A gas turbine blade with internal cooling channels is modeled as a rectangular solid with rectangular channels. The blade, which has a thermal conductivity of k= 25 W/m-K, is 6 mm thick, and each channel has a 2 mm x 6 mm rectangular cross section, with a 4 mm spacing between adjoining channels. Under operating conditions for which he = 1000 W/m-K, T.,0 = 1700 K, hi = 200 W/m-K, and T.,i = 400 K. Combustion gases Combustion de Air channel Toshi 2 mm 6 mm -6 mm 4 mm Turbine blade, k Combustion gases Tahoe Develop a computational heat transfer model using the finite-difference method to model steady- state heat transfer within the turbine blade in MATLAB. 1) Simplify and discretize the modeling domain using a grid of Ax, Ay = 0.5 mm. a. Emphasize why and how it can be simplified. 2) Find and plot the steady-state temperature distribution within the heat fin for the given conditions. 3) Find the location (x,y) of the maximum steady-state temperature within the turbine blade. What suggestions would you provide to reduce this temperature? 4) Perform a parametric study varying the h and k of the modeled domain and reflect on how to achieve enhanced steady-state cooling of the turbine blade. A gas turbine blade with internal cooling channels is modeled as a rectangular solid with rectangular channels. The blade, which has a thermal conductivity of k= 25 W/m-K, is 6 mm thick, and each channel has a 2 mm x 6 mm rectangular cross section, with a 4 mm spacing between adjoining channels. Under operating conditions for which he = 1000 W/m-K, T.,0 = 1700 K, hi = 200 W/m-K, and T.,i = 400 K. Combustion gases Combustion de Air channel Toshi 2 mm 6 mm -6 mm 4 mm Turbine blade, k Combustion gases Tahoe Develop a computational heat transfer model using the finite-difference method to model steady- state heat transfer within the turbine blade in MATLAB. 1) Simplify and discretize the modeling domain using a grid of Ax, Ay = 0.5 mm. a. Emphasize why and how it can be simplified. 2) Find and plot the steady-state temperature distribution within the heat fin for the given conditions. 3) Find the location (x,y) of the maximum steady-state temperature within the turbine blade. What suggestions would you provide to reduce this temperature? 4) Perform a parametric study varying the h and k of the modeled domain and reflect on how to achieve enhanced steady-state cooling of the turbine blade