Quiet@Remove["Global`*"];
$HistoryLength=2;
Off[FindRoot::lstol];
SetDirectory[NotebookDirectory[]];

(*air, free*)
Ts=80;
Ta=20;
Tdef=((Ts+Ta)/2);
Print["Tdef= ",Tdef," °C"];
β=(1./(Tdef+273));
cm=0.01;
Dchar=5cm;
g=9.81;
ΔT=Ts-Ta;
ν=17.88*(10^(-6));
Gr=((β*ΔT*g*(Dchar^3))/(ν^2));
Print["Gr= ",Gr," -" ]
Pr=0.705;
Print["Ra= Gr.Pr= ",Ra=Gr*Pr," -"];
Nu1=(((0.6+0.387*((((Ra/(((1+((((0.559/Pr)))^(9/16))))^(16/9)))))^(1/6))))^2);
Print["Nu1= ",Nu1," -"];
Nu2=0.54*(Ra^0.25);
Print["Nu2= ",Nu2," -"];
Print["difference Nu1 and Nu2: ",100*(((Nu2-Nu1)/Nu1))," %"];
λ=0.02808;
α=((Nu1*λ)/Dchar);
Print["α= ",α," W.(m^(-2)).(K^(-1))"]
S1LengthMeter=1*Pi*Dchar;
PowerOfHeatFrom1m=α*S1LengthMeter*ΔT;
Print["P= ",PowerOfHeatFrom1m," W"]

(*water, forced*)
Quiet@Remove["Global`*"];
cm=0.01;
Dchar=5cm;
VolumeFlow=1*(10^(-3));
ScrossSection=Pi*((Dchar^2)/4);
velocity=(VolumeFlow/ScrossSection);
Print["velocity= ",velocity," m.(s^(-1))"];
T1=80;
T2=79;
ν=3.639*(10^(-7));
Rey=((velocity*Dchar)/ν);
Print["Re= ",Rey," -"];
dataPr={{66.9,2.687},{86.9,2.04}};
Pr=Fit[dataPr,{1,T},T]/.T->80;
Print["Pr= ",Pr," -"];
Nu=0.0243*(Rey^0.8)*(Pr^0.4);
Print["Nu= ",Nu," -"];
λ=0.67;
α=Nu*(λ/Dchar);
Print["α= ",α," W.(m^(-2)).(K^(-1))"];
S1LengthMeter=1*Pi*Dchar;
PowerOfHeatFrom1m=α*S1LengthMeter*(T1-T2);
Print["P= ",PowerOfHeatFrom1m," W"]