A turbine blade 6.3 cm long with cross sectional area 4.6x10-4m^2 and perimeter 0.12 m is made of stainless steel (k=18 W/mK). The temperature of the root is 482oC. The blade is exposed to a hot gas flow at 871oC with a heat transfer coefficient 454 W/m^2K.
a.) Determine the temperature of the blade tip using analytical solution. Tip could be assumed to be insulated.
b.) Using 11 node points and uniform node size %u0394x write down the finite difference equations for interior nodes and other nodes where the temperature is unknown using energy balance method,
c.) Put the equations for each node into form [A][T]=[C] where [A] is the coefficient matrix, [T] is temperature column vector and [C] is the column vector of known constants,
d.) Solve the resulting equation for unknown temperatures using MATLAB (or use any other similar software or write your own code) by employing matrix inversion method. Plot temperature distribution as a function of axial distance and compare with the analytical solution. Please also provide a printout of computer program you wrote.
e.) Solve the unknown temperatures using MATLAB (or use any other similar software or write your own code) and employing Gauss-Seidel Iteration. Plot the temperatures as a function of number of iterations.
Plot the final temperature distribution as a function of axial distance and compare with the analytical solution.