Asquare rod of cross-section ac=w2 is attached between two heat reservoirs, maintained at the same temperature tb. the rod loses heat by convection to the air at t[infinity]. the following is given: w = 1 cm, 2l = 20cm, k = 10 w/(m-k), h = 25 w/(m2-k), tb=100°c, and t[infinity] = 20°c. (a) determine the temperature at x = l/2 and at x = l using an exact analysis. the following two options are acceptable: 1) derive the required governing equation using a differential energy balance and find the temperature profiles, and 2) use the proper temperature profile formula from your textbook. (b) determine the total heat transfer from the bar into the environment. (c) the rod under consideration is not a fin per se, but can be analyzed as a fin, what is the efficiency of this fin?

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?

An engine runs on the ideal diesel cycle. the cycle has a compression ratio of 20 and a cutoff ratio of 2. the highest temperature in the cycle is 1200 k. if the heat into the system is 300 kj/kg of working fluid and using variable specific heats determine the work produced per mass of working fluid

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?