Consider the series solution, Equation 5.42, for the plane wall with convection. Calculate midplane (x* = 0) and surface (x* = 1) temperatures θ* for Fo = 0.1 and 1, using Bi = 0.1, 1, and 10. Consider only the first four eigenvalues. Based on these results, discuss the validity of the approximate solutions, Equations 5.43 and 5.44.

On solidification from a melt, the polymer polyethylene forms a semi-crystalline spherulite structure. (i) sketch an individual spherulite and label the amorphous and crystalline regions. (ii) draw a schematic to show the changes in specific volume with temperature during cooling from the melt, comparing it to the theoretical extremes of fully crystalline and fully amorphous (indicate tm and tg)