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A good model for the melting of granules in one screw plastic extruders extruder is presented partly I. It is consistent with observations of earlier workers and retains a few of the strategies launched by Tadmor in his unit; however, it assumes that the stable bed of granules cannot stand large differences of principal stresses and so account must be considered explicitly of the downstream drive balance on the sturdy bed and in the melt pool area. Detailed quasi-analytic results are granted for a Newtonian liquid partly II. These illustrate the model for an especially simple case and also have relevance for a few materials. A more elaborate numerical scheme is usually described in Part III for a non-Newtonian model and results are presented for comparison with the predictions of various other theories and with experiments.