
Print["Recl= ",Recl," -"];
Nucl2=0.197*(Recl^0.6);
αnuccl=((Nucl2*λ30cl)/sirkacl);
Print["αNucena clovek= ",αnuccl," W.(m^(-2)).(K^(-1))"];
Scl=vyskacl*1;
Vykonnuccl=αnuccl*Scl*Abs[Tcl1-Tcl2];
Print["Vykon cloveka nuceneho= ",Vykonnuccl," W"];

Vykonnuccl==αcl*(Tcl1-Tfik)//Solve

?/;

NuVolna[grpr_]:=1.18*(grpr^(1/8))/;(10^(-3))≤grpr≤500;
NuVolna[grpr_]:=.54*(grpr^(1/4))/;500<grpr≤2*(10^7);
NuVolna[grpr_]:=.135*(grpr^(1/3))/;2*(10^7)<grpr≤(10^13);

Alfa na stěně jako funkce teploty

LogLogPlot[NuVolna[grpr],{grpr,(10^(-3)),(10^13)},AxesLabel->{"log[GrPr]","log[Nu]"},PlotStyle->Thick]