We describe the current state of a continuing project which addresses control of one aspect of a particular batch-continuous manufacturing process. Previous spatial time series modelling for this aspect of the process has been based on traditional nonparametric modeling techniques (a kernel-based smoothing procedure, in particular). Here we describe a substantially refined semi-parametric model. This model incorporates basic physical knowledge about this aspect of the process in the form of a coupled system of partial differential equations. The manuscript is accompanied by a video tape showing some of the data and the fitted models.