(*valcovy odpor*)

r*Div[Grad[T[r], {r,fi,z}, "Cylindrical"], {r,fi,z}, "Cylindrical"]

resT=T[r]/.DSolve[{0==r*Div[Grad[T[r], {r,fi,z}, "Cylindrical"], {r,fi,z}, "Cylindrical"],T[r1]==T1,T[r2]==T2},T[r],r][[1]]
Simplify[(-λ*Grad[resT, {r,fi,z}, "Cylindrical"][[1]]/.r->rmin)*2*Pi*rmin*l]

Plot[{Log[ksi],0.05*((ksi^2)+1)},{ksi,1,10}]

(*prutokovy ohrivac*)

msteckou=0.2;
ρ=1000;
cp=4186;
Vsteckou=(msteckou/ρ);
T1=4;
T2=45;
prikon=msteckou*cp*(T2-T1);
vx=(Vsteckou/(m*d));
(*resab=Solve[{10*a+b==(1/35.),50*a+b==(1/10.)}][[1]]*)
resab=Solve[{20*a+b==(1/70.),75*a+b==(1/30.)}][[1]]
U=230;
m=0.5;
cm=0.01;
d=0.5cm;
Ecko=(U/d);
rce=ρ*cp*vx*T'[x]==(a*T[x]+b)*(Ecko^2)/.resab;
poc=T[0]==T1;
res=DSolve[{rce,poc},T[x],x][[1]];
teplota=T[x]/.res;
Plot[{teplota,T2},{x,0,0.5},AxesLabel->{"x[m]","T[°C]"},PlotStyle->{Thickness[0.008],Thickness[0.008]}]

(*alfa*)

Rth1=(1/(5*50))+(0.4/(0.5*50));
Rth2=(1/(10*50));
Tepl=(Rth2/(Rth1+Rth2))*(20-0)+0

Plot[((1/(alfa*2*Pi*r2*l))+(1/(2Pi*λ*l))Log[(r2/r1)])/.{alfa->5.,l->1,λ->0.5,r1->0.001},{r2,0,1}]

(*Treti cviceni*)

4*5.66*(10^(-8))*0.9((((36+273))^4)-(((20+273))^4))

α=5;
ϵ=0.5;
S=2;
σ=5.66*(10^(-8));
T2=20+273;
Tv=T2;
Manipulate[{σ*ϵ*S*((((T1+273))^4)-(T2^4)),α*S*((T1+273)-Tv),((σ*ϵ*S*((((T1+273))^4)-(T2^4)))/(α*S*((T1+273)-Tv)))},{T1,-50,1000}]

((σ*ϵ*S*((T1^4)-(((T1^4)+(T2^4))/2)))/(σ*ϵ*S*((T1^4)-(T2^4))))//FullSimplify

FindRoot[(d^3)==(2000/2700),{d,1}]

Solve[(d^3)==(2000./2700),d]

cas=3.5*60*60;
Tkonec=700;
Tzacatek=Tokoli=20;
hmotnost=2000;
a=1;
diz=0.02;
λiz=0.8;
Tpovrch=40;
λSibral=0.18;
sVnitrni=6*(a^2);
Sstredni=(((((2a+diz+dsibral)/2.)))^2)*6
Chlinik=896;
α=5;

RthIzolPlusSibral=(diz/(λiz*Sstredni))+(dsibral/(λSibral*Sstredni));
Pztraty=α*(((a+2(diz+dsibral)))^2)*6*(Tpovrch-Tokoli);

resSibral=FindRoot[Pztraty==((Tkonec-Tpovrch)/RthIzolPlusSibral),{dsibral,1}]

Pztraty/.resSibral
Pohrev=((hmotnost*Chlinik*(Tkonec-Tzacatek)+hmotnost*10710)/cas)

100*(10^3)==3.*230*ii//Solve

5.66*(10^(-8))*0.9*(Sdrat/10000)*((((1350+273))^4)-(((700+273))^4))==100*(10^3)//Solve

400*(Sqrt[3])*proud==100000.//Solve

(((((5.66*(10^(-8))*0.9*((((1350+273))^4)-(((700+273))^4)))/((144^2)*10000))))^(-1))

(3248/(110.*6))

(*4. cviceni*)

Tan[(Pi/2)-fi]

Plot[{(300/proud),400-50*proud},{proud,0,10}]

i*U/.Solve[{U==(300./i),U==400-50*i}][[2]]//Quiet

cm=0.01;
a=25cm;
b=40cm;
Uef=231;
ϵr=80;
ϵ0=8.85*(10^(-12));
tanδ=2.5;
frekv=27*(10^6);
P=2.5*(10^3);

d/.FindRoot[P==2*Pi*frekv*ϵ0*ϵr*tanδ*((Uef^2)/d)*(a*b),{d,1}]

P*Tan[((Pi/2)-ArcTan[tanδ])]