Ametal plate (k = 180 w/m·k, rho = 2800 kg/m^3 , and cp = 880 j/kg·k) with a thickness of 1cm is being cooled by air at 5°c with a convection heat transfer coefficient of 30 w/m2 ·k. if the initial temperature of the plate is 300°c, determine the plate temperature gradient at the surface after 2 minutes of cooling. hint: use the lumped system analysis to calculate the plate surface temperature. make sure to verify the application of this method to this problem