Abstract
In this paper, the flow of a simplest Non-Newtonian fluid in a channel of varying cross-section with permeable boundaries is investigated. The paper finds its significance in understanding the flow of Bio-fluids in the ducts of varying cross section. Perturbation technique is used to solve the governing equations of the flow phenomenon. The expressions for velocity, flow rate, wall shear stress, and the pressure drop are derived. The flux is a function of external pressure, Jeffrey parameter, and the permeability parameter. Further, if \(\lambda_{1} \to 0\) our results agree with Krishna Prasad and Chandra (Proc Nat Acad Sci 60(A) III: 317–326, 1990 [1]). Mathematica software is used find the pressure, which place a vital role in varying cross sections. Shear stress increases with increasing effects of permeability and Jeffrey parameters which is observed graphically. It is noticed that shear thinning reduces the wall shear stress and this point is stresses in the paper as well. This work helps the young researcher to develop interest in the field of Bio-fluids with varying cross-section.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Krishna Prasad JSVR, Chandra P (1990) Flow in channels of varying cross-section with permeable boundaries. Proc Nat Acad Sci 60(A) III: 317–326
Vajravelu K, Sreenadh S, Devaki P, Prasad KV (2015) Peristaltic transport of Herschel Bulkley fluid in an elastic tube. Heat Transf Asian Res 44(7):585–598. https://doi.org/10.1002/htj.21137
Vajravelu K, Sreenadh S, Devaki P, Prasad KV (2016) Peristaltic transport of Casson fluid in an elastic tube. J Appl Fluid Mech 9(4):1897–1905. https://doi.org/10.18869/acadpub.jafm.68.235.24695
Badari Narayana CH, Devaki P, Sreenadh S (2017) Effect of elasticity and inclination on Hershel- Bulkley fluid flow in a tube. Int J Adv Inf Sci Technol 6(2):6–12. https://doi.org/10.15693/ijaist/2017.v6i2.6-12
Berhane Tesfahun (2017) Flow of a Newtonian fluid in a non-uniform wavy and permeable tube. New Trends Math Sci 5(4):12–23. https://doi.org/10.20852/ntmsci.2017.210
Devaki P, Sreenadh S, Vajravelu K, Prasad KV, Vaidya H (2018) Wall properties and slip consequences on peristaltic transport of a casson liquid in a flexible channel with heat transfer. Appl Math Nonlinear Sci 3(1):277–290. https://doi.org/10.21042/AMNS.2018.1.00021
Fakour M, Ganji DD, Khalili A, Bakhshi A (2017) Study of heat transfer in nanofluid mhd flow in a channel with permeable walls. Heat Transf Res 48(3):221–238. https://doi.org/10.1615/HeatTransRes.2016011839
Rasoulzadeh M, Panfilov M (2018) Asymptotic solution to the viscous/inertial flow in wavy channels with permeable walls. Phys Fluids 30:106604. https://doi.org/10.1063/1.5041748
Makinde OD (1995) Laminar flow in a channel of varying width with permeable boundaries. Rom J Phys 40(4–5):403–417
Makinde OD, Alagoa KD (1999) Effect of magnetic field on steady flow through an indented channel. AMSE Modell Measure Control B 68(1):25–32
Makinde OD (1999) Steady flow and heat transfer in a diverging tube. AMSE Modell Measure Control B 67(1):51–63
Makinde OD, Sibanda P (2000) Steady flow in a diverging symmetrical channel: numerical study of Bifurcation by analytic continuation. Quaestiones Math 23:45–57. https://doi.org/10.2989/16073600009485956
Mhone PY, Makinde OD (2006) Unsteady MHD flow with heat transfer in a diverging channel. Rom J Phys 51(9–10):967–979
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Devaki, P., Badari Narayana, C.H., Kavitha, A., Sreenadh, S. (2021). Effect of Permeable Boundaries on the Flow of a Jeffrey Fluid in a Channel of Varying Cross-Section. In: Rushi Kumar, B., Sivaraj, R., Prakash, J. (eds) Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4308-1_18
Download citation
DOI: https://doi.org/10.1007/978-981-15-4308-1_18
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-4307-4
Online ISBN: 978-981-15-4308-1
eBook Packages: EngineeringEngineering (R0)