Utilizing the integration by parts rule, a simple and general computational method is proposed for solving quasi-steady parallel plate flow problems and most types of fluids can be handled by this method, such as the Newtonian fluid, the Power-law fluid, the Bingham fluid, and the Herschel-Bulkley fluid. The flow rate-pressure gradient relation for quasi-steady parallel plate flows is derived based on an abstract piecewise constitutive equation. Moreover, the flow rate is directly expressed in terms of the constitutive equation in this method, so high efficiency is achieved. As an application example of the proposed method, a new quasi-steady magnetorheological damper model more general than the existing ones is developed with the material non-linearities considered in both the pre-yield and post-yield regimes. Finally, conversions of this model to the Bingham model, the Herschel-Bulkley model, the Biviscous model, etc., are demonstrated.
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