A square plate size \(100 \mathrm{~cm} \times 100 \mathrm{~cm}\) is subjected to an isothermal boundary condition of \(500^{\circ} \mathrm{C}\) on the top and to convection environment (on all the remaining three sides) of \(100^{\circ} \mathrm{C}\) with a heat transfer coefficient of \(10 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). The thermal conductivity of the material of the plate is \(10 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). Assume the thickness of the plate is \(1 \mathrm{~cm}\). Determine the temperature distribution in the plate using 

(a) Two triangles; 

(b) Eight triangles. Calculate the temperature at a location \((x=30 \mathrm{~cm}, y=30 \mathrm{~cm}\) ) and heat fluxes in \(x\) and \(y\) directions.