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

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w