Find the roots of an expression

Question

Deanna 2011-4-13

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Is there a function that can find the root(s) of an expression, which is not a polynomial? My constants and my final expression (for which I want to find the root) are listed below.

%Declare constants
Dw = 0.0000076;
S = 0.000239;
rho = 1.1;
h = 0.0030;
Nm=20,000;
Wo = 0.0025;
c1 = Dw*S/rho/h;
c2 = (3*Wo/(4*Nm*3.14159*rho))^(1/3);
c3 = (3*Wwf/(4*Nm*3.14159*rho))^(1/3);
twf=20;
%Need to determine the value of Wwf in the following expression
((c2 - c3 - h*log((h + c2)/(h + c3)))/c1)-twf=0;

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Answer 1

Matt Fig 2011-4-13

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FZERO can be used to find roots.

Dw = 0.0000076; 
S = 0.000239; 
rho = 1.1; 
h = 0.0030;
Nm=20000; 
Wo = 0.0025; 
c1 = Dw*S/rho/h; 
c2 = (3*Wo/(4*Nm*3.14159*rho))^(1/3); 
c3 = @(Wwf) (3*Wwf/(4*Nm*3.14159*rho)).^(1/3); 
twf=20;
G = @(Wwf) ((c2 - c3(Wwf) - h*log((h + c2)./(h + c3(Wwf))))/c1)-twf;
rt = fzero(G,.01)

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Matt Fig 2011-4-13

Try this:

Dw = 0.0000076;

S = 0.000239;

rho = 1.1;

h = 0.0030;

Nm=20000;

Wo = 0.0025;

c1 = Dw*S/rho/h;

c2 = (3*Wo/(4*Nm*3.14159*rho))^(1/3);

%initializations

twf(1)=1;

c3=@(Wwf) (3*Wwf/(4*Nm*3.14159*rho)).^(1/3);

rt = zeros(1,10800);

rt(1) = Wo;

for ii=2:10800

G = @(Wwf) ((c2 - c3(Wwf) - h*log((h + c2)./(h + c3(Wwf))))/c1)-(ii-1);

try

rt(ii) = fzero(G,rt(ii-1));

catch

disp('No value found, aborting....')

rt = rt(1:ii-1);

break

end

Deanna 2011-4-13

Yes, thanks, that works as long as I end the loop early enough. For the code about 10800 is too many iterations.

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Answer 2

Deanna 2011-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/5420-find-the-roots-of-an-expression#answer_7623

在 MATLAB Online 中打开

The following works. For the constants I gave I need to end the loop at 2600. If the loop runs longer an error occurs.

clear all
Dw = 0.0000076; 
S = 0.000239; 
rho = 1.1; 
h = 0.0030; 
Nm=8477.7;
Wo = 0.0025; 
c1 = Dw*S/rho/h; 
c2 = (3*Wo/(4*Nm*3.14159*rho))^(1/3); 
%initializations 
c3=@(Wwf) (3*Wwf/(4*Nm*3.14159*rho)).^(1/3); 
rt = zeros(1,2600); 
rt(1) = Wo;
time(1)=0;
for ii=2:2600 
G = @(Wwf) ((c2 - c3(Wwf) - h*log((h + c2)./(h + c3(Wwf))))/c1)-(ii-1); 
rt(ii) = fzero(G,[0 0.0025]);
time(ii)=time(ii-1)+ii;
end