Investigation of Power-Law Fluid on a Decelerated Rotating Disk

Year 2024, , 147 - 157, 30.09.2024

Serkan Ayan , Burhan Alveroğlu

https://doi.org/10.33401/fujma.1524621

Abstract

This study explores the behaviour of power-law fluids over decelerating rotating disks. The disk's angular velocity decreases inversely with time, and the unsteady governing equations modeling this flow yield similarity transformations that depend on the nondimensional parameter $\hat{\alpha}=\frac{\alpha}{\Omega_0}$. These transformations, introduced here for the first time in the literature, allow for a comprehensive analysis of the fluid dynamics for shear-thinning fluids within the range $0.5 < n \leq 1$.

We examine the no-slip boundary condition alongside the dimensionless unsteadiness parameter, which quantifies the initial deceleration or acceleration of the disk. We present velocity profiles and the viscosity function for various values of $\hat{\alpha}$. The boundary layer problem, formulated through dimensionless momentum and continuity equations derived via similarity transformations, is solved using the bvp4c function in MATLAB. This numerical method, employing the 4th-order Runge-Kutta algorithm, provides approximate solutions for the $U$, $V$, and $W$ velocity profiles and the $\mu$ viscosity function, considering different deceleration parameters and the power-law index $n$.

Our findings contribute novel insights into the fluid dynamics of power-law fluids in decelerating rotational systems, offering potential applications in industrial and engineering processes where such conditions are prevalent.

Keywords

decelerated rotating disk flows, boundary layer analysis, similarity solutions, non-newtonian fluids

References

• [1] T. Von Karman, Über laminare und turbulent reibung Z. angew., Math und Mech, 1 (1921), 233-52. $ \href{http://dx.doi.org/10.1002/zamm.19210010401}{\mbox{[CrossRef]}} $
• [2] W.G. Cochran, The flow due to a rotating disc, Math. Proc. Cambridge Philos. Soc., 303 (1934), 365-375. $ \href{https://doi.org/10.1017/S0305004100012561}{\mbox{[CrossRef]}}$
• [3] N. Gregory, J.T. Stuart,W.S.Walker, On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk, Philos. Trans. Roy. Soc. A, 248(943) (1955), 155-199. $ \href{https://doi.org/10.1098/rsta.1955.0013}{\mbox{[CrossRef]}} $
• [4] M.R. Malik, The neutral curve for stationary disturbances in rotating-disk flow, J. Fluid Mech., 164 (1986), 275-287. $\href{https://doi.org/10.1017/S0022112086002550}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0022680121&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=b&s=TITLE-ABS-KEY%28The+neutral+curve+for+stationary+disturbances+in+rotating-disk+flow%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=5}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1986A962700012}{\mbox{[Web of Science]}} $
• [5] R.J. Lingwood, Absolute instability of the boundary layer on a rotating disk, J. Fluid Mech., 299 (1995), 17-33. $ \href{https://doi.org/10.1017/S0022112095003405}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0029360906&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=cl&s=TITLE-ABS-KEY%28Absolute+instability+of+the+boundary+layer+on+a+rotating+disk%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=4}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1995RY30500002}{\mbox{[Web of Science]}} $
• [6] R.J. Lingwood, An experimental study of absolute instability of the rotating-disk boundary-layer flow, J. Fluid Mech., 314 (1996), 373-405. $ \href{https://doi.org/10.1017/S0022112096000365}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0030149749&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=cl&s=TITLE-ABS-KEY%28Absolute+instability+of+the+boundary+layer+on+a+rotating+disk%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=3}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1996UM65700016}{\mbox{[Web of Science]}} $
• [7] R.J. Lingwood, Absolute instability of the Ekman layer and related rotating flows, J. Fluid Mech., 331 (1997), 405-428. $ \href{https://doi.org/10.1017/S0022112096004144}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0030992654&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=b&s=TITLE-ABS-KEY%28Absolute+instability+of+the+Ekman+layer+and+related+rotating+flows%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1997WK09200016}{\mbox{[Web of Science]}} $
• [8] E. Appelquist, S. Imayama, P.H. Alfredsson, P. Schlatter and R.J. Lingwood, Linear disturbances in the rotating-disk flow: a comparison between results from simulations, experiments and theory, Eur. J. Mech. B Fluids, 55 (2016), 170-181. $ \href{https://doi.org/10.1016/j.euromechflu.2015.09.010}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84948457564&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Linear+disturbances+in+the+rotating-disk+flow%3A+a+comparison+between+results+from+simulations%2C+experiments+and+theory%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000367762900016}{\mbox{[Web of Science]}} $
• [9] J. Harris, P. Thomas and S. Garrett, On the stability of flows over rough rotating disks, In 42nd AIAA Fluid Dynamics Conference and Exhibit, (2012), 3075. $ \href{https://doi.org/10.2514/6.2012-3075}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85088340149&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+the+stability+of+flows+over+rough+rotating+disks%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=1}{\mbox{[Scopus]}} $
• [10] A.J. Cooper and P.W. Carpenter, The stability of rotating-disc boundary-layer flow over a compliant wall. Part 1. Type I and II instabilities, J. Fluid Mech., 350(1997), 231-259. $\href{https://doi.org/10.1017/S0022112097006976}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0031269673&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=b&s=TITLE-ABS-KEY%28The+stability+of+rotating-disc+boundary-layer+flow+over+a+compliant+wall.+Part+1.+Type+I+and+II+instabilities%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1997YJ01000009}{\mbox{[Web of Science]}} $
• [11] A.J. Cooper, J.H. Harris, S.J. Garrett, M. Özkan and P.J. Thomas, The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer, Phys. Fluids, 27(1) (2015). $ \href{https://doi.org/10.1063/1.4906091}{\mbox{[CrossRef]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000349068500031}{\mbox{[Web of Science]}} $
• [12] B. Alveroglu, A. Segalini and S.J. Garrett, The effect of surface roughness on the convective instability of the BEK family of boundary-layer flows, Eur. J. Mech. B Fluids, 56 (2016), 178-187. $\href{https://doi.org/10.1016/j.euromechflu.2015.11.013}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84953791139&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+effect+of+surface+roughness+on+the+convective+instability+of+the+BEK+family+of+boundary-layer+flows%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000378100300016}{\mbox{[Web of Science]}} $
• [13] C. Thomas, B. Alveroğlu, S.O. Stephen, M.A. Al-Malki and Z. Hussain, Effect of slip on the linear stability of the rotating disk boundary layer, Phys. Fluids, 35(8) (2023). $ \href{https://doi.org/10.1063/5.0162147}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85168725326&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Effect+of+slip+on+the+linear+stability+of+the+rotating+disk+boundary+layer%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001049438800013}{\mbox{[Web of Science]}} $
• [14] P. Mitschka, Nicht-newtonsche flussigkeiten ii. drehstromungen ostwald-de waelescher nicht-newtonscher flussigkeiten, Collect. Czechoslov. Chem. Commun., 29(12) (1964), 2892-2905. $ \href{https://doi.org/10.1135/cccc19642892}{\mbox{[CrossRef]}} $
• [15] P. Mitschka and J. Ulbrecht, Nicht-Newtonsche flussigkeiten IV. Str¨omung nicht-Newtonscher flussigkeiten Ostwald-de-Waeleschen typs in der umgebung rotierender drehkegel und scheiben, Collect. Czechoslov. Chem. Commun., 30(8) (1965), 2511-2526. $ \href{https://doi.org/10.1135/cccc19652511}{\mbox{[CrossRef]}} $
• [16] H.I. Andersson, E. De Korte and R. Meland, Flow of a power-law fluid over a rotating disk revisited, Fluid Dyn. Res., 28(2) (2001), 75. $ \href{https://doi.org/10.1016/S0169-5983(00)00018-6}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0035241695&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=b&s=DOI%2810.1016%2FS0169-5983%2800%2900018-6%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000166757800001}{\mbox{[Web of Science]}} $
• [17] S. Hussain, F. Ahmad, M. Shafique and S. Hussain, Numerical solution for accelerated rotating disk in a viscous fluid, Appl. Math., 4(6) (2013), 899-902. $ \href{https://doi.org/10.4236/am.2013.46124}{\mbox{[CrossRef]}} $
• [18] J.P. Denier and R.E. Hewitt, Asymptotic matching constraints for a boundary-layer flow of a power-law fluid, J. Fluid Mech., 518 (2004), 261–279. $\href{https://doi.org/10.1017/S0022112004001090}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-8644286613&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Asymptotic+matching+constraints+for+a+boundary-layer+++++flow+of+a+power-law+fluid%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000225335600011}{\mbox{[Web of Science]}} $
• [19] P.T. Griffiths, S.J. Garrett and S.O. Stephen, The neutral curve for stationary disturbances in rotating disk flow for power-law fluids, J. Non-Newton. Fluid Mech., 213 (2014), 73-81. $\href{https://doi.org/10.1016/j.jnnfm.2014.09.009}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84908156439&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+neutral+curve+for+stationary+disturbances+in+rotating+disk+flow+for+power-law+fluids%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000345804900009}{\mbox{[Web of Science]}} $
• [20] S.J. Garrett and N. Peake, The stability and transition of the boundary layer on a rotating sphere, J. Fluid Mech., 456 (2002), 199-218. $ \href{https://doi.org/10.1017/S0022112001007571}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0037052224&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+stability+and+transition+of+the+boundary+layer+on+a+rotating+sphere%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000175111300009}{\mbox{[Web of Science]}} $
• [21] R.J. Lingwood and S.J. Garrett, The effects of surface mass flux on the instability of the BEK system of rotating boundary-layer flows, Eur. J. Mech. B Fluids, 30(3) (2011), 299-310. $\href{https://doi.org/10.1016/j.euromechflu.2011.02.003}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-79953716504&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+effects+of+surface+mass+flux+on+the+instability+of+the+BEK+system+of+rotating+boundary-layer+flows%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000291071200006}{\mbox{[Web of Science]}} $
• [22] M.A. Abdulameer, P.T. Griffiths, B. Alveroglu and S.J. Garrett, On the stability of the BEK family of rotating boundary-layer flows for power-law fluids, J. Non-Newton. Fluid Mech., 236 (2016), 63-72. $ \href{https://doi.org/10.1016/j.jnnfm.2016.08.006}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84984852185&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+the+stability+of+the+BEK+family+of+rotating+boundary-layer+flows+for+power-law+fluids%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000386642700005}{\mbox{[Web of Science]}} $
• [23] A.A. Alqarni, B. Alveroglu, P.T. Griffiths and S.J. Garrett, The instability of non-Newtonian boundary-layer flows over rough rotating disks, J. Non-Newton. Fluid Mech., 273 (2019), 104174. $ \href{https://doi.org/10.1016/j.jnnfm.2019.104174}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85073530847&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+instability+of+non-Newtonian+boundary-layer+flows+over+rough+rotating+disks%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000503909000004}{\mbox{[Web of Science]}}$
• [24] R.J. Lingwood and P. Henrik Alfredsson, Instabilities of the von Karman boundary layer, Appl. Mech. Rev., 67(3) (2015), 030803. $ \href{ https://doi.org/10.1115/1.4029605}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84953798925&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=b&s=TITLE-ABS-KEY%28Instabilities+of+the+von+K%C3%A1rm%C3%A1n+boundary+layer%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=9}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000360285400003}{\mbox{[Web of Science]}} $
• [25] L.T. Watson and C. Wang, Deceleration of a rotating disk in a viscous fluid, Phys. Fluids, 22(12) (1979), 2267-2269. $ \href{https://doi.org/10.1063/1.862535}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0018313533&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Deceleration+of+a+rotating+disk+in+a+viscous+fluid%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} $
• [26] A. Majeed, A. Zeeshan, T. Mahmood, S.U. Rahman and I. Khan, Impact of magnetic field and second-order slip flow of casson liquid with heat transfer subject to suction/injection and convective boundary condition, J. Magn., 24(1) (2019), 81-89. $\href{https://doi.org/10.4283/JMAG.2019.24.1.081}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85065860463&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Impact+of+magnetic+field+and+second-order+slip+flow+of+casson+liquid+with+heat+transfer+subject+to+suction%2Finjection+and+convective+boundary+condition%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000463846400013}{\mbox{[Web of Science]}} $
• [27] M. Rahman, M. Turkyılmazoglu, M. Bilal and F. Sharif, On heat transfer with unsteady MHD nanofluid von Karman flow with uniform suction, Pramana - J. Phys., 97(4) (2023), 146. $ \href{https://doi.org/10.1007/s12043-023-02618-w}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85170372952&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+heat+transfer+with+unsteady+MHD+nanofluid+von+Karman+flow+with+uniform+suction%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001116272400001}{\mbox{[Web of Science]}} $
• [28] M. Rahman, F. Sharif, M. Turkyılmazoglu and M.S. Siddiqui, Unsteady three-dimensional magnetohydrodynamics flow of nanofluids over a decelerated rotating disk with uniform suction Pramana, 96(4) (2022), 170. $ \href{https://doi.org/10.1007/s12043-022-02404-0}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85138015423&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Unsteady+three-dimensional+magnetohydrodynamics+flow+of+nanofluids+over+a+decelerated+rotating+disk+with+uniform+suction%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000852401300003}{\mbox{[Web of Science]}} $
• [29] T. Fang and H. Tao, Unsteady viscous flow over a rotating stretchable disk with deceleration, Commun. Nonlinear Sci. Numer. Simul., 17(12) (2012), 5064-5072. $ \href{https://doi.org/10.1016/j.cnsns.2012.04.017}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84864416230&origin=resultslist&sort=plf-f&src=s&sid=fb8e6e8493cf4fdd5b1eac20a0b63a3f&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Unsteady+viscous+flow+over+a+rotating+stretchable+disk+with+deceleration%22%29&sl=105&sessionSearchId=fb8e6e8493cf4fdd5b1eac20a0b63a3f&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000307104000054}{\mbox{[Web of Science]}} $
• [30] J. Kierzenka and L.F. Shampine, A BVP solver based on residual control and the Maltab PSE, ACM Trans. Math. Softw., 27(3) (2001), 299-316. $ \href{https://doi.org/10.1145/502800.502801}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0012027011&origin=resultslist&sort=plf-f&src=s&sid=c73f0f878acca5d51e6a6a04056dca36&sot=b&sdt=b&s=ISSN%280098-3500%29&sl=46&sessionSearchId=c73f0f878acca5d51e6a6a04056dca36&relpos=6}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000173589000001}{\mbox{[Web of Science]}} $
• [31] K. Zhang and X. Liao, Theory and modeling of rotating fluids: convection, inertial waves and precession, Cambridge University Press, (2017).