Effects of Viscous Dissipation and Concentration Based Internal Heat Source on Convective Instability in a Porous Medium with Throughflow
Linear stability analysis of double diffusive convection
in a horizontal porous layer saturated with fluid is examined by
considering the effects of viscous dissipation, concentration based
internal heat source and vertical throughflow. The basic steady
state solution for Governing equations is derived. Linear stability
analysis has been implemented numerically by using shooting
and Runge-kutta methods. Critical thermal Rayleigh number Rac
is obtained for various values of solutal Rayleigh number Sa,
vertical Peclet number Pe, Gebhart number Ge, Lewis number
Le and measure of concentration based internal heat source
γ. It is observed that Ge has destabilizing effect for upward
throughflow and stabilizing effect for downward throughflow. And
γ has considerable destabilizing effect for upward throughflow and
insignificant destabilizing effect for downward throughflow.
[1] B. Gebhart, “Effects of viscous dissipation in natural convection”, J.
Fluid Mech. vol. 14, pp. 225-232, 1962.
[2] D. L.Turcotte, A. T. Hsui, K. E. Torrance and G. Schubert, “Influence
of viscous dissipation on Benard convection”, J. Fluid Mech. vol. 64,
pp. 369-374, 1974.
[3] A. Barletta and L. Storesletten, “Viscous dissipation and
thermoconvective instabilities in a horizontal porous channel heated
from below”, Int. J. of Thermal Sciences, vol. 49, pp. 621-630, 2010.
[4] D. A. Nield, A. Barletta and M. Celli, “The effect of viscous dissipation
on the onset of convection in an inclined porous layer”, J. Fluid Mech.
vol. 679, pp. 544-558, 2011.
[5] A. Barletta and D. A. Nield, “Thermosolutal convective instability and
viscous dissipation effect in a fluid-saturated porous medium”, Int. J.
Heat Mass Transfer, vol. 54, 1641-1648, 2011.
[6] D. A. Nield and A. Bejan, “Convection in Porous Media”, 4th ed.
Springer New York, 2013.
[7] F. Chen, “Throughflow effects on convective instability in superposed
fluid and porous layers”, J. Fluid Mech. vol. 231, pp. 113-133, 1990.
[8] L. Brevdo and M. S. Ruderman, “On the Convection in a Porous Medium
with Inclined Temperature Gradient and Vertical Throughflow. Part I.
Normal Modes”, Transp Porous Med. vol. 80, pp. 137-151, 2009.
[9] I. S. Shivakumara and A. Khalili, “On the stability of double diffusive
convection in a porous layer with throughflow”, Acta Mechanica, vol.
152, pp. 165- 175, 2001.
[10] A. Barletta, E. R.di Schio and L. Storesletten, “Convective Roll
Instabilities of Vertical Throughflow with Viscous Dissipation in a
Horizontal Porous Layer”, Transp Porous Med. vol. 81, pp. 461-477,
2010.
[11] D. A. Nield and A. V. Kuznetsov, “The Onset of Convection in a Layered
Porous Medium with Vertical Throughflow”, Transp Porous Med. vol.
98, pp. 363-376, 2013.
[12] R. Thirlby, “Convection in an internally heated layer”, J. Fluid Mech.
vol. 44, pp. 673-693, 1970.
[13] M. Tveitereid and E. Palm, ”Convection due to internal heat sources”,
J. Fluid Mech. vol.76, pp. 481-499, 1976.
[14] C. Parthiban and P. R. Patil, “Effect of non-uniform boundary
temperatures on thermal instability in a porous medium with internal
heat source”, Int. Comm. Heat Mass Transfer, vol. 22, pp. 683-692,
1995.
[15] A. A. Hill, “Double-diffusive convection in a porous medium with a
concentration based internal heat source”, Proc. R. Soc. A. vol. 461, pp.
561-574, 2005.
[16] A. A. Hill and M. S. Malashetty, “An operative method to obtain sharp
nonlinear stability for systems with spatially dependent coefficients”,
Proc. R. Soc. A. vol. 468, pp. 323-336, 2012.
[1] B. Gebhart, “Effects of viscous dissipation in natural convection”, J.
Fluid Mech. vol. 14, pp. 225-232, 1962.
[2] D. L.Turcotte, A. T. Hsui, K. E. Torrance and G. Schubert, “Influence
of viscous dissipation on Benard convection”, J. Fluid Mech. vol. 64,
pp. 369-374, 1974.
[3] A. Barletta and L. Storesletten, “Viscous dissipation and
thermoconvective instabilities in a horizontal porous channel heated
from below”, Int. J. of Thermal Sciences, vol. 49, pp. 621-630, 2010.
[4] D. A. Nield, A. Barletta and M. Celli, “The effect of viscous dissipation
on the onset of convection in an inclined porous layer”, J. Fluid Mech.
vol. 679, pp. 544-558, 2011.
[5] A. Barletta and D. A. Nield, “Thermosolutal convective instability and
viscous dissipation effect in a fluid-saturated porous medium”, Int. J.
Heat Mass Transfer, vol. 54, 1641-1648, 2011.
[6] D. A. Nield and A. Bejan, “Convection in Porous Media”, 4th ed.
Springer New York, 2013.
[7] F. Chen, “Throughflow effects on convective instability in superposed
fluid and porous layers”, J. Fluid Mech. vol. 231, pp. 113-133, 1990.
[8] L. Brevdo and M. S. Ruderman, “On the Convection in a Porous Medium
with Inclined Temperature Gradient and Vertical Throughflow. Part I.
Normal Modes”, Transp Porous Med. vol. 80, pp. 137-151, 2009.
[9] I. S. Shivakumara and A. Khalili, “On the stability of double diffusive
convection in a porous layer with throughflow”, Acta Mechanica, vol.
152, pp. 165- 175, 2001.
[10] A. Barletta, E. R.di Schio and L. Storesletten, “Convective Roll
Instabilities of Vertical Throughflow with Viscous Dissipation in a
Horizontal Porous Layer”, Transp Porous Med. vol. 81, pp. 461-477,
2010.
[11] D. A. Nield and A. V. Kuznetsov, “The Onset of Convection in a Layered
Porous Medium with Vertical Throughflow”, Transp Porous Med. vol.
98, pp. 363-376, 2013.
[12] R. Thirlby, “Convection in an internally heated layer”, J. Fluid Mech.
vol. 44, pp. 673-693, 1970.
[13] M. Tveitereid and E. Palm, ”Convection due to internal heat sources”,
J. Fluid Mech. vol.76, pp. 481-499, 1976.
[14] C. Parthiban and P. R. Patil, “Effect of non-uniform boundary
temperatures on thermal instability in a porous medium with internal
heat source”, Int. Comm. Heat Mass Transfer, vol. 22, pp. 683-692,
1995.
[15] A. A. Hill, “Double-diffusive convection in a porous medium with a
concentration based internal heat source”, Proc. R. Soc. A. vol. 461, pp.
561-574, 2005.
[16] A. A. Hill and M. S. Malashetty, “An operative method to obtain sharp
nonlinear stability for systems with spatially dependent coefficients”,
Proc. R. Soc. A. vol. 468, pp. 323-336, 2012.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:70868", author = "N. Deepika and P. A. L. Narayana", title = "Effects of Viscous Dissipation and Concentration Based Internal Heat Source on Convective Instability in a Porous Medium with Throughflow", abstract = "Linear stability analysis of double diffusive convection
in a horizontal porous layer saturated with fluid is examined by
considering the effects of viscous dissipation, concentration based
internal heat source and vertical throughflow. The basic steady
state solution for Governing equations is derived. Linear stability
analysis has been implemented numerically by using shooting
and Runge-kutta methods. Critical thermal Rayleigh number Rac
is obtained for various values of solutal Rayleigh number Sa,
vertical Peclet number Pe, Gebhart number Ge, Lewis number
Le and measure of concentration based internal heat source
γ. It is observed that Ge has destabilizing effect for upward
throughflow and stabilizing effect for downward throughflow. And
γ has considerable destabilizing effect for upward throughflow and
insignificant destabilizing effect for downward throughflow.", keywords = "Porous medium, concentration based internal heat
source, vertical throughflow, viscous dissipation.", volume = "9", number = "7", pages = "399-5", }