A model for the melting of granules within a screw extruder is presented partly I. It is in keeping twin screw extruder manufacturer with observations of previous workers and retains some of the strategies brought in by Tadmor in his style; even so, it assumes that the stable bed of granules cannot stand large differences of principal stresses therefore account must be considered explicitly of the downstream push balance on the stable bed and in the melt pool. Detailed quasi-analytic email address details are provided for a Newtonian fluid partly II. These illustrate the model for a particularly simple case and have relevance for a few materials. A more elaborate numerical scheme is described in Part III for a non-Newtonian model and email address details are presented for evaluation with the predictions of different theories and with experiments.