Abstract
Explicit, analytical solutions are obtained for the flow of a non-Newtonian Reiner–Rivlin fluid between two coaxially rotating and radially stretching disks. The rotor–stator case and the cases of co- and counter-rotation are discussed elucidating the effects of various parameters of interest, such as stretching parameters, non-Newtonian parameter and Reynolds number.
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
Kármán ThV (1921) Über laminare und turbulente Reibung. ZAMM-J Appl Math Mech 1(4):233–252
Bödewadt UT (1940) Die drehströmung über festem grunde. ZAMM-J Appl Math Mech 20(5):241–253
Zandbergen PJ, Dijkstra D (1987) Von Kármán swirling flows. Annu Rev Fluid Mech 19(1):465–491
Gregory N, Stuart JT, Walker WS (1955) On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Philos Trans R Soc Lond Ser A, Math Phys Sci, 248:155–199
Lingwood RJ (1996) An experimental study of absolute instability of the rotating-disk boundary-layer flow. J Fluid Mech 314:373–405
Childs PR (2010) Rotating flow. Elsevier
Batchelor GK (1951) Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Q J Mech Appl Math 4(1):29–41
Stewartson K (1953) On the flow between two rotating coaxial disks. Math Proc Camb Philos Soc 49(2):333–341
Lance GN, Rogers MH (1962) The axially symmetric flow of a viscous fluid between two infinite rotating disk. Proc R Soc Lond Ser A Math Phys Sci, 266:109–121
Holodniok M, Kubicek M, Hlavacek V (1977) Computation of the flow between two rotating coaxial disks. J Fluid Mech 81(4):689–699
Soong CY, Wu CC, Liu TP, Liu TP (2003) Flow structure between two co-axial disks rotating independently. Exp Therm Fluid Sci 27(3):295–311
Turkyilmazoglu M (2006) Flow and heat simultaneously induced by two stretchable rotating disks. Phys Fluids 28(4):043601
Fang T (2007) Flow over a stretchable disk. Phys Fluids 19(12):128105
Reiner M (1945) A mathematical theory of dilatancy. Am J Math 67(3):350–362
Rivlin R.S (1948) The hydrodynamics of non-Newtonian fluids. I. Proc R Soc Lond A, 193(1033):260–281
Liao S.J (1992) The proposed homotopy analysis technique for the solution of nonlinear problems. Diss. PhD Thesis, Shanghai Jiao Tong University
Xu H, Liao SJ (2006) Series solutions of unsteady MHD flows above a rotating disk. Mecc 41(6):599–609
Das A, Sahoo B (2018) Flow of a Reiner-Rivlin fluid between two infinite coaxial rotating disks. Math Methods Appl Sci 41(14):5602–5618
Das A, Sahoo B (2018) Flow and heat transfer of a second grade fluid between two stretchable rotating disks. Bull Braz Math Soc 49(3):531–547
Das A, Bhuyan SK (2018) Application of HAM to the von Kármán swirling flow with heat transfer over a rough rotating disk. Int J Appl Comput Math 4(5):113
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Das, A., Sarkar, S. (2020). Flow Analysis of Reiner–Rivlin Fluid Between Two Stretchable Rotating Disks. In: Chakraverty, S., Biswas, P. (eds) Recent Trends in Wave Mechanics and Vibrations. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0287-3_5
Download citation
DOI: https://doi.org/10.1007/978-981-15-0287-3_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0286-6
Online ISBN: 978-981-15-0287-3
eBook Packages: EngineeringEngineering (R0)