Python can/should be used here!

Consider one-dimensional heat conduction in a slab of thickness L = 0.2m, governed by: d dc Q k Ak The thermal conductivity of the slab varies with the temperature as k = 30(1 + 0.002T), where T is in kelvin. One surface of the slab is cooled to a constant temperature To = 290K and the other surface is adjacent to a vacuum (no conduction/convection) and is heated through radiation by the surroundings, which are modeled as a black body at temperature TB = 1273K, according to: = CEL = 0(T4 TB) Where o = 5.676 x 10-8Wm-2K-4 is the Stefan-Boltzmann constant. There is no heat generation within the slab and therefore the heat flux Qr is constant. vacuum body at TB x = 0 T= T. x=L T = TS Solve the equation, plot the results and determine the surface temperature. Hint: the problem is fairly easy to solve as an IVP for a given constant Qx. Therefore, the problem is to iterate until you find a Qx that matches the radiation heat transfer condition. This is equivalent to a shooting problem (note that this problem is non-linear as a result of the 4th power in the boundary condition). You need to: guess Q.x, solve the problem, calculate Qx from the solution; iterate until the guessed and calculated Qx agree