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Solve a function and plot its contour plot. Not getting the desired contour plot?

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AD
AD 2023-12-4
回答： Walter Roberson 2023-12-5
I have defined the temperature field as Z..and want to plot the temperature contour. However, I am unable to get the desired contour plot. Can someone please help me with this? I have also trield fcontour by defining X,Y as variables..but with no results.
P = 50;
v = 0.1;
k = 113;
Tm = 843;
T0 = 300;
a = 4.63 * 10^(-5);
eps = 0.9;
sig = 5.67 * 10^-8;
A = 10^-5;
kp = 0.21;
x = linspace(-3, 3);
y = linspace(-3, 0);
% Remove NaN values by replacing them with a default value (e.g., 0)
x(x == 0) = 0;
y(y == 0) = 0;
[X, Y] = meshgrid(x, y);
% Ensure that r is not zero to avoid division by zero issues
r = sqrt((X.*(10^-3)).^2 + (Y.*(10^-3)).^2);
r(r == 0) = 10^-6; % Replace zeros with a small value (eps) to avoid division by zero
Z = (1./(4*k*pi.*r.*(Tm-T0))) .* (P * exp((-v.*(r+X.*10^-3))./(2*a)) - A*(h.*(Z-T0)+eps*sig*(Z.^4-T0^4)+(kp.*(Z-T0)./r)));
figure
contourf(X, Y, Z)
colorbar;
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Walter Roberson
Walter Roberson 2023-12-5
Because of the Z.^4 on the right hand size, you are defining a quartic -- a polynomial in degree 4. There are 4 solutions for each point. An even number of those solutions will be real-valued.

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采纳的回答

Walter Roberson
Walter Roberson 2023-12-5
Ran in:
%h was not defined in original code -- make sure you assign a meaningful
%value!
h = 1;
syms X Y Z real
Q = @(v) sym(v);
P = Q(50);
v = Q(0.1);
k = Q(113);
Tm = Q(843);
T0 = Q(300);
a = Q(463) * Q(10)^(-7);
eps = Q(0.9);
sig = Q(567) * Q(10)^-10;
A = Q(10)^-5;
kp = Q(0.21);
Pi = Q(pi);
R = sqrt((X.*(Q(10)^-3)).^2 + (Y.*(Q(10)^-3)).^2);
r = piecewise(R == 0, 1e-6, R);
eqn = Z == (1./(4*k*Pi.*r.*(Tm-T0))) .* (P * exp((-v.*(r+X.*10^-3))./(2*a)) - A*(h.*(Z-T0)+eps*sig*(Z.^4-T0^4)+(kp.*(Z-T0)./r)));
zsol = solve(eqn, Z, 'returnconditions', true)
zsol = struct with fields:
Z: [6×1 sym] parameters: [1×0 sym] conditions: [6×1 sym]
x = linspace(-3, 3);
y = linspace(-3, 0);
[xG, yG] = meshgrid(x, y);
%warning: zsolfun returns a matrix and must be invoked on scalars!
zsolfun = matlabFunction(reshape(zsol.Z, 1, 1,[]), 'File', 'zsol.m', 'Vars', [X, Y], 'optimize', false);
zcondfun = matlabFunction(reshape(zsol.conditions, 1, 1, []), 'File', 'zcond.m', 'Vars', [X, Y], 'optimize', false);
[xG, yG] = meshgrid(x, y);
Zcell = arrayfun(zsolfun, xG, yG, 'uniform', 0);
Zmat = cell2mat(Zcell);
Zcondcell = arrayfun(zcondfun, xG, yG, 'uniform', 0);
Zcond = cell2mat(Zcondcell);
for L = 1 : size(Zcond,3)
mask = ~Zcond(:,:,L);
layer = Zmat(:,:,L);
layer(mask) = NaN;
if nnz(~isnan(layer)) == 0; continue; end
figure;
subplot(2,1,1)
contour(xG, yG, layer, 7);
colorbar();
title("root #" + L);
subplot(2,1,2)
scatter(xG(:), yG(:), [], layer(:));
colorbar();
end

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