Oliver Johnson & Sam Wilding

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Oliver Johnson & Sam Wilding. Heat Transfer Me 340-2. Winter Semester, 2010. Nusselt Number Calculator.

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Oliver Johnson & Sam Wilding

Heat Transfer

Me 340-2

Winter Semester, 2010

Nusselt Number Calculator

Using inputs like fluid type, internal or external flow, and parameters given in the problem, this program will automatically select the applicable Nusselt Number equation(s) and return the Nusselt Number(s)

The Code

if config == 2; % External Flow

% Find fluid properties at film temperature

Tf = (Tinf+Ts)/2;

[rho,mu,nu,Pr] = props(fluid,Tf,quality);

% Fixed Surface Temperature

if geometry == 3; % Flat Plate, Parallel Flow

Re = v*D/nu;

xcritical = 5e5*nu/v;

if isnan(qs) && isnan(Xi);

if D <= 1.05*xcritical % Laminar

if Pr >= 0.6

Nu{1,1} = 0.332*Re^(1/2)*Pr^(1/3); %Eq. 7.23

Nu{1,2} = 'Eq. 7.23';

if Re < 5.3e5

Nu{2,1} = 0.664*Re^(1/2)*Pr^(1/3); %Eq. 7.30

Nu{2,2} = 'Eq. 7.30';

end

end

% Liquid Metals

if isequal('hg',fluid) && Pr <= 0.05 && Pr*Re >= 100

Nu{3,1} = 0.565*(Re*Pr)^(1/2); %Eq. 7.32

Nu{3,2} = 'Eq. 7.32';

end

% Churchill-Ozoe

if Pr*Re >= 100

Nu{4,1} = 0.3387*Re^(1/2)*Pr^(1/3)/(1+(0.0468/Pr)^(2/3))^(1/4); %Eq. 7.33

Nu{4,2} = 'Eq. 7.33 (Churchill-Ozoe)';

if Re < 5.3e5

Nu{5,1} = 2*Nu;

Nu{5,2} = 'Nu_ave ';

end

end

elseif D > 1.05*xcritical && D < 20*xcritical % Mixed Laminar/Turbulent

if Pr > 0.6 && Pr < 60

Nu{6,1} = (0.037*Re^(4/5)-871)*Pr^(1/3); %Eq. 7.38

Nu{6,2} = 'Eq. 7.38';

end

elseif D >= 20*xcritical % Fully Turbulent

if Pr > 0.6 && Pr < 60

Nu{7,1} = 0.0296*Re^(4/5)*Pr^(1/3); %Eq. 7.36

Nu{7,2} = 'Eq. 7.36';

end

if Re > 10^8

Nu{8,1} = 0.037*Re^(4/5)*Pr^(1/3); %Eq. 7.38

Nu{8,2} = 'Eq. 7.38';

end

end

% Unheated Starting Length

elseif isnan(qs) && ~isnan(Xi)

if Re < 5e5 %Laminar

Nu{9,1} = 0.332*Re^(1/2)*Pr^(1/3)/(1-(Xi/D)^(3/4))^(1/3); %Eq. 7.42

Nu{9,2} = 'Eq. 7.42';

else %Turbulent

Nu{10,1} = 0.0296*Re^(1/2)*Pr^(1/3)/(1-(Xi/D)^(3/4))^(1/3); %Eq. 7.43

Nu{10,2} = 'Eq. 7.43';

end

% Fixed Heat Flux

elseif isnan(Ts) && isnan(Xi)

if Re < 5e5 && Pr >= 0.6

Nu{11,1} = 0.453*Re^(1/2)*Pr^(1/3); %Eq. 7.45

Nu{11,2} = 'Eq. 7.45';

elseif Re > 5e5 && Pr > 0.6 && Pr < 60

Nu{12,1} = 0.0308*Re^(4/5)*Pr^(1/3); %Eq. 7.46

Nu{12,2} = 'Eq. 7.46';

end

end

elseif geometry == 4; % Cylinder

Re = v*D/nu;

% Hilpert

if Re > 0.4 && Re < 4e5 && Pr >= 0.6

if Re >= 0.4 && Re < 4

C = 0.989;

m = 0.330;

elseif Re >= 4 && Re < 40

C = 0.911;

m = 0.385;

elseif Re >= 40 && Re < 4000

C = 0.683;

m = 0.466;

elseif Re >= 4000 && Re < 40000

C = 0.193;

m = 0.618;

elseif Re >=40000 && Re <= 400000

C = 0.027;

m = 0.805;

end

Nu{13,1} = C*Re^m*Pr^(1/3); %Eq. 7.52

Nu{13,2} = 'Eq. 7.52 (Hilpert)';

end

% Churchill

if Re*Pr >= 0.2

Nu{14,1} = 0.3+0.62*Re^(1/2)*Pr^(1/3)*(1+(Re/282000)^(5/8))^(4/5)/(1+(0.4/Pr)^(2/3))^(1/4); %Eq. 7.54

Nu{14,2} = 'Eq. 7.54 (Churchill)';

end

% Zhukauskas

[rhoinf,muinf,nuinf,Prinf] = props(fluid,Tinf,quality);

[rhos,mus,nus,Prs] = props(fluid,Ts,quality);

Reinf = v*D/nuinf;

if Prinf > 0.7 && Prinf < 500 && Reinf > 1 && Reinf < 10^6

if Reinf >= 1 && Reinf < 40

C = 0.75;

m = 0.4;

elseif Reinf >= 40 && Reinf < 1000

C = 0.51;

m = 0.5;

elseif Reinf >= 10^3 && Reinf < 2e5

C = 0.26;

m = 0.6;

elseif Reinf >= 2e5 && Reinf < 1e6

C = 0.076;

m = 0.7;

end

if Prinf <= 10

n = 0.37;

else

n = 0.36;

end

Nu{15,1} = C*Reinf^m*Prinf^n*(Prinf/Prs)^(1/4); %Eq. 7.53

Nu{15,2} = 'Eq. 7.53 (Zhukauskas)';

end

% Sphere

elseif geometry == 5;

% Whitaker

[rhoinf,muinf,nuinf,Prinf] = props(fluid,Tinf,quality);

[rhos,mus,nus,Prs] = props(fluid,Ts,quality);

Reinf = v*D/nuinf;

muratio = muinf/mus;

if ffld == 0;

if Prinf > 0.71 && Prinf < 380 && Reinf > 3.5 && Reinf < 7.6e4 && muratio > 1 && muratio < 3.2

Nu{16,1} = 2+(0.4*Reinf^(1/2)+0.06*Reinf^(2/3))*Prinf^(0.4)*(muratio)^(1/4); %Eq. 7.56

Nu{16,2} = 'Eq. 7.56 (Whitaker)';

end

% Ranz and Marshall for freely falling liquid drops

elseif ffld == 1;

Nu{17,1} = 2+0.6*Reinf^(1/2)*Pr^(1/3); %Eq. 7.57

Nu{17,2} = 'Eq. 7.57 (Ranz and Marshall)';

end

end

elseif config == 1; % Internal Flow

if geometry == 1; % Circular Pipe

Tmave = (Tmi+Tmo)/2;

[rho,mu,nu,Pr] = props(fluid,Tmave,quality);

[rhos,mus,nus,Prs] = props(fluid,Ts,quality);

if isnan(mdot);

Re = rho*v*D/mu;

elseif isnan(v);

Re = 4*mdot/(pi*mu*D);

end

muratio=mu/mus;

f Re < 2300 % Laminar

xhydro = D*0.05*Re;

xthermal = xhydro*Pr;

xratio = xthermal/xhydro;

S = (Re*Pr/(L/D))^(1/3)*(muratio)^0.14;

if S >= 2

if xratio >= 0.5 && xratio <= 1.5 && Pr > 0.48 && Pr < 16700 && muratio > 0.0044 && muratio < 9.75

Nu{18,1} = 1.86*S; %Eq. 8.57

Nu{18,2} = 'Eq. 8.57';

elseif xratio > 1.5

Nu{19,1} = 3.66 + (0.0668*(D/L)*Re*Pr)/(1+0.04*((D/L)*Re*Pr)^(2/3)); %Eq. 8.56

Nu{19,2} = 'Eq. 8.56';

end

elseif S < 2

if ~isnan(qs)

Nu{20,1} = 4.36; %Eq. 8.53

Nu{20,2} = 'Eq. 8.53';

Nu{21,1} = Nu{20,1};

Nu{21,2} = 'Nu_ave';

elseif ~isnan(Ts)

Nu{22,1} = 3.66; %Eq. 8.55

Nu{22,2} = 'Eq. 8.55';

Nu{23,1} = Nu{22,1};

Nu{23,2} = 'Nu_ave';

else

disp('Error: Cannot have Ts == const and qs == const simultaneously.')

return

end

end

elseif Re > 2300 % Turbulent

if L < 60*D % Short Pipe

L = 60*D*1.01;

% This is here to calculate a fully developed Nu needed to find the

% Nu for a short pipe. 1.01 is 101% of fully developed length

shortpipe = 1;

end

if ~isequal('hg',fluid)

if isnan(qs) && isnan(f)

% Dittus

if Pr > 0.7 && Pr < 160 && Re > 10000 && L > 60*D

if Ts > Tmave

n = 0.4;

elseif Ts < Tmave

n = 0.3;

end

Nu{24,1} = 0.023*Re^(4/5)*Pr^n; %Eq. 8.60

Nu{24,2} = 'Eq. 8.60';

Nuave = Nu{24,1};

end

elseif ~isnan(qs) || ~isnan(Ts)

if isnan(f)

% Sieder

if Pr > 0.7 && Pr < 16700 && Re > 10000 && L > 60*D

Nu{25,1} = 0.027*Re^(4/5)*Pr^(1/3)*(muratio)^0.14; %Eq. 8.61

Nu{25,2} = 'Eq. 8.61 (Sieder)';

Nuave = Nu{25,1};

end

elseif ~isnan(qs) || ~isnan(Ts) && ~isnan(f)

% Gnielinski

if Pr > 0.5 && Pr < 2000 && Re > 3000 && Re < 5e6 && L > 60*D

Nu{26,1} = (f/8)*(Re-1000)*Pr/(1+12.7*(f/8)^(1/2)*(Pr^(2/3)-1)); %Eq. 8.62

Nu{26,2} = 'Eq. 8.62 (Gnielinski)';

Nuave = Nu{26,1};

end

end

end

elseif isequal('hg',fluid)

% Liquid Metals

Pe = Pr*Re;

if isnan(Ts) && ~isnan(qs)

if Pe > 100 && Pe < 10000 && Re > 3.63e3 && Re < 9.05e6

Nu{27,1} = 4.82+0.0185*(Pe)^0.287; %Eq. 8.64

Nu{27,2} = 'Eq. 8.64';

Nuave = Nu{27,1};

end

elseif isnan(qs) && ~isnan(Ts)

if Pe >= 100

Nu{28,1} = 5+0.025*Pe^0.8; %Eq. 8.65

Nu{28,2} = 'Eq. 8.65';

Nuave = Nu{28,1};

end

end

end

end

if shortpipe == 1;

C = 2.4254;

m = 0.676;

Nu{29,1} = Nuave*(1+C/(L/D)^m); %Eq. 8.63

Nu{29,2} = 'Eq. 8.63 (Short Tubes)';

end

elseif geometry == 2; % Non-Circular Cross Section

Tmave = (Tmi+Tmo)/2;

[rho,mu,nu,Pr] = props(fluid,Tmave,quality);

[rhos,mus,nus,Prs] = props(fluid,Ts,quality);

muratio=mu/mus;

Dh = 4*Ac/P;

if isnan(mdot);

Reh = rho*v*Dh/mu;

elseif isnan(v);

Reh = 4*mdot/(pi*mu*Dh);

end

if Reh < 2300

Nu{30,1} = 'See Table 8.1';

Nu{30,2} = '';

elseif Reh > 2300

% Sieder

if Pr > 0.7 && Pr < 16700 && Reh > 10000

if L > 60*Dh

Nu{31,1} = 0.027*Reh^(4/5)*Pr^(1/3)*(muratio)^0.14; %Eq. 8.61

Nu{31,2} = 'Eq. 8.61 (Sieder - Non-Circular Cross Section)';

elseif L <= 60*Dh % Short Pipe

L = 60*Dh*1.01; % This is here to calculate a fully developed

% Nu needed to find the Nu for a short pipe. 1.01 is 101% of fully developed length

Nuave = 0.027*Reh^(4/5)*Pr^(1/3)*(muratio)^0.14; %Eq. 8.61

C = 2.4254;

m = 0.676;

Nu{29,1} = Nuave*(1+C/(L/Dh)^m); %Eq. 8.63

Nu{29,2} = 'Eq. 8.63 (Short Tubes)';

end

end

end

end

end