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AN ANALYTICAL STUDY OF HEAT AND MASS TRANSPORT IN BÉNARD−DARCY CONVECTION WITH G-JITTER AND VARIABLE VISCOSITY LIQUIDS IN POROUS MEDIA

Volumen 10, Edición 4, 2019, pp. 323-338
DOI: 10.1615/SpecialTopicsRevPorousMedia.2019016040
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SINOPSIS

This research article deals with the thermorheological effect of temperature dependent viscous fluid in the presence of imposed time periodic gravity modulation. We perform weak non-linear analysis of gravity modulation with temperature dependent viscosity using the power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. Nusselt number and Sherwood number are calculated numerically through the non-autonomous equation involving amplitude of convection using Ginzburg−Landau equation. We explore the non-linear effect of solute Rayleigh number, Lewis number, Vadász number, thermorheological parameter and amplitude of gravity modulation analytically. The curve for heat and mass transfer with respect to slow time variation is depicted graphically. Furthermore we also draw streamlines, isotherms, and isohalines at different times.

REFERENCIAS
  1. Bhadauria, B.S., Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source, Trans. Porous Media, vol. 92, pp. 299-320,2012.

  2. Bhadauria, B.S. and Kiran, P., Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid under Temperature Modulation, Trans. Porous Media, vol. 100, pp. 279-295,2013.

  3. Bhadauria, B.S., Hashim, I., and Siddheshwar, P.G., Study of Heat Transport in a Porous Medium under G-Jitter and Internal Heating Effects, Trans. Porous Media, vol. 96, pp. 21-37,2013.

  4. Govender, S., Stability of Convection in a Gravity Modulated Porous Layer Heated from Below, Trans. Porous Media, vol. 57, pp. 113-123,2004.

  5. Govender, S., Weak Non-Linear Analysis of Convection in a Gravity Modulated Porous Layer, Trans. Porous Media, vol. 60, pp. 33-42,2005a.

  6. Govender, S., Linear Stability and Convection in a Gravity Modulated Porous Layer Heated from Below: Transition from Synchronous to Subharmonic Solutions, Trans. Porous Media, vol. 59, pp. 227-238,2005b.

  7. Griffith, R.W., Layered Double-Diffusive Convection in Porous Media, J. FluidMech., vol. 102, pp. 221-248,1981.

  8. Holzbecher, E., The Influence of Variable Viscosity on Thermal Convection in Porous Media, in Int. Conf. on Advanced Computational Methods in Heat Transfer, pp. 115-124, Krakow, Poland, June 17-19,1998.

  9. Ingham, D.B. and Pop, I., Transport Phenomena in Porous Media, vol. III, Oxford, UK: Elsevier, 2005.

  10. Kuznetsov, A.V., The Onset of Bioconvection in a Suspension of Negatively Geotactic Microorganisms with High-Frequency Vertical Vibration, Int. Comm. Heat Mass Transf., vol. 32, pp. 1119-1127,2005.

  11. Kuznetsov, A.V., Linear Stability Analysis of the Effect of Vertical Vibration on Bioconvection in a Horizontal Porous Layer of Finite Depth, J. Porous Media, vol. 9, pp. 597-608,2006a.

  12. Kuznetsov, A.V., Investigation of the Onset of Bioconvection in a Suspension of Oxytactic Microorganisms Subjected to High Frequency Vertical Vibration, Theor. Comput. Fluid Dynam., vol. 20, pp. 73-87,2006b.

  13. Kuznetsov, A.V. and Nield, D.A., The Effects of Combined Horizontal and Vertical Heterogeneity on the Onset of Convection in a Porous Medium: Double Diffusive Case, Trans. Porous Media, vol. 72, pp. 157-170,2008.

  14. Kuznetsov, A.V. and Nield, D.A., The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium, Trans. PorousMedia, vol. 85, pp. 941-951,2010.

  15. Kuznetsov, A.V. and Nield, D.A., Double-Diffusive Natural Convective Boundary-Layer Flow of a Nanofluid past a Vertical Plate, Int. J. Therm. Sci., vol. 50, pp. 712-717,2011.

  16. Malashetty, M.S. and Basavaraja, D., Effect of Thermal/Gravity Modulation on the Onset of Rayleigh-Benard Convection in a Couple Stress Fluid, Int. J. Trans. Phenom., vol. 7, pp. 31-44,2005.

  17. Malashetty, M.S. and Padmavathi, V., Effect of Gravity Modulation on the Onset of Convection in a Fluid and Porous Layer, Int. J. Eng. Sci., vol. 35, pp. 829-839,1997.

  18. Matta, A. and Lakshmi Narayana, P. A., Effect of Variable Gravity on Linear and Non-Linear Stability of Double Diffusive Hadley Flow in Porous Media, J. Porous Media, vol. 19, no. 4, pp. 287-301,2016.

  19. Mulone, G. and Straughan, B., An Operative Method to Obtain Necessary and Sufficient Stability Conditions for Double Diffusive Convection in Porous Media, ZAMM, vol. 86, pp. 507-520,2006.

  20. Nield, D.A., Onset of Thermohaline Convection in a Porous Medium, Water Resour. Res., vol. 4, p. 553,1968.

  21. Nield, D.A., the Effect of Temperature-Dependent Viscosity on the Onset of Convection in a Saturated Porous Medium, ASMEJ. Heat Transf., vol. 118, pp. 803-805,1996.

  22. Nield, D.A. and Bejan, A., Convection in Porous Media, 3rd ed., New York, NY: Springer, 2006.

  23. Nield, D.A. and Kuznetsov, A.V., The Cheng-Minkowycz Problem for the Double-Diffusive Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid, Int. J. Heat Mass Transf., vol. 54, pp. 374-378,2011.

  24. Payne, L.E., Song, J.C., and Straughan, B., Continuous Dependence and Convergence for Brinkman and Forchheimer Models with Variable Viscosity, Proc. R. Soc. London, vol. 452, pp. 2173-2190,1999.

  25. Poulikakos, D., Double Diffusive Convection in a Horizontally Sparsely Packed Porous Layer, Int. Commun. Heat Mass Transf., vol. 13, p. 587,1986.

  26. Qin, Y. and Chadam, J., Non-Linear Convective Stability in a Porous Medium with Temperature-Dependent Viscosity and Inertial Drag, Stud. Appl. Math, vol. 96, pp. 273-288,1996.

  27. Razi, Y.P., Mojtabi, I., and Charrier-Mojtabi, M.C., A Summary of New Predictive High Frequency Thermo-Vibrational Modes in Porous Media, Trans. Porous Media, vol. 77, pp. 207-208,2009.

  28. Rees, D.A.S. and Pop, I., The Effect of G-Jitter on Vertical Free Convection Boundary-Layer Flow in Porous Media, Int. Comm. Heat Mass Transf., vol. 27, no. 3, pp. 415-424,2000.

  29. Rees, D.A.S. and Pop, I., The Effect of G-Jitter on Free Convection Near a Stagnation Point in a Porous Medium, Int. J. Heat Mass Transf., vol. 44, pp. 877-883,2001.

  30. Rees, D.A.S. and Pop, I., The Effect of Large-Amplitude G-Jitter Vertical Free Convection Boundary-Layer Flow in Porous Media, Int. J. Heat Mass Transf., vol. 46, pp. 1097-1102,2003.

  31. Rees, D.A.S., Hossain, M.A., and Kabir, S., Natural Convection of Fluid with Variable Viscosity from a Heated Vertical Wavy Surface, ZAMP, vol. 53, pp. 48-57,2002.

  32. Richardson, L. and Straughan, B., Convection with Temperature-Dependent Viscosity in a Porous Medium: Non-Linear Stability and the Brinkman Effect, Atti. Accad. Naz. Lincei-Ci-Sci-Fis. Mat., vol. 4, pp. 223-232,1993.

  33. Rudraiah, N. and Siddheshwar, P.G., A Weak Non-Linear Stability Analysis of Double Diffusive Convection with Cross-Diffusion in a Fluid-Saturated Porous Medium, Heat Mass Transf., vol. 33, pp. 287-293,1998.

  34. Rudraiah, N., Srimani, P.K., and Friedrich, R., Finite Amplitude Convection in a Two-Component Fluid Saturated Porous Layer, Heat Mass Transf., vol. 25, pp. 715-722,1982.

  35. Saravanan, S. and Arunkumar, A., Convective Instability in a Gravity Modulated Anisotropic Thermally Stable Porous Medium, Int. J. Eng. Sci., vol. 48, pp. 742-750,2010.

  36. Saravanan, S. and Purusothaman, A., Floquent Instability of a Modulated Rayleigh-Benard Problem in an Anisotropic Porous Medium, Int. J. Therm. Sci, vol. 48, pp. 2085-2091,2009.

  37. Saravanan, S. and Sivakumar, T., Onset of Filteration Convection in a Vibrating Medium: The Brinkman Model, Phys. Fluids, vol. 22, p. 034104,2010.

  38. Saravanan, S. and Sivakumar, T., Thermovibrational Instability in a Fluid Saturated Anisotropic Porous Medium, ASME J. Heat Transf., vol. 133, pp. 051601.1-051601.9,2011.

  39. Siddheshwar, P.G., Bhadauria, B.S., and Srivastava, A., An Analytical Study of Non-Linear Double Diffusive Convection in a Porous Medium under Temperature/Gravity Modulation, Trans. Porous Media, vol. 91, pp. 585-604,2012.

  40. Siddheshwar, P.G. and Chan, A.T., Thermorheological Effect on Benard and Marangoni Convections in Anisotropic Porous Media, in Hydrodynamics VI Theory and Applications, L. Cheng, and K. Yeow, Eds., London, UK: Taylor and Francis, pp. 471-476, 2004.

  41. Siddheshwar, P.G. and Vanishree, R.K., Study of Heat Transport in Benard-Darcy Convection with G-Jitter and Thermo-Mechanical Anisotropy in Variable Viscosity Liquids, Trans. Porous Media, vol. 92, pp. 277-288, 2012.

  42. Siddhavaram, V.K. and Homsy, G.M., The Effects of Gravity Modulation on Fluid Mixing. Part 1. Harmonic Modulation, J. Fluid Mech., vol. 562, pp. 445-475,2006.

  43. Srivastava, A., Bhadauria, B.S., Siddheshwar, P.G., and Hashim, I., Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid under G-Jitter and Internal Heating Effects, Trans. Porous Media, vol. 99, pp. 359-376,2013.

  44. Strong, N., Effect of Vertical Modulation on the Onset of Filtration Convection, J. Math. Fluid Mech., vol. 10, pp. 488-502,2008a.

  45. Strong, N., Double-Diffusive Convection in a Porous Layer in the Presence of Vibration, SIAM J. Appl. Math, vol. 69, pp. 1263-1276,2008b.

  46. Swamy, M., Effect of G-Jitter on the Onset of Double-Diffusive Convection in Fluid/Porous Layer, J. Porous Media, vol. 17, no. 2, pp. 117-128,2014.

  47. Taunton, J.W.,Lightfoot,E.N., and Green, T., Thermohaline Instability and Salt Fingers in a Porous Medium, Phys. Fluids, vol. 15, pp. 748-753,1972.

  48. Vadasz, P., Ed., Emerging Topics in Heat and Mass Transfer in Porous Media, New York, NY: Springer, 2008.

  49. Vadasz, P., Coriolis Effect on Gravity-Driven Convection in a Rotating Porous Layer Heated from Below, J. Fluid Mech., vol. 376, 351-375,1998.

  50. Vafai, K., Porous Media: Applications in Biological Systems and Biotechnology, Boca Raton, FL: CRC Press, 2010.

  51. Vafai, K., Handbook of Porous Media, 3rd ed., Boca Raton, FL: CRC Press, 2015.

  52. Vanishree, R.K. and Siddheshwar, P.G., Effect of Rotation on Thermal Convection in an Anisotropic Porous Medium with Temperature-Dependent Viscosity, Trans. Porous Media, vol. 81, pp. 73-87,2010.

CITADO POR
  1. Pranesh S., Saha Richa, Three-Component Convection in a Vertically Oscillating Oldroyd-B Fluid With Cross Effects, Microgravity Science and Technology, 34, 2, 2022. Crossref

  2. Badday Alaa Jabbar , Harfash Akil J., THERMOSOLUTAL CONVECTION IN ROTATING BIDISPERSIVE POROUS MEDIA WITH GENERAL BOUNDARY CONDITIONS , Special Topics & Reviews in Porous Media: An International Journal, 13, 6, 2022. Crossref

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