1. A straight rectangular fin of pure aluminum has a length of 5.5 cm, a depth of 25 cm, and a thickness of 2 mm is fixed to a wall at a base temperature of 105C. The fin is exposed to a convection environment at 20C where the convective heat transfer coefficient is 500 W/m2 C. L 5.5 cm To=20C h : 5004 T. +105C R-2800 -25 cm w 2mm t a. Calculate the temperature at the end of the fin, the total rate of heat loss from the fin, and the fin's efficiency, assuming negligible heat loss from the tip. b. Calculate only the temperature at the end of the fin, assuming convective heat loss from the tip. Briefly explain if the negligible heat loss assumption from part a is reasonable. c. It is found that the finis cracking at its base, producing a contact resistance there. The contact coefficient is estimated at 2500 W/m C. Re-evaluate the fin efficiency under these conditions, assuming negligible heat loss from the fin tip. Hint: Note that, because of the crack, T) is no longer equal to T. To solve, write an expression for the heat lost from the fin, assuming a fin base temperature of "7" To satisfy steady state, the heat loss through the fin must be equal to the heat loss across the crack. You're given a contact resistance in units of W/m C, which is the same units as h. Write an expression for heat transfer q across the crack using appropriate units. Set them equal and solve for TX