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Effect of Rotational Modulation on Rayleigh – B´enard Convection in a Couple Stress Liquid
DOI:
https://doi.org/10.12723/mjs.50.1Keywords:
Rotational Modulation, couple stress fluid, Rayleigh-B´enard convection, correction Rayleigh numberAbstract
The Rayleigh-B´enard convection in a couple stress liquid with rotational modulation is studied using the linear analysis based on normal mode technique. The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady rotation, a time-periodic sinusoidal perturbation is applied. The expression for Rayleigh number and correction Rayleigh number are obtained using regular perturbation method. The expression for correction Rayleigh number is obtained as a function of frequency of modulation, Taylor number, Couple Stress parameter and Prandtl number. It is observed that rotational modulation leads to delay in onset of convection. Rotation modulation is an example of external control of internal convection.
References
[1] H. B´enard, “Les tourbillions cellulariesdansunenappeliquidetransportant de la chaleut par convection en regime permanent,” Annual Review of Physical Chemistry, vol. 23, pp. 62-144, 1900.
[2] J. K. Bhattacharjee, “Rotating Rayleigh-B´enard convection with modulation,” Journal of Physics A: Mathematical and General, vol. 22, no. 24, pp. L1135, 1989.
[3] J. K. Bhattacharjee, “Convective instability in a rotating fluid layer under modulation of the rotating rate,” Physical Review A, vol. 41, pp. 5491-5494, 1990.
[4] B. S. Bhadauria, P. G. Siddheshwar, A. K. Singh and V. K. Gupta, “A local nonlinear stability analysis of modulated double diffusive
stationary convection in a couple stress fluid,” Journal of Applied Fluid Mechanics, vol. 9, no. 3, pp. 1255-1264, 2016.
[5] S. Chandrasekhar, Hydrodynamic and hydromagnetic stability. Oxford: Clarendon Press, 1961.
[6] P. Drazin and W. Reid, Hydrodynamic instability. Cambridge University Press, UK, 1981.
[7] S. Govender, “Coriolis effect on the linear stability of convection in a porous layer placed far away from the axis of rotation,”
Transport in Porous Media, vol. 51, no. 3, pp. 315–326, 2003.
[8] G. K¨uppers and D. Lortz, “Transition from laminar convection to thermal turbulence in a rotating fluid layer,” Journal of Fluid
Mechanics, vol. 35, pp. 609 – 620, 1969.
[9] M. S. Malashetty and D. Basavaraja, “Effect of thermal/gravity modulation on the onset of Rayleigh-B´enard convection in a
couple stress fluid,” International Journal of Transport Phenomena, vol. 7, no. 1, pp. 45-53, 2005.
[10] P. S. Om, B. S. Bhadauria and A. Khan, “Modulated centrifugal convection in a vertical rotating porous layer distant from axis
of rotation,” Transport in Porous Media, vol. 79, pp. 255-264, 2009.
[11] P. S. Om, B. S. Bhadauria and A. Khan, “Rotating Brinkman-Lapwood convection with modulation,” Transport in Porous Media,
vol. 88, pp. 369-383, 2011.
[12] L. Rayleigh, “On convection currents in a horizontal layer of fluid when the higher temperature is on the under side,” Philosophical
Magazine, vol. 32, pp. 529, 1916.
[13] I. S. Shivakumara, S. Sureshkumar and N. Devaraju, “Coriolis effect on thermal convection in a couple-stress fluid-saturated
rotating rigid porous layer,” Archive of Applied Mechanics, vol. 81, no. 4, pp. 513-530, 2011.
[14] P. G. Siddheshwar and S. Pranesh, “An analytical study of linear and non-linear convection in Boussinesq-Stokes suspensions,”
International Journal of Non-Linear Mechanics, vol. 39, pp. 165-172, 2004.
[15] S. Pranesh and S. George, “ Effect of magnetic field on the onset of Rayleigh-Benard convection in Boussinesq Stokes suspensions
with time periodic boundary temperatures,” International Journal of Applied Mathematics and Mechanics, vol. 6, no. 16, pp. 38-55, 2010.
[16] S. Tarannum and S. Pranesh, “Effect of gravity modulation on the onset of Rayleigh B´enard convection in a weak electrically
conducting couple stress fluid with saturated porous layer,” International Journal of Engineering Research and Technology, vol.
5, no. 1, pp. 914 – 928, 2016.
[17] S. Tarannum and S. Pranesh, “Heat and mass transfer of triple diffusive convection in a rotating couple stress liquid using
Ginzburg-Landau model,” International Journal of Mechanical, Aerospace,Industrial, Mechatronic and Manufacturing Engineering, vol. 11, no. 3, pp. 545 – 550, 2017.
[18] P. Vadasz and S. Govender, “Stability and stationary convection induced by gravity and centrifugal forces in a rotating porous layer distant from the axis of rotation,” International Journal of Engineering Science, vol. 39, no. 6, pp. 715 – 732, 2001.
[19] G. Venezian,“Effect of modulation on the onset of thermal convection,” Journal of Fluid Mechanics, vol. 35, pp. 243, 1969.
[20] G. Veronis, “ Cellular convection with finite amplitude in a rotating fluid,” Journal of Fluid Mechanics, vol. 5, no. 3, pp. 401-435, 1959.
[2] J. K. Bhattacharjee, “Rotating Rayleigh-B´enard convection with modulation,” Journal of Physics A: Mathematical and General, vol. 22, no. 24, pp. L1135, 1989.
[3] J. K. Bhattacharjee, “Convective instability in a rotating fluid layer under modulation of the rotating rate,” Physical Review A, vol. 41, pp. 5491-5494, 1990.
[4] B. S. Bhadauria, P. G. Siddheshwar, A. K. Singh and V. K. Gupta, “A local nonlinear stability analysis of modulated double diffusive
stationary convection in a couple stress fluid,” Journal of Applied Fluid Mechanics, vol. 9, no. 3, pp. 1255-1264, 2016.
[5] S. Chandrasekhar, Hydrodynamic and hydromagnetic stability. Oxford: Clarendon Press, 1961.
[6] P. Drazin and W. Reid, Hydrodynamic instability. Cambridge University Press, UK, 1981.
[7] S. Govender, “Coriolis effect on the linear stability of convection in a porous layer placed far away from the axis of rotation,”
Transport in Porous Media, vol. 51, no. 3, pp. 315–326, 2003.
[8] G. K¨uppers and D. Lortz, “Transition from laminar convection to thermal turbulence in a rotating fluid layer,” Journal of Fluid
Mechanics, vol. 35, pp. 609 – 620, 1969.
[9] M. S. Malashetty and D. Basavaraja, “Effect of thermal/gravity modulation on the onset of Rayleigh-B´enard convection in a
couple stress fluid,” International Journal of Transport Phenomena, vol. 7, no. 1, pp. 45-53, 2005.
[10] P. S. Om, B. S. Bhadauria and A. Khan, “Modulated centrifugal convection in a vertical rotating porous layer distant from axis
of rotation,” Transport in Porous Media, vol. 79, pp. 255-264, 2009.
[11] P. S. Om, B. S. Bhadauria and A. Khan, “Rotating Brinkman-Lapwood convection with modulation,” Transport in Porous Media,
vol. 88, pp. 369-383, 2011.
[12] L. Rayleigh, “On convection currents in a horizontal layer of fluid when the higher temperature is on the under side,” Philosophical
Magazine, vol. 32, pp. 529, 1916.
[13] I. S. Shivakumara, S. Sureshkumar and N. Devaraju, “Coriolis effect on thermal convection in a couple-stress fluid-saturated
rotating rigid porous layer,” Archive of Applied Mechanics, vol. 81, no. 4, pp. 513-530, 2011.
[14] P. G. Siddheshwar and S. Pranesh, “An analytical study of linear and non-linear convection in Boussinesq-Stokes suspensions,”
International Journal of Non-Linear Mechanics, vol. 39, pp. 165-172, 2004.
[15] S. Pranesh and S. George, “ Effect of magnetic field on the onset of Rayleigh-Benard convection in Boussinesq Stokes suspensions
with time periodic boundary temperatures,” International Journal of Applied Mathematics and Mechanics, vol. 6, no. 16, pp. 38-55, 2010.
[16] S. Tarannum and S. Pranesh, “Effect of gravity modulation on the onset of Rayleigh B´enard convection in a weak electrically
conducting couple stress fluid with saturated porous layer,” International Journal of Engineering Research and Technology, vol.
5, no. 1, pp. 914 – 928, 2016.
[17] S. Tarannum and S. Pranesh, “Heat and mass transfer of triple diffusive convection in a rotating couple stress liquid using
Ginzburg-Landau model,” International Journal of Mechanical, Aerospace,Industrial, Mechatronic and Manufacturing Engineering, vol. 11, no. 3, pp. 545 – 550, 2017.
[18] P. Vadasz and S. Govender, “Stability and stationary convection induced by gravity and centrifugal forces in a rotating porous layer distant from the axis of rotation,” International Journal of Engineering Science, vol. 39, no. 6, pp. 715 – 732, 2001.
[19] G. Venezian,“Effect of modulation on the onset of thermal convection,” Journal of Fluid Mechanics, vol. 35, pp. 243, 1969.
[20] G. Veronis, “ Cellular convection with finite amplitude in a rotating fluid,” Journal of Fluid Mechanics, vol. 5, no. 3, pp. 401-435, 1959.
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