The wall can be modelled as a 1-D steady-state system. The conductivity of the wall K(T)= ko+ α(T-To), where k0 = 0.62 W/m-K is the conductivity at room temperature, T0 = 300 K is a reference temperature, and a = 0.0012 W/m-K^2 . The outer surface of the wall experiences only convection with a gas a Tg, out = 300 K and hout = 25 W/m^2 K. The inner surface experiences both convection and radiation. Radiation takes place with a flame at Tflame = 1900 K and the emissivity of the wall is ε = 0.5. Convection takes place with gases at Tg. in = 800 K and hin = 65 W/m²K. The thickness of the wall is L = 8 cm. Required:
a. Start with the proper form of the heat conduction equation and simplify it to obtain the governing equation for this problem.
b. Indicate the boundary conditions.
c. Solve the differential equation in terms of the variables in the statement. After applying the boundary conditions, you will obtain a system of six equations with six variables. You can easily solve this system of equations using EES
d. Plot the temperature profile using EES or Matlab. Explain why the temperature profile is not linear.
e. What is the heat flux through the wall (analytical expression and numerical value)?