%%LightBulbMatrixCode

clear

clc

% given values

k_fil = 25;% W/m-K

k_air =

k_glass =

dx = 0.001; % m

h_outer = 1000; % W/m^2-K

h_inner = 200; % W/m^2-K

T_outer = 1700; % K

T_inner = 400; % K

% blank matrix A and constant vector C

% row x column

A = zeros(15,15);

C = zeros(15,1);

% node 1

A(1,1) = -(k_fil+k_air);

A(1,2) = k_fil;

A(1,7) = k_air;

C(1) = -0.5*q_dot*(dx)^2 ;

% node 2

A(2,1) = k_fil;

A(2,2) = -2*k_fil + k_air);

A(2,3) = k_fil;

A(2,8) = k_air;

C(2) = -q_dot*(dx)^2;

% node 3

A(3,2) = k_fil;

A(3,3) = -(k_fil+3*k_air);

A(3,4) = k_air;

A(3,9) = 2*k_air;

C(3) = -q_dot*(dx)^2;

% node 4

A(4,3) = k_fil;

A(4,4) = (-2*k_air + k_glass + k_fil);

A(4,5) = k_glass;

A(4,10) = 2*k_air;

C(4) = 0;

% node 5

A(5,4) = k_air;

A(5,5) = -(k_air + 3*k_glass);

A(5,6) = k_glass;

A(5,11) = 2*k_air;

C(5) = 0;

% node 6

A(6,5) = k_glass;

A(6,6) = -(k_glass2*(h_conv+h_rad)*dx));

C(6) = -2*dx*(h_conv_h_rad)*T_inf;

% node 7

A(7,1) = k_fil;

A(7,7) = -(k_fil + 2*k_air + k_glass);

A(7,8) = 2*k_air;

A(7,12) = k_glass;

C(7) = 0;

% node 8

A(8,2) = k_fil;

A(8,7) = k_air;

A(8,8) = -(2*k_air + k_fil + k_glass);

A(8,9) = k_air;

A(8,13) = k_glass;

C(8) = 0;

% node 9

A(9,3) = 1;

A(9,8) = k_air;

A(9,9) = -(2*k_air + k_fil + k_glass);

A(9,10) = k_air;

A(9,14) = k_glass;

C(9) = 0;

% node 10

A(10,4) = k_air;

A(10,9) = k_air;

A(10,10) = -2*(k_air + k_glass);

A(10,11) = k_glass;

A(10,15) = k_glass;

C(10) = 0;

% Node 11

A(11,5) = k_glass*dx;

A(11,10) = k_air;

A(11,11) = -(k_air + k_glass*dx + 2*(h_conv + h_rad)*dy);

C(11) = -2*(h_conv + h_rad)*dy*T_inf;

% node 12

A(12,7) = k_air;

A(12,12) = -(k_air + 2*k_glass+(h_conv+h_rad)*dx);

A(12,13) = 2*k_glass;

C(12) = -(h_conv+h_rad)*dy*t_inf;

% node 13

A(13,8) = k_air;

A(13,12) = k_glass;

A(13,13) = -(k_air + 2*k_glass + (h_conv + h_rad)*dx);

A(13,14) = k_glass;

C(13) = -(h_conv + h_rad)*dy*T_inf;

% node 14

A(14,9) = k_air;

A(14,13) = k_glass;

A(14,14) = -(k_air + 2*k_glass + (h_conv+h_rad)*dx);

A(14,15) = k_glass;

C(14) = -(h_conv + h_rad)*dy*t_inf;

% node 15

A(15,10) = k_air;

A(15,14) = k_glass;

A(15,15) = -2*(k_glass + k_air + (h_conv + h_rad)&dy);

C(15) = -2*((h_conv + h_rad)*dy)*T_inf;

% solve for nodal temperatures

T = A \ C;

% results

disp('Nodal temperatures for Light Bulb (K):')

for n = 1:15

fprintf('T%-2.0f = %8.2f K\n', n, T(n))

end