Using the stress strain relations you developed in part: 1. derive the theoretical torque versus angle of twist relationship for the cast iron and for the steel. a. for every angle of twist recorded in the lab, determine which part of the shaft cross section is in the linear elastic range, which part is in perfectly plastic range (if any) and which part is in strain hardening (if any). b. given the shearing stress-strain models you developed, derive the equations for the torque for each of the parts identified above.

Asteel tube (k=50 w/mk) of inner and outer diameter di = 20mm and do=26mm, respectively, is used to transfer heat from hot gases flowing over the tube (h-hot = 200w/m2k) to cold water flowing through the tube (h-cold = 8000 w/m2k). what is the cold-side overall heat transfer coefficient uc? to enhance heat transfer 16 straight fins of rectangular profile are installed longitudinally along the outer surface of the tube. the fins are equally spaced around the circumference of the tube, each having a thickness of 2mm and a length of 15mm. what is the corresponding overall heat transfer coefficient uc? *solve for uc in both cases*