Document Type : Full Length Research Article
Authors
1
Mechanical Engineering, Associate Professor, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, India
2
Civil Enginering, Student, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, India
3
Civil Engineering, Senior Professor, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, India
Abstract
Numerous industrial and biological processes like water filtering, air filtering, blood flow through arteries, absorption of digested foods are few examples of flow with suction/injection at the walls. Studies related to injection/suction of Newtonian fluids are reported by several researchers, but studies related to flow of non-Newtonian fluids with injection/suction are scarce in open literature. Rivlin-Eriksen fluid (also known as third-grade fluids) is an important class of non-Newtonian fluids which is applied for modelling blood flow, petroleum etc. Considering this, flow of a Rivlin-Ericksen fluid of grade three through large porous parallel plates with bottom injection and top suction (same velocity of suction and injection) is studied in the current study. The least square method, is applied for solving the governing equation which is an important part of the present study. Choosing the trial function for the least square method in this particular case is a difficult task since the velocity profile turns out to be asymmetric for higher velocity of suction and injection. In this study, proper implementation of least square method is demonstrated for such types of asymmetric velocity distribution which is a novelty. Solution for non-dimensional velocity distribution is obtained and the results are validated with the solution obtained by perturbation method in the present study. The results reveal that with increase in the non-Newtonian parameter (when cross-flow Reynolds number is low), velocity decreases at the same rate both near the bottom and top walls. However, when the cross-flow Reynolds number is higher, velocity near the bottom plate is nearly unaffected by decrease in the non-Newtonian parameter, whereas near the top plate, velocity decreases with increase in non-Newtonian parameter.
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