Generalized flow rate functions arising in study of effects of processing on shear rate of yoghurt

In this work, the generalized flow rate functions arising in the study of flow problems are introduced. The efficient and accurate formulas through the hypergeometrical and incomplete beta functions are established. It is shown that the flow rate functions C(m) and D(m,ε) describing the effects of processing on shear rate of yoghurt are special cases of generalized flow rate functions. Comparative numerical examples are presented to demonstrate the efficiency of the proposed approaches.