In the method of separation of variables for two-dimensional, steady-state conduction, the separation constant λ2^ must be a positive constant. Show that a negative or zero value of λ^2 will result in solutions that cannot satisfy the prescribed boundary conditions.

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?

Consider airflow over a flat plate of length l = 1.5 m under conditions for which transition occurs at le = 0.9 m based on the critical reynolds number, re, e = 5 x 10. evaluating the thermophysical properties of air at 400 k, determine the air velocity. (hint: use the tables to find the properties of air)

A12 mm diameter shaft runs in a plain cylindrical bush 30 mm long that is located in an 18 mm diameter hole in a housing. the shaft-inner bush fit is h8 f and the outer bush-housing fit is h7-p6. make a fully cimensioned sketch of the bush with tolerances. find the maximum and minimum clearance or interference for both fits on the inner and outer diameters of the bush