A square plate of size 100 cm by 100 cm is subjected to an isothermal boundary condition of 500 °C on the top and to a convection environment on all the remaining three sides of 100 ?C with a heat transfer coefficient of 10 W/m2K. The thermal conductivity of the plate is 10 W/m2K. Assume the thickness of the plate is 1 cm. Determine the temperature distribution in the plate using
(a) two triangles and
(b) eight triangles. Calculate the temperature and heat fluxes in the x and y directions at a location (x = 30 cm, y = 30 cm).