Throughflow Effects on Thermal Convection in Variable Viscosity Ferromagnetic Liquids
The problem of thermal convection in temperature and
magnetic field sensitive Newtonian ferromagnetic liquid is studied
in the presence of uniform vertical magnetic field and throughflow.
Using a combination of Galerkin and shooting techniques the critical
eigenvalues are obtained for stationary mode. The effect of Prandtl
number (Pr > 1) on onset is insignificant and nonlinearity of
non-buoyancy magnetic parameter M3 is found to have no influence
on the onset of ferroconvection. The magnetic buoyancy number, M1
and variable viscosity parameter, V have destabilizing influences on
the system. The effect of throughflow Peclet number, Pe is to delay
the onset of ferroconvection and this effect is independent of the
direction of flow.
[1] Finlayson, B. A., 1970, Convective instability of ferromagnetic fluids, J.
Fluid Mech., 40, 753-767.
[2] Das Gupta, M. and Gupta A. S., 1979, Convective instability of a layer
of ferromagnetic fluid rotating about a vertical axis, Int J Eng Sci., 17,
271-277.
[3] Gotoh, and Yamada, 1982, Thermal convection in a horizontal layer of
magnetic fluids, J. Phys. Soc. Jpn. 51, 3042-3048.
[4] Stiles,and Kagan, 1990, Thermoconvective instability of a horizontal layer
of ferrofluid in a strong vertical magnetic field, JMMM, 85, 196-198.
[5] Sekhar, G. N. and Rudraiah, N., 1991, Convection in magnetic fluids with
internal heat generation,Trans. ASME: J. Heat Trans., 113, 122-127.
[6] Siddheshwar, P. G., 1995, Convective instability of ferromagnetic fluids
bounded by fluid-permeable, magnetic boundaries, JMMM, 149, 148-150.
[7] Siddheshwar, P. G., 1999, Rayleigh-B´enard convection in a second-order
ferromagnetic fluid with second sound, Proc. of 8th Asian Congress of
fluid Mech. 6-10.
[8] Siddheshwar, P. G., 2002a, Oscillatory convection in viscoelastic,
ferromagnetic/dielectric liquids, Int. J. Modern Phy B. 16, 2629-2633.
[9] Siddheshwar, P. G., 2002b, Ferrohydrodynamic and electrodynamic
instabilities in Newtonian liquids: Analogy, East West J. Math. 16,
143-146.
[10] Abraham, A., 2002, Convective instability in magnetic fluids and
polarized dielectric liquids, Ph.D. Thesis, Bangalore University, (India).
[11] Maruthamanikandan, S, 2005, Instabilities in ferromagnetic, dielectric
and other complexliquids, Ph.D. Thesis, Bangalore University, (India).
[12] Shivakumara, I. S., Rudraiah, N., and Nanjundappa, C. E., 2002, Effect of
non-uniform basic temperature gradient on Rayleigh-Benard-Marangoni
convection in ferrofluids, JMMM, 248, 379-395.
[13] Siddheshwar, P. G., and Abraham, A., 2003, Effect of time-periodic
boundary temperatures/body force on Rayleigh-Benard convection in a
ferromagnetic fluid, Acta Mechanica, 161, 131-150.
[14] Sunil, Sharma, A., Sharma, D. and Kumar, P. 2008, Effect
of magnetic-field dependent viscosity on thermal convection in a
ferromagnetic fluid, Chem. Engg. Comm. 195, 571-583.
[15] Sunil, Sharma, P. and Mahajan, A. 2008, A nonlinear stability analysis
for thermoconvective magnetized ferrofluid with magnetic field dependent
viscosity, Int. Comm.Heat and Mass Transfer., 35, 1281-1287.
[16] Rosensweig, R. E., Kaiser, R. and Miskolczy, 1969, Viscosity of
magnetic fluid in a magnetic field, J. Colloid and Interface Sci., 29,
680-686.
[17] Odenbach, S., 2004, Recent progress in magnetic fluid research, J Phys:
Condens Matter., 16, R1135-R1150.
[18] Nield, D. A., 1987, Throughflow effects in the Rayleigh-B´enard
convective instability problem, J. Fluid. Mech., 185, 353-360.
[19] Siddheshwar, P. G., 1995, Suction-injection effects on Rayleigh-B´enard
convection in a closely packed porous bed with general boundary
condition on temperature, VI Asian Cong. of Fluid Mech., 1, 590-594.
[20] Shivakumara, I. S., 1999, Boundary and inertia effects on convection in
porous media with throughflow, Acta Mech., 137, 151-165.
[21] Shivakumara, I. S. and Suma, R., 2000, Effects of throughflow and
internal heat generation on the onset of convection in a fluid layer, Acta
Mech., 140, 207-217.
[22] Siddheshwar, P. G., and Pranesh, S., 2001, Suction-injection effects on
the onset of Rayleigh-B´enard- Marangoni convection in a fluid with
suspended particles, Acta Mechanica,152, 241-252.
[23] Nield, D. A., and Kuznetsov, A. V., 2011, Onset of convection in a
porous medium with strong vertical throughflow, Transp. Porous Med.,90,
883-888.
[24] Nanjundappa, C. E., Shivakumara, I. S. and Arunkumar R., 2014,
Ferroconvection in a porous medium with vertical throughflow, Acta
Mech.,226,1515-1528.
[25] Vanishree, R. K., 2014, Effects of throughflow and internal heat
generation on thermoconvective instability in an anisotropic porous
medium,J.App. Fluid Mechanics, 7, 581-590.
[26] Siddheshwar, P. G., Ramachandramurthy, V. and Uma, D., 2011,
Rayleigh-B´enard and Marangoni magnetoconvection in Newtonian liquid
with thermorheological effects, Int. J. Engg. Sci.,49, 1078-1094.
[27] Sekhar, G. N. and Jayalatha, G., 2009, Elastic effects
on Rayleigh-B´enard-Marangoni convection in liquids with
temperature-dependent viscosity, Proc. of the ASME 2009, ISBN
978-07918-3863-1, 1-10.
[28] Sekhar, G. N. and Jayalatha, G., 2010, Elastic effects on
Rayleigh-B´enard convection in liquids with temperature-dependent
viscosity, Int. J. of Thermal Sci., 49, 67-79.
[29] Sekhar, G.N., Jayalatha, G. and Prakash, R., 2013,
Thermorheological and magnetorheological effects on
Rayleigh-B´enard-Marangoni-Marangoni convection in ferromagnetic
liquids with non-uniform basic temperature gradient, Proc. ASME, Vol
7A, ISBN: 978-0-7918-5631-4, 1-10.
[30] Siddheshwar, P. G., 2004, Thermorheological effect on
magnetoconvection in weak electrically conducting fluids under 1g
and μg , Pramana, 62, 61-68.
[31] Siddheshwar, P. G., Sekhar, G.N. and Jayalatha, G., 2011, Surface
tension driven convection in viscoelastic liquids with thermorheological
effect, Int. Comm. Heat and Mass trans. 38, 468-473.
[32] Siddheshwar, P. G. Vanishree, R. K. and Melson, A. C., 2012,
Study of heat transport in B´enard-Darcy convection with g-jitter and
thermomechanical anisotropy in variable viscosity liquids, Trans-in
Porous Media, 92, 277-288.
[33] Siddheshwar, P. G. and Maruthamanikandan, S., 2016, Derivation of
various possible boundary conditions for the ferroconvection problem,
(Private communication).
[34] Siddheshwar, P. G. and Revathi, B. R., 2009, Shooting method for good
estimates of the eigenvalue in the Rayleigh-B´enard-Marangoni convection
Problem with general boundary conditions on velocity and temperature, Proc. ASME, Heat transfer, fluid flows and Thermal systems, 9, ISBN:
978-0-7918-4382-6, 1-10.
[35] Sekhar, G.N., Jayalatha, G. and Prakash, R., 2017, Thermal Convection
in Variable Viscosity Ferromagnetic Liquids with Heat Source , Int.
J. Appl. Comput. Math, DOI: 10.1007/s40819-017-0313-9, ISSN:
2349-5103.
[36] Platten, J. K. and Legros, J. C., 1984, Convection in liquids,
Springer-Verlag, Berlin Heidelberg,New York.
[1] Finlayson, B. A., 1970, Convective instability of ferromagnetic fluids, J.
Fluid Mech., 40, 753-767.
[2] Das Gupta, M. and Gupta A. S., 1979, Convective instability of a layer
of ferromagnetic fluid rotating about a vertical axis, Int J Eng Sci., 17,
271-277.
[3] Gotoh, and Yamada, 1982, Thermal convection in a horizontal layer of
magnetic fluids, J. Phys. Soc. Jpn. 51, 3042-3048.
[4] Stiles,and Kagan, 1990, Thermoconvective instability of a horizontal layer
of ferrofluid in a strong vertical magnetic field, JMMM, 85, 196-198.
[5] Sekhar, G. N. and Rudraiah, N., 1991, Convection in magnetic fluids with
internal heat generation,Trans. ASME: J. Heat Trans., 113, 122-127.
[6] Siddheshwar, P. G., 1995, Convective instability of ferromagnetic fluids
bounded by fluid-permeable, magnetic boundaries, JMMM, 149, 148-150.
[7] Siddheshwar, P. G., 1999, Rayleigh-B´enard convection in a second-order
ferromagnetic fluid with second sound, Proc. of 8th Asian Congress of
fluid Mech. 6-10.
[8] Siddheshwar, P. G., 2002a, Oscillatory convection in viscoelastic,
ferromagnetic/dielectric liquids, Int. J. Modern Phy B. 16, 2629-2633.
[9] Siddheshwar, P. G., 2002b, Ferrohydrodynamic and electrodynamic
instabilities in Newtonian liquids: Analogy, East West J. Math. 16,
143-146.
[10] Abraham, A., 2002, Convective instability in magnetic fluids and
polarized dielectric liquids, Ph.D. Thesis, Bangalore University, (India).
[11] Maruthamanikandan, S, 2005, Instabilities in ferromagnetic, dielectric
and other complexliquids, Ph.D. Thesis, Bangalore University, (India).
[12] Shivakumara, I. S., Rudraiah, N., and Nanjundappa, C. E., 2002, Effect of
non-uniform basic temperature gradient on Rayleigh-Benard-Marangoni
convection in ferrofluids, JMMM, 248, 379-395.
[13] Siddheshwar, P. G., and Abraham, A., 2003, Effect of time-periodic
boundary temperatures/body force on Rayleigh-Benard convection in a
ferromagnetic fluid, Acta Mechanica, 161, 131-150.
[14] Sunil, Sharma, A., Sharma, D. and Kumar, P. 2008, Effect
of magnetic-field dependent viscosity on thermal convection in a
ferromagnetic fluid, Chem. Engg. Comm. 195, 571-583.
[15] Sunil, Sharma, P. and Mahajan, A. 2008, A nonlinear stability analysis
for thermoconvective magnetized ferrofluid with magnetic field dependent
viscosity, Int. Comm.Heat and Mass Transfer., 35, 1281-1287.
[16] Rosensweig, R. E., Kaiser, R. and Miskolczy, 1969, Viscosity of
magnetic fluid in a magnetic field, J. Colloid and Interface Sci., 29,
680-686.
[17] Odenbach, S., 2004, Recent progress in magnetic fluid research, J Phys:
Condens Matter., 16, R1135-R1150.
[18] Nield, D. A., 1987, Throughflow effects in the Rayleigh-B´enard
convective instability problem, J. Fluid. Mech., 185, 353-360.
[19] Siddheshwar, P. G., 1995, Suction-injection effects on Rayleigh-B´enard
convection in a closely packed porous bed with general boundary
condition on temperature, VI Asian Cong. of Fluid Mech., 1, 590-594.
[20] Shivakumara, I. S., 1999, Boundary and inertia effects on convection in
porous media with throughflow, Acta Mech., 137, 151-165.
[21] Shivakumara, I. S. and Suma, R., 2000, Effects of throughflow and
internal heat generation on the onset of convection in a fluid layer, Acta
Mech., 140, 207-217.
[22] Siddheshwar, P. G., and Pranesh, S., 2001, Suction-injection effects on
the onset of Rayleigh-B´enard- Marangoni convection in a fluid with
suspended particles, Acta Mechanica,152, 241-252.
[23] Nield, D. A., and Kuznetsov, A. V., 2011, Onset of convection in a
porous medium with strong vertical throughflow, Transp. Porous Med.,90,
883-888.
[24] Nanjundappa, C. E., Shivakumara, I. S. and Arunkumar R., 2014,
Ferroconvection in a porous medium with vertical throughflow, Acta
Mech.,226,1515-1528.
[25] Vanishree, R. K., 2014, Effects of throughflow and internal heat
generation on thermoconvective instability in an anisotropic porous
medium,J.App. Fluid Mechanics, 7, 581-590.
[26] Siddheshwar, P. G., Ramachandramurthy, V. and Uma, D., 2011,
Rayleigh-B´enard and Marangoni magnetoconvection in Newtonian liquid
with thermorheological effects, Int. J. Engg. Sci.,49, 1078-1094.
[27] Sekhar, G. N. and Jayalatha, G., 2009, Elastic effects
on Rayleigh-B´enard-Marangoni convection in liquids with
temperature-dependent viscosity, Proc. of the ASME 2009, ISBN
978-07918-3863-1, 1-10.
[28] Sekhar, G. N. and Jayalatha, G., 2010, Elastic effects on
Rayleigh-B´enard convection in liquids with temperature-dependent
viscosity, Int. J. of Thermal Sci., 49, 67-79.
[29] Sekhar, G.N., Jayalatha, G. and Prakash, R., 2013,
Thermorheological and magnetorheological effects on
Rayleigh-B´enard-Marangoni-Marangoni convection in ferromagnetic
liquids with non-uniform basic temperature gradient, Proc. ASME, Vol
7A, ISBN: 978-0-7918-5631-4, 1-10.
[30] Siddheshwar, P. G., 2004, Thermorheological effect on
magnetoconvection in weak electrically conducting fluids under 1g
and μg , Pramana, 62, 61-68.
[31] Siddheshwar, P. G., Sekhar, G.N. and Jayalatha, G., 2011, Surface
tension driven convection in viscoelastic liquids with thermorheological
effect, Int. Comm. Heat and Mass trans. 38, 468-473.
[32] Siddheshwar, P. G. Vanishree, R. K. and Melson, A. C., 2012,
Study of heat transport in B´enard-Darcy convection with g-jitter and
thermomechanical anisotropy in variable viscosity liquids, Trans-in
Porous Media, 92, 277-288.
[33] Siddheshwar, P. G. and Maruthamanikandan, S., 2016, Derivation of
various possible boundary conditions for the ferroconvection problem,
(Private communication).
[34] Siddheshwar, P. G. and Revathi, B. R., 2009, Shooting method for good
estimates of the eigenvalue in the Rayleigh-B´enard-Marangoni convection
Problem with general boundary conditions on velocity and temperature, Proc. ASME, Heat transfer, fluid flows and Thermal systems, 9, ISBN:
978-0-7918-4382-6, 1-10.
[35] Sekhar, G.N., Jayalatha, G. and Prakash, R., 2017, Thermal Convection
in Variable Viscosity Ferromagnetic Liquids with Heat Source , Int.
J. Appl. Comput. Math, DOI: 10.1007/s40819-017-0313-9, ISSN:
2349-5103.
[36] Platten, J. K. and Legros, J. C., 1984, Convection in liquids,
Springer-Verlag, Berlin Heidelberg,New York.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:76230", author = "G. N. Sekhar and P. G. Siddheshwar and G. Jayalatha and R. Prakash", title = "Throughflow Effects on Thermal Convection in Variable Viscosity Ferromagnetic Liquids", abstract = "The problem of thermal convection in temperature and
magnetic field sensitive Newtonian ferromagnetic liquid is studied
in the presence of uniform vertical magnetic field and throughflow.
Using a combination of Galerkin and shooting techniques the critical
eigenvalues are obtained for stationary mode. The effect of Prandtl
number (Pr > 1) on onset is insignificant and nonlinearity of
non-buoyancy magnetic parameter M3 is found to have no influence
on the onset of ferroconvection. The magnetic buoyancy number, M1
and variable viscosity parameter, V have destabilizing influences on
the system. The effect of throughflow Peclet number, Pe is to delay
the onset of ferroconvection and this effect is independent of the
direction of flow.", keywords = "Ferroconvection, throughflow, temperature dependent
viscosity, magnetic field dependent viscosity.", volume = "11", number = "6", pages = "1269-9", }
