Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer with Internal Heating and Soret Effect.
Main Article Content
Abstract
In this paper, the effect of internal heat source and Soret effect has been
investigated on double diffusive convection in a rotating anisotropic porous medium saturated with a couple stress fluids, heated and salted from below. Linear stability analysis has been performed by using Normal mode technique and for nonlinear analysis, minimal representation of Fourier series up to two terms has been considered. The modified Darcy model, which includes the time derivative term and Coriolis term, has been employed in the momentum equation. The effect of Taylor number, couple stress parameter, solute Rayleigh number, internal heat source parameter, Lewis number, Darcy-Prandtl number, thermal and mechanical anisotropy parameter on the stationary and oscillatory modes of convection has been obtained and shown graphically, Also the heat and mass transports are obtained in terms of the Nusselt number and Sherwood number respectively, and shown graphically.
investigated on double diffusive convection in a rotating anisotropic porous medium saturated with a couple stress fluids, heated and salted from below. Linear stability analysis has been performed by using Normal mode technique and for nonlinear analysis, minimal representation of Fourier series up to two terms has been considered. The modified Darcy model, which includes the time derivative term and Coriolis term, has been employed in the momentum equation. The effect of Taylor number, couple stress parameter, solute Rayleigh number, internal heat source parameter, Lewis number, Darcy-Prandtl number, thermal and mechanical anisotropy parameter on the stationary and oscillatory modes of convection has been obtained and shown graphically, Also the heat and mass transports are obtained in terms of the Nusselt number and Sherwood number respectively, and shown graphically.
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Singh, A., & Shakya, K. (2018). Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer with Internal Heating and Soret Effect. SAMRIDDHI : A Journal of Physical Sciences, Engineering and Technology, 10(02), 121-136. https://doi.org/10.18090/samriddhi.v10i02.7
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Research Article
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
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[2] S. N. Gaikwad M. S. Malashetty K. Rama Prasad,
“Linear and Non-linear Double Diffusive convection
in a Fluid-Saturated Anisotropic Porous Layer with
Cross-Diffusion Effects”, Transp Porous Med
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[3] M.S. Malashetty,B.S.Biradar, “ Linear and nonlinear
double diffusive convection in a fluid saturated
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Transp.Porous Media 91 649670,2012.
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Transf., 2013.
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rotating anisotropic porous layer with internal heat”,
Transp. Porous Medium, vol. 90, iss. 2, pp. 687-
705, 2011.
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saturated anisotropic porous layer with internal heat
source”, Transp. Porous Med., vol. 9,pp. 299-320,
2012.
[9] Alok Srivastava, B. S. Bhadauria, I. Hashim, “Effect
of Internal Heating on Double Diffusive Convection
in a Couple Stress Fluid Saturated Anisotropic
Porous Medium”, Advances in Materials Science and
Applications,Vol. 3 Iss. 1, PP. 24-45, 2014.
[10] A. Chakrabarti, A.S. Gupta, “Nonlinear thermohaline
convection in a rotating porous medium”, Mech. Res.
Commun. 8 915, 1981.
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effect of rotation on linear and nonlinear double
diffusive convection in a sparsely packed porous
medium” Int. J. Heat Mass Transfer 29 130117 1986.
[12] M.S. Malashetty, Dulal Pal, Premila Kollur,” Double
diffusive convection in a Darcy porous medium
saturated with couple stress fluid,” Fluid Dyn. Res.
42. pp. 035502-03523, 2010.
[13] M.S. Malashetty, Premila Kollur, W. Sidram, “Effect
of rotation on the onset of double diffusive
convection in a Darcy porous medium saturated with
a couple stress fluid”, Applied Mathematical
Modelling 37 172186, 2013.
[14] M.S. Malashetty, Rajasekhar Heera,” The effect of
rotation on the onset of double diffusive convection
in a horizontal anisotropic porous layer”, Transp.
Porous Media 74 105127, 2008.
[15] Gaikwad, S. N., and Kamble, S. S., Analysis of linear
stability on double diffusive convection in a fluid
saturated anisotropic porous layer with Soret effect.
Adv. Appl. Sci. Res., 3(3), 1611, 2012.
[16] C. Sulochana, Premila Kollur and G. Sudhaamsh
Mohan Reddy, “The onset of double diffusive
convection in a couple stress fluid saturated Rotating
Anisotropic Porous Layer”, International Journal of
Mathematical Archive-3(12), 4763-4780,2012.
[17] B. S. Bhadauria, I. Hashim,Alok Srivastava,
Jogendra Kumar, “Cross Diffusion Convection in a
Newtonian Fluid-Saturated Rotating Porous
Medium.” Transp Porous Med 98,683697, 2013.
[18] Nield D. A., Onset of thermohaline convection in a
porous medium, Water Resour. Res., vol. 4, iss. 4,
pp. 553-560, 1968.
[19] Stokes V. K., Couple stresses in fluids, Phys. Fluids,
vol. 9, pp. 1709-1716, 1966.
[20] Sharma R. C. and Thakur K. D., “On couple stress
fluid heated from below in porous medium in
hydrodynamics”, Czechoslov. J. Phys., vol. 50, iss.
6, pp. 753-758, 2000.
[21] Sunil, R. C. Sharma and R. S. Chandel, “Effect of
Suspended Particles on Couple-Stress Fluid Heated
and Soluted from Below in Porous Medium”, J.
Porous Media, vol. 7, iss. 1, pp. 9-18, 2004.
[22] R. C. Sharma and M. Sharma, Effect of suspended
particles on couple-stress fluid heated from below
in the presence of rotation and magnetic field, Indian
J. Pure Appl. Math., vol. 35, pp. 973-989, 2004.
[23] M. S. Malashetty, S. N. Gaikwad and M. Swamy,
“An analytical study of linear and non-linear double
diffusive convection with Soret effect in couple stress
liquids”, Int. J. Therm. Sci., vol. 45, iss. 9, pp. 897-
907, 2006.
[24] Gaikwad, S. N. and S. S. Kamble .,” Linear stability
analysis of double diffusive convection in a
horizontal sparsely packed rotating anisotropic
porous layer in the presence of Soret effect”. J.
Applied Fluid Mech. 7, 459-471, 2014.
[25] M. S. Malashetty and K. Premila,” The onset of
Double Diffusive convection in a Couple stress fluid
saturated anisotropic porous layer”, Transp. Porous
Med., vol. 86, pp. 435-459, 2011.
[26] Nalluri, S. K., & Parasaram, V. K. B. (2015).
Automating Software Builds with Jenkins: Design
Patterns and Failure Handling. International
Journal of Technology, Management and
Humanities, 1(02), 16-33.
[27] I. S. Shivakumara, J. Lee and S. Suresh Kumar,
Linear and nonlinear stability of double diffusive
convection in a couple stress fluid-saturated porous
layer,
convection”, J. fluid Mech. 47 667687, 1971.
[2] S. N. Gaikwad M. S. Malashetty K. Rama Prasad,
“Linear and Non-linear Double Diffusive convection
in a Fluid-Saturated Anisotropic Porous Layer with
Cross-Diffusion Effects”, Transp Porous Med
80:537560,2009.
[3] M.S. Malashetty,B.S.Biradar, “ Linear and nonlinear
double diffusive convection in a fluid saturated
porous layer with cross diffusion effect”,
Transp.Porous Media 91 649670,2012.
[4] A.A.Altawallbeh, B. S. Bhadauria, I Hashim, “Linear
and nonlinear double-diffusive convection in a
saturated anisotropic porous layer with Soret effect
and internal heat source”, Int. J. Heat Mass and
Transf., 2013.
[5] M. Tveitereid, “Thermal convection in a horizontal
porous layer with internal heat sources”, Int. J. Heat
Mass Transf., vol. 20, pp. 1045-1050, 1977.
[6] A. A. Hill, “Double-diffusive convection in a porous
medium with a concentration based internal heat
source”, Proc. R. Soc., vol. A461, pp. 561-574, 2005.
[7] B. S. Bhadauria, Anoj Kumar, Jogendra Kumar,N.
C. Sacheti, P. Chandran, “Natural convection in a
rotating anisotropic porous layer with internal heat”,
Transp. Porous Medium, vol. 90, iss. 2, pp. 687-
705, 2011.
[8] B. S. Bhadauria, “Double diffusive convection in a
saturated anisotropic porous layer with internal heat
source”, Transp. Porous Med., vol. 9,pp. 299-320,
2012.
[9] Alok Srivastava, B. S. Bhadauria, I. Hashim, “Effect
of Internal Heating on Double Diffusive Convection
in a Couple Stress Fluid Saturated Anisotropic
Porous Medium”, Advances in Materials Science and
Applications,Vol. 3 Iss. 1, PP. 24-45, 2014.
[10] A. Chakrabarti, A.S. Gupta, “Nonlinear thermohaline
convection in a rotating porous medium”, Mech. Res.
Commun. 8 915, 1981.
[11] Rudraiah N, Shivakumara I S and Friedrich R, “The
effect of rotation on linear and nonlinear double
diffusive convection in a sparsely packed porous
medium” Int. J. Heat Mass Transfer 29 130117 1986.
[12] M.S. Malashetty, Dulal Pal, Premila Kollur,” Double
diffusive convection in a Darcy porous medium
saturated with couple stress fluid,” Fluid Dyn. Res.
42. pp. 035502-03523, 2010.
[13] M.S. Malashetty, Premila Kollur, W. Sidram, “Effect
of rotation on the onset of double diffusive
convection in a Darcy porous medium saturated with
a couple stress fluid”, Applied Mathematical
Modelling 37 172186, 2013.
[14] M.S. Malashetty, Rajasekhar Heera,” The effect of
rotation on the onset of double diffusive convection
in a horizontal anisotropic porous layer”, Transp.
Porous Media 74 105127, 2008.
[15] Gaikwad, S. N., and Kamble, S. S., Analysis of linear
stability on double diffusive convection in a fluid
saturated anisotropic porous layer with Soret effect.
Adv. Appl. Sci. Res., 3(3), 1611, 2012.
[16] C. Sulochana, Premila Kollur and G. Sudhaamsh
Mohan Reddy, “The onset of double diffusive
convection in a couple stress fluid saturated Rotating
Anisotropic Porous Layer”, International Journal of
Mathematical Archive-3(12), 4763-4780,2012.
[17] B. S. Bhadauria, I. Hashim,Alok Srivastava,
Jogendra Kumar, “Cross Diffusion Convection in a
Newtonian Fluid-Saturated Rotating Porous
Medium.” Transp Porous Med 98,683697, 2013.
[18] Nield D. A., Onset of thermohaline convection in a
porous medium, Water Resour. Res., vol. 4, iss. 4,
pp. 553-560, 1968.
[19] Stokes V. K., Couple stresses in fluids, Phys. Fluids,
vol. 9, pp. 1709-1716, 1966.
[20] Sharma R. C. and Thakur K. D., “On couple stress
fluid heated from below in porous medium in
hydrodynamics”, Czechoslov. J. Phys., vol. 50, iss.
6, pp. 753-758, 2000.
[21] Sunil, R. C. Sharma and R. S. Chandel, “Effect of
Suspended Particles on Couple-Stress Fluid Heated
and Soluted from Below in Porous Medium”, J.
Porous Media, vol. 7, iss. 1, pp. 9-18, 2004.
[22] R. C. Sharma and M. Sharma, Effect of suspended
particles on couple-stress fluid heated from below
in the presence of rotation and magnetic field, Indian
J. Pure Appl. Math., vol. 35, pp. 973-989, 2004.
[23] M. S. Malashetty, S. N. Gaikwad and M. Swamy,
“An analytical study of linear and non-linear double
diffusive convection with Soret effect in couple stress
liquids”, Int. J. Therm. Sci., vol. 45, iss. 9, pp. 897-
907, 2006.
[24] Gaikwad, S. N. and S. S. Kamble .,” Linear stability
analysis of double diffusive convection in a
horizontal sparsely packed rotating anisotropic
porous layer in the presence of Soret effect”. J.
Applied Fluid Mech. 7, 459-471, 2014.
[25] M. S. Malashetty and K. Premila,” The onset of
Double Diffusive convection in a Couple stress fluid
saturated anisotropic porous layer”, Transp. Porous
Med., vol. 86, pp. 435-459, 2011.
[26] Nalluri, S. K., & Parasaram, V. K. B. (2015).
Automating Software Builds with Jenkins: Design
Patterns and Failure Handling. International
Journal of Technology, Management and
Humanities, 1(02), 16-33.
[27] I. S. Shivakumara, J. Lee and S. Suresh Kumar,
Linear and nonlinear stability of double diffusive
convection in a couple stress fluid-saturated porous
layer,