(a) In a water pool at 32°C, a hot bullet (T, = 212°C) horizontally enters water 1 m below its surface. A spectator at the surface is observing this phenomenon.

Using definitions and concepts of dimensionless numbers discussed in this course and data easily available in the book (or online), explain what the spectator should expect at the surface to feel first: movement of water layers or warm water? If instead of water we have air at 32°C, what the spectator should expect now? Justify your answer by appropriate equations and be concise. [20 points] (b) For a laminar flow inside a pipe, starting with the scaled profile equation: \frac{T_{s}(x)-T(r, x)}{T_{s}(x)-T_{m}(x)} prove that the ratio of film coefficient to the fluid thermal conductivity (h/k) does not change with x in the fully developed region. If k is constant, plot the change of h with x in both the entry and the fully developed region in the figure given below: [20 points]