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Sains Malaysiana 38(1): 119-124(2009)
Feedback Control of Thermocapillary Convection
in a
Rotating Fluid Layer with Free-Slip Bottom
(Kawalan Suapbalik Olakan Termokapilari dalam Lapisan Bendalir Berputar dengan Bawahnya Tergelincir)
Ishak Hashim
School of
Mathematical Sciences, Universiti Kebangsaan
43600 Bangi Selangor, Malaysia
Zailan Siri Institute of Mathematical Sciences, University of Malaya 50603 Kuala Lumpur, Malaysia
Received: 2 May 2008 / Accepted:
20 June 2008
abstract
The
linear stability theory is applied to investigate the effects of rotation and
feedback control on the onset of steady and oscillatory thermocapillary
convection in a horizontal fluid layer heated from below with a free-slip
bottom. The thresholds and codimension-2 points for the onset of steady and
oscillatory convection are determined. The effect of feedback control on the
Keyword: Feedback control; marangoni convection; rotation; surface tension; thermocapillary
ABSTRAK
Teori
kestabilan linear digunakan untuk mengkaji kesan putaran dan kawalan suapbalik
terhadap permulaan olakan termokapilari mantap dan berayun dalam lapisan
mengufuk bendalir yang dipanaskan dari bawah dengan bawahnya tergelincir. Titik
di ambang dan kodimensi-2 untuk permulaan olakan mantap dan berayun ditentukan.
Kesan kawalan suapbalik terhadap ruang parameter
Kata
kunci: Kawalan suapbalik; ketegangan permukaan; olakan marangoni; putaran; termokapilari
REFERENCES/RUJUKAN
Arifin, N. M., Nazar, R. M.
& Senu, N. 2007. Feedback control of the Marangoni-Bẽnard instability
in a fluid layer with a free-slip bottom. J. Phys.
Soc. Japan. 76: 014401.
Bau, H. H. 1999. Control of Marangoni-Bẽnard convection. Int. J. Heat Mass Transfer. 42: 1327-1341.
Boeck, T., Thess, A. 1997. Inertial Bẽnard-Marangoni convection. J. Fluid
Mech. 350:149-175.
Chandrasekhar, S. 1961. Hydrodynamic
and Hydromagnetic Stability, Oxford,
UK. Oxford University Press.
Chang, F.P. & Chiang, K.T.
1998. Oscillatory instability analysis of Bẽnard-Marangoni convection in
a rotating fluid under a uniform magnetic field. Int. J. Heat Mass Transfer. 41(17):2667-2675.
Char, M.I., Chiang, K.T. &
Jou, J.J. 1997. Oscillatory instability analysis of Bẽnard-Marangoni
convection in a rotating fluid with internal heat generation. Int. J. Heat Mass Transfer. 40(4):857-867.
Garcia-Ybarra, P. L., Castillo, J.
L. & Velarde, M. G. 1987. Bẽnard-Marangoni
convection with a deformable interface and poorly conducting boundaries. Phys. Fluids. 30(9): 2655-2661.
Gouesbet, G., Maquet, J., Rozẽ,
C. & Darrigo, R. 1990. Surface-tension-and coupled buoyancy-driven
instability in a horizontal liquid layer: Overstability and exchange of
stability. Phys. Fluids. A 2 (6):903-911.
Hashim,
Hashim, I. & Sarma, W. 2007. On oscillatory Marangoni convection in a
rotating fluid layer subject to a uniform heat flux from below. Int.
Comm. Heat & Mass Trans. 34: 225-230.
Hashim, I. & Sarma, W. 2007. On oscillatory Marangoni convection in
rotating fluid layer with flat free surface subject to uniform heat flux from
below. Int. J. Heat Mass Transfer. 50:4508-4511.
Hayat, T. 2005. Oscillatory flow of a JohnsonSegalman fluid in
a rotating system. Z. angew. Math. Mech. 18:313-321.
Hayat, T., Fetecau, C. &
Sajid, M. 2008. On MHD transient flow of a Maxwell fluid in a porous medium and
rotating frame. Phys. Lett. A 10 :1639-1644.
Hayat, T., Khan, S. & Khan, M. 2008. Exact solution for rotating flows of a
generalized Burgers' fluid in a porous space. Appl.
Mathl. Model. 32:749-760.
Hayat, T., Nadeem, S. &
Asghar, S., Siddiqui, A. 2001. Fluctuating flow of a third order fluid on a
porous plate in a rotating medium. Int.
J. Non-Linear Mech. 36 :901-916.
Hayat, T., Nadeem, S., Asghar.
2004. Hydromagnetic Couette flow of an Oldroyd-B fluid in a rotating system. Int. J. Engrng. Sci. 42: 65-78.
Johnson D., & Narayanan, R.
1996. Experimental Observation of dynamic mode switching in
interfacial-tension-driven convection near a codimension-two point. Phys. Rev.
E 54(4): 31-2-3104
Kaddame, A., Lebon, G. 1994. Bẽnard-Marangoni convection in a
rotating fluid with and without surface deformation. Appl.
Sci. Res. 52:295-308.
Kaddame, A. & Lebon, G.
1994. Overstability in rotating Bẽnard-Marangoni cells. Microgravity Quart. 4(2): 69-74.
McConaghy, G.A. & Finlayson,
B.A. 1969. Surface tension driven oscillatory instability in a rotating fluid
layer. J. Fluid Mech. 39 (part 1): 49-55.
Namikawa, T., Takashima, M.
& Matsushita, S. 1970. The effect of rotation on convective instability
induced by surface tension and buoyancy. J.
Phys. Soc. Japan 28(5):1340-1349.
Pearson, J.R.A. 1958. On
convection cells induced by surface tension. J. Fluid Mech. 4: 489-500.
Sarma, G.S.R. 1979. Marangoni
convection in a fluid layer under the action of a transverse magnetic field. Space
Res. 19:575-578.
Sarma, G.S.R. 1981. Marangoni
convection in a liquid layer under the simultaneous action of a transverse
magnetic field and rotation. Adv. Space Res. 1:55-58.
Sarma, G.S.R. 1983. Bẽnard-Marangoni instability in a
rotating liquid layer subjected to a transverse magnetic field. Adv.
Space Res. 3(5):33-36.
Sarma, G.S.R. 1985. Effects of interfacial curvature and gravity
waves on the onset of thermocapillary convective instability in a rotating
liquid layer subjected to a transverse magnetic field. PhysicoChem.
Hydrodyn. 6(3):283:300.
Sarma, G.S.R. 1987. Interaction of surface-tension and buoyancy
mechanisms in horizontal liquid layers. J.
Thermophysics. 1(2):129-135.
Scriven, L.E. & Sternling,
C. V. 1964. On cellular convection
driven by surface-tension gradients: Effects of mean surface tension and
surface viscosity. J. Fluid Mech. 19:
321-340.
Tagare, S., Babu, A. B. &
Rameshwar, Y. 2008. Rayleigh-Bẽnard
convection in rotating fluids. Int. J.
Heat Mass Transfer. 51:1168-1178.
Takashima, M. & Namikawa, T.
1971. Surface-tension-driven convection under the simultaneous action of a
magnetic field and rotation. Phys. Lett. 37A:55-56.
Tang, J. & Bau, H. H. 1993. Feedback control stabilization of the
no-motion state of a fluid confined in a horizontal. J. Fluid Mech. 257: 485-505.
Tang, J. & Bau, H. H. 1998. Numerical investigation of the stabilization
of the no-motion state of a fluid layer heated from below and cooled from above. Phys.
Fluids. 10:1597-1610.
Vidal, A. & Acrivos, A. 1996.
The influence of Coriolis force on surface-tension-driven convection. J. Fluid
Mech. 26: 807-818.
Wilson, S. K. 1994 The effect of
a uniform magnetic field on the onset of steady Marangoni convection in a layer
of conducting fluid with a prescribed heat flux at its lower boundary. Phys. Fluids. 6 (11): 3591-3600.
Wilson, S. K. 1997. The effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of fluid. Acta Mechanica 124:63-78.
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