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J. M, Shivaraja
- Non-uniform Temperature Gradients Impact on Rayleigh-Darcy Convection: A Composite System with Couple Stress Fluid
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PDF Views:0
Authors
Affiliations
1 Associate Professor, IN
2 Research Scholar Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka,, IN
1 Associate Professor, IN
2 Research Scholar Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka,, IN
Source
Journal of Mines, Metals and Fuels, Vol 70, No 7A (2022), Pagination: 78-89Abstract
The impact of non-uniform temperature gradients on Rayleigh-Darcy convection in a composite system of couple stress fluid is discussed. The composite system is bounded by stress-free surfaces and adiabatically insulated,and the fluid-porous layers are coupled by employing appropriate interfacial boundary conditions. To determine the eigen value, the regular perturbation method is used. The effect of dimensionless parameters on Rayleigh Darcy convection is analysed graphically, and it is demonstrated that the couple stress parameter and couple stress viscosity ratio stabilise the system, while the opposite effect is observed for the Darcy number and thermal diffusivity ratio.Keywords
Rayleigh-Darcy Convection, Couple stress fluid, Composite system, Non-uniform temperature gradient
References
- Nield, D. A., and Bejan, A., “Convection in porous media”. Springer-Verlag New York Inc, (1999).
- Sun, W. J., “Convective instability in superposed porous and free layers”. Ph.D. dissertation, University of Minnesota, Minneapolis, (1973).
- Nield, D. A., “Onset of convection in a fluid layer overlying a layer of a porous medium”, J. Fluid Mech., 81, pp. 513–522, (1977).
- Beckermann, C., Ramadhyani, S., and Viskanta, R., “Natural convection flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure.” J. Heat Trans., 109, pp. 363–370, (1987).
- Chen F. and C. F. Chen, “Convection in superposed fluid and porous layers,” J. Fluid Mech., 234, 97-119 (1992).
- Robert McKibbian “Anisotropic modelling of thermal convection in multilayered porous media” J. Fluid Mech., vol. 118, pp. 315-339, Printed in Great Britain 315, (1982).
- Jamet, D., Chandesris, M., and Goyeau, B., “On the equivalence of the discontinuous one- and two-domain approaches”. Trans. Porous Med., 78, p. 403-418, (2009).
- Chang, M., “Thermal convection in superposed fluid and porous layers subjected to a plane poiseuille flow”, Physics of Fluids, 18(3), pp. 1–7, (2006).
- Hill, A. A., and Straughan, B., “Poiseuille flow in a fluid overlying a porous medium”, J. Fluid Mech., 603, pp. 137–149, (2008).
- Hirata, S. C., Goyeau, B., Gobin, D., and Cotta, R. M., “Stability in natural convection in superposed fluid and porous layers using integral transforms”. Num. Heat Trans., 50(5), pp. 409–424, (2006).
- Hirata, S. C., Goyeau, B., Gobin, D., Chandesris, M., and Jamet, D., “Stability of natural convection in superposed fluid and porous layers: equivalence of the one-and two-domain approaches”, Int. J. Heat Mass Trans., 52(1-2), pp. 533–536, (2009).
- Beavers, G. S., and Joseph, D. D., 1967. “Boundary conditions at a naturally permeable wall”, J. Fluid Mech., 30, pp.197–207, (1967). [13] Alberto Ochoa-Tapia J., Stephen Whitaker, “Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development”, International Journal of Heat and Mass Transfer, Volume 38, Issue 14, Pages 2635-2646, (1995).
- Vafai K and Thiyagaraja R, “Analysis of flow and heat transfer at the interface region of a porous medium”, International Journal of Heat and Mass Transfer Volume 30, Issue 7, 1391-1405, (1987).
- Alazmi, B., and Vafai, K., “Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer”, International Journal of Heat and Mass Transfer, 44(9), 1735–1749, (2001).
- Sumithra R. and Manjunatha.N, “Effects of parabolic and inverted parabolic temperature profiles on magneto Marangoni convection in a composite layer”, International Journal current Research, 6, 5435-5450, (2014).
- Sumithra, R., Vanishree, R. K., & Manjunatha, N., “Effect of constant heat source/sink on single component Marangoni convection in a composite layer bounded by adiabatic boundaries in presence of uniform & non uniform temperature gradients”, Malaya Journal of Matematik, 8(2), 306–313, (2020).
- Stokes V.K. “Couple stresses in fluids”, Phys. Fluids, 9 1709-1716, (1966).
- Sharma R. C. and Shivani Sharma, “Couplestress fluid heated from below in porous medium”, Indian Journal of Physics, 75B (2), 137- 139, (2001).
- Malashetty M. S. and D. Basavaraja, ”Effect of JOURNAL OF MINES, METALS & FUELS 11 thermal/gravity modulation on the onset of Rayleigh-Benard convection in a couple stress fluid”, International Journal of Transport Phenomena, vol. 7, pp. 31–44, (2005).
- Rudraiah, N., Veerapa, B., Balachandra, R.S: “Effects of non-uniform thermal gradient and adiabatic boundaries on convection in porous media”, Journal of Heat Transfer, 102, 254, (1980).
- Shivakumara, I. S., Sureshkumar, S., & Devaraju, N., “Effect of non-uniform temperature gradients on the onset of convection in a couplestress fluid-saturated porous medium”, Journal of Applied Fluid Mechanics, 5(1):49-55, (2012).
- Shankar B.M., Shivakumara I.S., Chiu-On Ng., “Stability of couple stress fluid flow through horizontal porous layer”, Journal of Porous Media, 19, 5, pp.391-404, (2016).
- P.G. Siddheshwar and S. Pranesh, “Effect of a non-uniform basic temperature gradient on Rayleigh-Benard convection in a micropolar fluid”, International Journal of Engineering Science, vol.36, 11, 1183–1196, (1998).
- Shivakumara I.S., “Onset of convection in a couplestress fluid saturated porous medium: Effects of non-uniform temperature gradients”, Archive of Applied Mechanics, Vol.80, No.8, pp.949-957, (2010).
- Sumithra, R., and Selvamary, T. A., “Single component Darcy-Benard surface tension driven convection of couple stress fluid in a composite layer”, Malaya Journal of Matematik (MJM), 9(1, 2021), 797–804, (2021)
- Non-Uniform Temperature Gradients Impact on Rayleigh-Darcy Convection : A Composite System with Couple Stress Fluid
Abstract Views :64 |
PDF Views:0
Authors
Affiliations
1 Associate Professor, Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka, IN
2 Research Scholar Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka, IN
1 Associate Professor, Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka, IN
2 Research Scholar Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka, IN
Source
Journal of Mines, Metals and Fuels, Vol 70, No 7A (2022), Pagination: 76-87Abstract
The impact of non-uniform temperature gradients on Rayleigh-Darcy convection in a composite system of couple stress fluid is discussed. The composite system is bounded by stress-free surfaces and adiabatically insulated, and the fluid-porous layers are coupled by employing appropriate interfacial boundary conditions. To determine the eigen value, the regular perturbation method is used. The effect of dimensionless parameters on Rayleigh-Darcy convection is analysed graphically, and it is demonstrated that the couple stress parameter and couple stress viscosity ratio stabilise the system, while the opposite effect is observed for the Darcy number and thermal diffusivity ratio.Keywords
Rayleigh-Darcy Convection, Couple Stress Fluid, Composite System, Non-Uniform Temperature Gradient.References
- Nield, D. A., and Bejan, A., “Convection in porous media”. Springer-Verlag New York Inc, (1999).
- Sun, W. J., “Convective instability in superposed porous and free layers”. Ph.D. dissertation, University of Minnesota, Minneapolis, (1973).
- Nield, D. A., “Onset of convection in a fluid layer overlying a layer of a porous medium”, J. Fluid Mech., 81, pp. 513–522, (1977).
- Beckermann, C., Ramadhyani, S., and Viskanta, R., “Natural convection flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure.” J. Heat Trans., 109, pp. 363–370, (1987).
- Chen F. and C. F. Chen, “Convection in superposed fluid and porous layers,” J. Fluid Mech., 234, 97-119 (1992).
- Robert McKibbian “Anisotropic modelling of thermal convection in multilayered porous media” J. Fluid Mech., vol. 118, pp. 315-339, Printed in Great Britain 315, (1982).
- Jamet, D., Chandesris, M., and Goyeau, B., “On the equivalence of the discontinuous one- and two-domain approaches”. Trans. Porous Med., 78, p. 403-418, (2009).
- Chang, M., “Thermal convection in superposed fluid and porous layers subjected to a plane poiseuille flow”, Physics of Fluids, 18(3), pp. 1–7, (2006).
- Hill, A. A., and Straughan, B., “Poiseuille flow in a fluid overlying a porous medium”, J. Fluid Mech., 603, pp. 137–149, (2008).
- Hirata, S. C., Goyeau, B., Gobin, D., and Cotta, R. M., “Stability in natural convection in superposed fluid and porous layers using integral transforms”. Num. Heat Trans., 50(5), pp. 409–424, (2006).
- Hirata, S. C., Goyeau, B., Gobin, D., Chandesris, M., and Jamet, D., “Stability of natural convection in superposed fluid and porous layers: equivalence of the one-and two-domain approaches”, Int. J. Heat Mass Trans., 52(1-2), pp. 533–536, (2009).
- Beavers, G. S., and Joseph, D. D., 1967. “Boundary conditions at a naturally permeable wall”, J. Fluid Mech., 30, pp.197–207, (1967).
- Alberto Ochoa-Tapia J., Stephen Whitaker, “Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development”, International Journal of Heat and Mass Transfer, Volume 38, Issue 14, Pages 2635-2646, (1995).
- Vafai K and Thiyagaraja R, “Analysis of flow and heat transfer at the interface region of a porous medium”, International Journal of Heat and Mass Transfer Volume 30, Issue 7, 1391-1405, (1987).
- Alazmi, B., and Vafai, K., “Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer”, International Journal of Heat and Mass Transfer, 44(9), 1735–1749, (2001).
- Sumithra R. and Manjunatha.N, “Effects of parabolic and inverted parabolic temperature profiles on magneto Marangoni convection in a composite layer”, International Journal current Research, 6, 5435-5450, (2014).
- Sumithra, R., Vanishree, R. K., & Manjunatha, N., “Effect of constant heat source/sink on single component Marangoni convection in a composite layer bounded by adiabatic boundaries in presence of uniform & non uniform temperature gradients”, Malaya Journal of Matematik, 8(2), 306–313, (2020).
- Stokes V.K. “Couple stresses in fluids”, Phys. Fluids, 9 1709-1716, (1966).
- Sharma R. C. and Shivani Sharma, “Couple-stress fluid heated from below in porous medium”, Indian Journal of Physics, 75B (2), 137-139, (2001).
- Malashetty M. S. and D. Basavaraja, ”Effect of JOURNAL OF MINES, METALS & FUELS 11 thermal/gravity modulation on the onset of Rayleigh-Benard convection in a couple stress fluid”, International Journal of Transport Phenomena, vol. 7, pp. 31–44, (2005).
- Rudraiah, N., Veerapa, B., Balachandra, R.S: “Effects of non-uniform thermal gradient and adiabatic boundaries on convection in porous media”, Journal of Heat Transfer, 102, 254, (1980).
- Shivakumara, I. S., Sureshkumar, S., & Devaraju, N., “Effect of non-uniform temperature gradients on the onset of convection in a couple-stress fluid-saturated porous medium”, Journal of Applied Fluid Mechanics, 5(1):49-55, (2012).
- Shankar B.M., Shivakumara I.S., Chiu-On Ng., “Stability of couple stress fluid flow through horizontal porous layer”, Journal of Porous Media, 19, 5, pp.391-404, (2016).
- P.G. Siddheshwar and S. Pranesh, “Effect of a non-uniform basic temperature gradient on Rayleigh-Benard convection in a micropolar fluid”, International Journal of Engineering Science, vol.36, 11, 1183–1196, (1998).
- Shivakumara I.S., “Onset of convection in a couple-stress fluid saturated porous medium: Effects of non-uniform temperature gradients”, Archive of Applied Mechanics, Vol.80, No.8, pp.949-957, (2010).
- Sumithra, R., and Selvamary, T. A., “Single component Darcy-Benard surface tension driven convection of couple stress fluid in a composite layer”, Malaya Journal of Matematik (MJM), 9(1, 2021), 797–804, (2021).
- Linear, Parabolic, and Inverted Parabolic Temperature Gradients Impact on Double-Diffusive Rayleigh-Darcy Convection : A Composite System with Couple Stress Fluid
Abstract Views :71 |
PDF Views:0
Authors
Affiliations
1 Associate Professor,Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka,, IN
2 Research Scholar Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka,, IN
1 Associate Professor,Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka,, IN
2 Research Scholar Department of UG, PG Studies and Research in Mathematics, Government Science College (Autonomous), Nrupathunga University, Nrupathunga Road, Bengaluru-560 001, Karnataka,, IN
Source
Journal of Mines, Metals and Fuels, Vol 70, No 7A (2022), Pagination: 88-100Abstract
The influence of linear, parabolic and inverted parabolic temperature gradients on the onset of double-diffusive Rayleigh-Darcy convection is theoretically investigated. The composite system is constrained horizontally by adiabatic and free-free thermal boundaries, and appropriate interfacial boundary conditions are used to connect fluid-porous layers. The regular perturbation approach is used to determine the critical Rayleigh number expression for different temperature gradients. Graphs are used to investigate the significance of a variety of dimensionless characteristics. The couple stress parameter, couple stress viscosity ratio, solute Rayleigh number, and solute diffusivity ratio clearly have a stabilizing effect on the system, whereas the Darcy number and thermal diffusivity ratio destabilize it.Keywords
Double-Diffusive Convection, Couple Stress Fluid, Thermal Rayleigh Number, Solute Rayleigh Number, Composite SystemReferences
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