One end of a glass rod is kept in boiling water and the other end in ice water until temperature equilibrium is reached. then the two ends are switched, so that the hot end is in ice water and the cold end in boiling water. how does the temperature of the rod change with time? is the temperature harmonic?

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.