Ametal plate (k=180 w/m-k, p-=2800 kg/m, and cp=880 j/kg k) with a thickness of 1 cm is being cooled by air at 5°c with a convection heat transfer coefficient of 30 w/m^2 k. if the initial temperature of the plate is 300°c, determine the plate temperature gradient at the surface after 3 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