Heat transfer application. Double-pane windows are an engineering triumph. I have a double-paned window. The glass panes are Delta x_glass = 0.004 thick, and the argon in between is Delta x_argon = 0.01. The outside heat transfer coefficient is h_o = 45. and the inside coefficient is h_i = 12. The thermal conductivity of the glass is kg = 0.8, and the conductivity of the argon is 0.016. Let the outside temperature be T_out, and assume that the inside temperature is 23 (room temperature). The temperatures of the four glass surfaces, T_1, T_2, T_3, and T_4 are given by the system of four equations (obtained by balancing heat flux at each interface): h_o (T_out – T_1) = k_g T_1 – T_2/Delta x_glass k_g T_1 – T_2/Delta x_glass = k_a T_2 – T_3/Delta x_argon k_a T_2 – T_3/Delta x_argon = k_g T_3 – T_4/Delta x_glass kg T_3 – T_4/Delta x_glass = h_i (T_4 – 23) Write a Matlab script file to find a vector containing the T_1, T_2, T_3, and T_4 temperatures. What are the temperatures if T_out = 39?

## Expert Answer

syms T1 T2 T3 T4

Tout=input(‘Enter Tout:’);

kg=.8;ka=.016;

dg=.004;da=.01;

ho=45;hi=12;

eq1=ho*(Tout-T1)==kg*(T1-T2)/dg;

eq2=kg*(T1-T2)/dg==ka*(T2-T3)/da;

eq3=ka*(T2-T3)/da==kg*(T3-T4)/dg;

eq4=kg*(T3-T4)/dg==hi*(T4-23);

sol=solve([eq1,eq2,eq3,eq4],[T1,T2,T3,T4]);

T1=double(sol.T1);

T2=double(sol.T2);

T3=double(sol.T3);

T4=double(sol.T4);

T=[T1 T2 T3 T4]