To estimate the temperature profile of the computer bottom a matrix of 0.5" x 0.5" cells was created with (0,0) corresponding to the upper left hand corner of the computer when viewed from the top. Temperatures on the bottom of the computer were measured at the following locations on the grid:
|
Thermocouple |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
|
x-coordinate |
2.0 |
2.0 |
2.0 |
2.0 |
4.5 |
4.5 |
4.0 |
7.25 |
7.0 |
6.25 |
9.0 |
8.5 |
|
y-coordinate |
3.0 |
5.0 |
7.0 |
9.0 |
3.63 |
5.75 |
8.25 |
3.0 |
5.0 |
8.25 |
3.63 |
5.5 |
To create a color map and plot contour lines, values for the temperature at each node of the matrix are required. Using the measured values at the twelve locations summarized above and specifying a constant temperature of 70°F on the periphery of the computer, a third order interpolating polynomial was developed for each case. (see: http://zunzun.com/). The polynomials for the six case plotted are summarized on the following pages.
An algorithm was written in Matlab to carry out the plotting and the code is reproduced on the next page.
%TP1 Temperature Contours for Aluminum Desktop Stand Studies
%Generate Grid
x=[1:0.5:14];
y=[1:0.5:12];
%Initialize Temperature Profile
TI=zeros(27,23);
%Generate Temperature Profile
for i=1:27
for j=1:23
TI(i,j)=65.73155786 + 4.11667*(x(i)-1) + 2.0531622*(y(j)-1)-0.59214302*(x(i)-1)^2 + 0.00808101*(y(j)-1)^2 + 0.021397858*(x(i)-1)^3 - 0.01844709*(y(j)-1)^3;
end
end
%Generate Contour Plots
%Scale Temperature Profile
cmax=max(max(TI));
TI=TI*88/cmax;
%Plot Temperature Profiles with Contour Lines
colormap(jet)
pcolor(TI)
set(gca,'clim',[70,130])
shading interp
colorbar
hold on
contour(TI,20,'k')
hold off
The computer resting on a flat rigid insulated surface to simulate a desk (Insulfoam, R = 4.17/inch) - Case 1
% To the best of my knowledge this code is correct.
% If you find any errors or problems please contact
% me using zunzun@zunzun.com or the feedback form.
% James
% Fitting target is lowest sum of squared (SSQ) absolute error (traditional)
function z=Simplified_Cubic_model(x_in, y_in)
temp = 0.0;
% coefficients
a = 5.8888163651230371E+01;
b = 1.0110573412164740E+01;
c = 3.7576297845788602E+00;
d = -1.4054885844932996E+00;
e = 3.8343141145021270E-01;
f = 4.8979159472397837E-02;
g = -6.8174941197561498E-02;
temp = temp + a;
temp = temp + b .* x_in;
temp = temp + c .* y_in;
temp = temp + d .* (x_in .^ 2.0);
temp = temp + e .* (y_in .^ 2.0);
temp = temp + f .* (x_in .^ 3.0);
temp = temp + g .* (y_in .^ 3.0);
Computer resting on a soft insulated surface, similar to a blanket - Case 2
% To the best of my knowledge this code is correct.
% If you find any errors or problems please contact
% me using zunzun@zunzun.com or the feedback form.
% James
% Fitting target is lowest sum of squared (SSQ) absolute error (traditional)
function z=Simplified_Cubic_model(x_in, y_in)
temp = 0.0;
% coefficients
a = 5.7236720898665659E+01;
b = 1.2073694810207668E+01;
c = 3.6318466634132620E+00;
d = -1.7154501970269127E+00;
e = 6.4237319963564299E-01;
f = 6.1335249339654389E-02;
g = -9.1212898446591612E-02;
temp = temp + a;
temp = temp + b .* x_in;
temp = temp + c .* y_in;
temp = temp + d .* (x_in .^ 2.0);
temp = temp + e .* (y_in .^ 2.0);
temp = temp + f .* (x_in .^ 3.0);
temp = temp + g .* (y_in .^ 3.0);
z = temp;
Computer resting on the Aluminum Desktop Stand in its fully-collapsed position (0° incline) - Case 3
% To the best of my knowledge this code is correct.
% If you find any errors or problems please contact
% me using zunzun@zunzun.com or the feedback form.
% James
% Fitting target is lowest sum of squared (SSQ) absolute error (traditional)
function z=Simplified_Cubic_model(x_in, y_in)
temp = 0.0;
% coefficients
a = 5.6699790297971226E+01;
b = 9.1116418645080532E+00;
c = 5.6399071132524341E+00;
d = -1.2403296634471026E+00;
e = -1.9436797221231633E-01;
f = 4.1947000105406279E-02;
g = -3.0485734269561807E-02;
temp = temp + a;
temp = temp + b .* x_in;
temp = temp + c .* y_in;
temp = temp + d .* (x_in .^ 2.0);
temp = temp + e .* (y_in .^ 2.0);
temp = temp + f .* (x_in .^ 3.0);
temp = temp + g .* (y_in .^ 3.0);
z
= temp;
Computer resting on the Aluminum Desktop Stand at 21° - the short incline that raises the screen by 3 ½ inches - Case 4
% To the best of my knowledge this code is correct.
% If you find any errors or problems please contact
% me using zunzun@zunzun.com or the feedback form.
% James
% Fitting target is lowest sum of squared (SSQ) absolute error (traditional)
function z=Simplified_Cubic_model(x_in, y_in)
temp = 0.0;
% coefficients
a = 6.3214629504489558E+01;
b = 5.4571092354987680E+00;
c = 3.1419479820221428E+00;
d = -7.7623000517385166E-01;
e = -8.6655868372971567E-02;
f = 2.7676920670864448E-02;
g = -1.8990638455399930E-02;
temp = temp + a;
temp = temp + b .* x_in;
temp = temp + c .* y_in;
temp = temp + d .* (x_in .^ 2.0);
temp = temp + e .* (y_in .^ 2.0);
temp = temp + f .* (x_in .^ 3.0);
temp = temp + g .* (y_in .^ 3.0);
z = temp;
Computer resting on the Aluminum Desktop Stand at 37° - the steep incline that raises the screen by 6 inches - Case 5
% To the best of my knowledge this code is correct.
% If you find any errors or problems please contact
% me using zunzun@zunzun.com or the feedback form.
% James
% Fitting target is lowest sum of squared (SSQ) absolute error (traditional)
function z=Simplified_Cubic_model(x_in, y_in)
temp = 0.0;
% coefficients
a = 6.5731557863415588E+01;
b = 4.1166701240404135E+00;
c = 2.0531622328624977E+00;
d = -5.9214302152148979E-01;
e = 8.0810103712241760E-03;
f = 2.1397858111919500E-02;
g = -1.8447091704189008E-02;
temp = temp + a;
temp = temp + b .* x_in;
temp = temp + c .* y_in;
temp = temp + d .* (x_in .^ 2.0);
temp = temp + e .* (y_in .^ 2.0);
temp = temp + f .* (x_in .^ 3.0);
temp = temp + g .* (y_in .^ 3.0);
z = temp;