1. An aluminum circular cylinder 50 mm in diameter with ends insulated is initially at 100?C. Approximate the temperature at the center of the cylinder after 2 s if the lateral surface is kept at 0?C.For aluminum, k = 8.6 × 10-5m2 /s.
2. A circular cylinder 1 m in radius is completely insulated and has an initial temperature distribution 100r ?C. Find an expression for the temperature as a function of r and t. Write integral expressions for at least three coefficients in the series expansion.