(a) Let the ends of a copper rod 44 cm long be maintained at 0°C. Suppose that the center of the bar is heated to 44°C by an external heat source and that this situation is maintained until a steady state results. Find this steady state temperature distribution. f(x) 2x + 44 sin 2πx 44 0 ≤ x ≤ 22 2πX 88 - 44 sin 2x, 22 ≤ x ≤ 44 f(x) = 44 (1-) f(x) = 4x 1 44 f(x) Rx) = 44 sin()+4x(1-4) f(x) [2x, 0 ≤ x ≤ 22 88 - 2x, 22 ≤ x ≤ 44 (b) At a time t = 0 [after the steady state of part (a) has been reached], let the heat source be removed. At the same instant let the end x = 0 be placed in thermal contact with a reservoir at 22°C, while the other end remains at 0°C. Find the temperature as a function of position and time. (Assume the thermal diffusivity of copper is 1.14 cm²/sec.) 22 - + 44(30 ΣΟ 44 30 sin πη лn sin 2 Tnx 44 x ) 1.14m nt n = 1 리 2 n'e 10000