Library Subscription: Guest

THERMAL DIFFUSIVITY VARIATION EFFECT ON A HYDRO-THERMAL CONVECTIVE FLOW IN A POROUS MEDIUM

Volume 23, Issue 5, 2020, pp. 497-515
DOI: 10.1615/JPorMedia.2020028604
Get accessGet access

ABSTRACT

We consider a hydrothermal convective flow in a porous medium to investigate the effect of the vertical rate of change in thermal diffusivity. Using a weakly nonlinear approach, we derive the linear and first-order systems assuming a no-flow basic state system. The solutions for the linear and first-order systems are computed numerically using both the fourth-order Runge-Kutta and shooting methods. Numerical results obtained in this study show a stabilizing effect on the dependent variables for the case of a positive vertical rate of change in diffusivity, whereas a destabilizing effect is noticed for the case of a negative vertical rate of change in diffusivity. The present results indicate that convective flow driven by the buoyancy force is more effective if thermal diffusivity is weaker, while the opposite result holds for a stronger diffusivity effect. In particular, both velocity and convective temperature decrease with increasing diffusivity, while they increase with decreasing diffusivity. At the middle of the layer (z = 0) for x = 0, the contribution of the linear and first-order solutions to the velocity component are 0.3345, 0.3031, and 0.3679 for the respective values 0.0, 0.6, and -0.4 of the diffusivity parameter. For temperature, these contributions are 0.0167, 0.0116, and 0.0229, respectively. Some other quantitative results are provided in tabular form.

REFERENCES
  1. Bhatta, D. and Riahi, D.N., Convective Flow in an Aquifer Layer, Fluids, vol. 52, pp. 1-19, 2017.

  2. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford: Oxford University Press, 1981.

  3. Das, S. andMorsi, Y., Natural Convection in Domed Porous Enclosures: Non-Darcian Flow, J. Porous Media, vol. 6, pp. 159-175, 2003.

  4. Drazin, P.G. and Reid, W.H., Hydrodynamic Stability, 2nd Ed., Cambridge, England: Cambridge University Press, 2004.

  5. Fowler, A.C., Mathematical Models in the Applied Sciences, Cambridge, England: Cambridge University Press, 1997.

  6. Fusi, L., Farina, A., and Rosso, F., Mathematical Models for Fluids with Pressure-Dependent Viscosity Flowing in Porous Media, Int. J. Eng. Sci., vol. 87, pp. 110-118, 2015.

  7. Hassanien, I.A. and Omar, G.M., Mixed-Convection Flow Adjacent to a Horizontal Surface in a Porous Medium with Variable Permeability and Surface Heat Flux, J. Porous Media, vol. 8, pp. 225-235, 2005.

  8. Hsiao, S.W., Natural Convection in an Inclined Porous Cavity with Variable Porosity and Thermal Dispersion Effects, Int. J. Num. Methods Heat Fluid Flow, vol. 8, pp. 97-117, 1998.

  9. Kim, S.J. and Vafai, K., Analysis of Natural Convection about a Vertical Plate Embedded in a Porous Medium, Int. J. Heat Mass Transf., vol. 32, pp. 665-677, 1989.

  10. Kleinstreuer, C. and Xu, Z., Mathematical Modeling and Computer Simulations of Nanofluid Flow with Applications to Cooling and Lubrication, Fluids, vol. 1, no. 16, pp. 1-33,2016.

  11. Lai, F.C. and Kulacki, F.A., Natural Convection across a Vertical Layered Porous Cavity, Int. J. Heat Mass Transf., vol. 31, pp. 1247-1260, 1988.

  12. Nadeem, S. and Jiaz, S., Theoretical Analysis of Metallic Nanoparticles on Blood Flow through Artery with Permeable Walls, Phys. Lett. A, vol. 379, pp. 542-554,2015.

  13. Nakshatrala, K.B. and Rajagopal, K.R., A Numerical Study of Fluids with Pressure-Dependent Viscosity Flowing through a Rigid Porous Medium, Int. J. Numer. Methods Fluids, vol. 67, pp. 342-368, 2011.

  14. Nield, D.A. and Bejan, A., Convection in a Porous Media, 5th Ed., New York: Springer, 2017.

  15. Nield, D.A. and Kuznetsov, A.V., The Effect of a Transition Layer between a Fluid and a Porous Medium: Shear Flow in a Channel, Transp. Porous Media, vol. 78, pp. 477-487, 2009.

  16. Oliveski, R.D.C. and Macrczak, L.D.F., Natural Convection in a Cavity Filled with Porous Medium with Variable Porosity and Darcy Number, J. Porous Media, vol. 11, pp. 255-264, 2008.

  17. Rao, A.S., Prasad, V.R., Beg, O.A., and Rashidi, M., Free Convection Heat and Mass Transfer of a Nanofluid past a Horizontal Cylinder Embedded in a Non-Darcy Porous Medium, J. Porous Media, vol. 21, no. 3, pp. 279-294, 2018.

  18. Rees, D.A.S. and Barletta, A., Linear Instability of the Isoflux Darcy-Benard Problem in an Inclined Porous Layer, Transp. Porous Media, vol. 87, pp. 665-667, 2011.

  19. Rees, D.A.S. and Pop, I., Vertical Free Convection in a Porous Medium with Variable Permeability Effects, Int. J. Heat Mass Transf, vol. 43, pp. 2565-2571,2000.

  20. Riahi, D.N., Nonlinear Convection in a Porous Layer with Finite Conducting Boundaries, J. Fluid Mech., vol. 129, pp. 153-171, 1983.

  21. Riahi, D.N., Nonlinear Convection in a Porous Layer with Permeable Boundaries, Int. J. Non-Linear Mech, vol. 24, pp. 459-463, 1989.

  22. Riahi, D.N., Modal Package Convection in a Porous Layer with Boundary Imperfections, J. Fluid Mech., vol. 318, pp. 107-128, 1996.

  23. Rubin, H., Onset of Thermohaline Convection in Heterogeneous Porous Media, Israel J. Tech, vol. 19, pp. 110-117, 1981.

  24. Rubin, H., Thermohaline Convection in a Nonhomogeneous Aquifer, J. Hydrology, vol. 57, pp. 307-320, 1982.

  25. Saleh, H., Natural Convection from a Cylinder in Square Porous Enclosure Filled with Nanofluids, J. Porous Media, vol. 18, no. 6, pp. 559-567,2015.

  26. Shcheritsa, Q.V., Getling, A.V., and Mazhorova, O.S., Effects of Variable Thermal Diffusivity on the Structure of Convection, Phys. Lett. A, vol. 382, no. 9, pp. 639-645, 2018.

  27. Shit, G.C., Roy, M., and Sinha, A., Mathematical Modelling of Blood Flow through a Tapered Overlapping Stenosed Artery with Variable Viscosity, Appl. Bionics Biomech., vol. 11, pp. 185-195,2014.

  28. Umavathi, J.C., Chamkha, A.J., and Mohite, M.B., Convective Transport in a Nanofluid Saturated Porous Layer with Cross Diffusion and Variation of Viscosity and Conductivity, Spec. Topics Rev. Porous Media: Int. J., vol. 6, pp. 11-27, 2015?.

  29. Vafai, K., Convective Flow and Heat Transfer in Variable-Porosity Media, J. Fluid Mech., vol. 147, pp. 233-259, 1984. Vafai, K., Handbook of Porous Media, 2nd Ed., Boca Raton, FL: Taylor & Francis, 2005.

Forthcoming Articles

ON THERMAL CONVECTION IN ROTATING CASSON NANOFLUID PERMEATED WITH SUSPENDED PARTICLES IN A DARCY-BRINKMAN POROUS MEDIUM Pushap Sharma, Deepak Bains, G. C. Rana Effect of Microstructures on Mass Transfer inside a Hierarchically-structured Porous Catalyst Masood Moghaddam, Abbas Abbassi, Jafar Ghazanfarian Insight into the impact of melting heat transfer and MHD on stagnation point flow of tangent hyperbolic fluid over a porous rotating disk Priya Bartwal, Himanshu Upreti, Alok Kumar Pandey Numerical Simulation of 3D Darcy-Forchheimer Hybrid Nanofluid Flow with Heat Source/Sink and Partial Slip Effect across a Spinning Disc Bilal Ali, Sidra Jubair, Md Irfanul Haque Siddiqui Fractal model of solid-liquid two-phase thermal transport characteristics in the rough fracture network shanshan yang, Qiong Sheng, Mingqing Zou, Mengying Wang, Ruike Cui, Shuaiyin Chen, Qian Zheng Application of Artificial Neural Network for Modeling of Motile Microorganism-Enhanced MHD Tangent Hyperbolic Nanofluid across a vertical Slender Stretching Surface Bilal Ali, Shengjun Liu, Hongjuan Liu Estimating the Spreading Rates of Hazardous Materials on Unmodified Cellulose Filter Paper: Implications on Risk Assessment of Transporting Hazardous Materials Heshani Manaweera Wickramage, Pan Lu, Peter Oduor, Jianbang Du ELASTIC INTERACTIONS BETWEEN EQUILIBRIUM PORES/HOLES IN POROUS MEDIA UNDER REMOTE STRESS Kostas Davanas Gravity modulation and its impact on weakly nonlinear bio-thermal convection in a porous layer under rotation: a Ginzburg-Landau model approach Michael Kopp, Vladimir Yanovsky Pore structure and permeability behavior of porous media under in-situ stress and pore pressure: Discrete element method simulation on digital core Jun Yao, Chunqi Wang, Xiaoyu Wang, Zhaoqin Huang, Fugui Liu, Quan Xu, Yongfei Yang Influence of Lorentz forces on forced convection of Nanofluid in a porous lid driven enclosure Yi Man, Mostafa Barzegar Gerdroodbary SUTTERBY NANOFLUID FLOW WITH MICROORGANISMS AROUND A CURVED EXPANDING SURFACE THROUGH A POROUS MEDIUM: THERMAL DIFFUSION AND DIFFUSION THERMO IMPACTS galal Moatimid, Mona Mohamed, Khaled Elagamy CHARACTERISTICS OF FLOW REGIMES IN SPIRAL PACKED BEDS WITH SPHERES Mustafa Yasin Gökaslan, Mustafa Özdemir, Lütfullah Kuddusi Numerical study of the influence of magnetic field and throughflow on the onset of thermo-bio-convection in a Forchheimer‑extended Darcy-Brinkman porous nanofluid layer containing gyrotactic microorganisms Arpan Garg, Y.D. Sharma, Subit K. Jain, Sanjalee Maheshwari A nanofluid couple stress flow due to porous stretching and shrinking sheet with heat transfer A. B. Vishalakshi, U.S. Mahabaleshwar, V. Anitha, Dia Zeidan ROTATING WAVY CYLINDER ON BIOCONVECTION FLOW OF NANOENCAPSULATED PHASE CHANGE MATERIALS IN A FINNED CIRCULAR CYLINDER Noura Alsedais, Sang-Wook Lee, Abdelraheem Aly Porosity Impacts on MHD Casson Fluid past a Shrinking Cylinder with Suction Annuri Shobha, Murugan Mageswari, Aisha M. Alqahtani, Asokan Arulmozhi, Manyala Gangadhar Rao, Sudar Mozhi K, Ilyas Khan CREEPING FLOW OF COUPLE STRESS FLUID OVER A SPHERICAL FIELD ON A SATURATED BIPOROUS MEDIUM Shyamala Sakthivel , Pankaj Shukla, Selvi Ramasamy
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections Prices and Subscription Policies Begell House Contact Us Language English 中文 Русский Português German French Spain