Выходит 4 номеров в год
ISSN Печать: 2151-4798
ISSN Онлайн: 2151-562X
Indexed in
EFFECT OF VISCOUS DISSIPATION AND INTERNAL HEAT SOURCE ON MONO-DIFFUSIVE THERMOCONVECTIVE STABILITY IN A HORIZONTAL POROUS MEDIUM LAYER
Краткое описание
A mathematical model is developed for studying the onset of mono-diffusive convective fluid flow in a horizontal porous layer with temperature gradient, internal heat generation, and viscous dissipation effects. Darcy's model is used for the porous medium, which is considered to be isotropic and homogenous. A linear instability analysis is conducted, and transverse or longitudinal roll disturbances are examined. The dimensionless emerging eigenvalue problem is solved numerically with the Runge-Kutta and shooting methods for both cases of disturbances, i.e,. longitudinal and transverse rolls. Critical wave number and critical vertical thermal Rayleigh number Rz are identified. For higher values of Gebhart number, Ge, a significant destabilizing effect of Hadley−Prats flow is computed. Internal heat generation also strongly modifies the critical vertical Rayleigh number. Extensive interpretation of the solutions related to the onset of convection is provided. The study is relevant to geophysical flows and materials processing systems.
-
Abdelsalam, S.I. and Zaher, A., Leveraging Elasticity to Uncover the Role of Rabinowitsch Suspension through a Wavelike Conduit: Consolidated Blood Suspension Application, Math., MDPI, vol. 9, no. 16, pp. 1-25,2021.
-
Abdelsalam, S.I., Velasco-Hernandez, J.X., and Zaher, A.Z., Electro-Magnetically Modulated Self-Propulsion of Swimming Sperms via Cervical Canal, Biomech. Model. Mechanobiol, vol. 20, pp. 861-878,2021.
-
Barletta, A. andNield, D.A., On Hadley Flow in a Porous Layer with Vertical Heterogeneity, J. FluidMech., vol. 710, pp. 304-323, 2012.
-
Barletta, A. and Nield, D.A., Instability of Hadley-Prats Flow with Viscous Heating in a Horizontal Porous Layer, Transp. Porous Media, vol. 84, pp. 241-256,2010.
-
Barletta, A. and Nield, D.A., Thermosolutal Convective Instability and Viscous Dissipation Effect in a Fluid-Saturated Porous Medium, Int. J. Heat Mass Transf., vol. 54, pp. 1641-1648,2011.
-
Barletta, A. and Storesletten, L., Viscous Dissipation and Thermo Convective Instabilities in a Horizontal Porous Channel Heated from Below, Int. J. Therm. Sci., vol. 49, pp. 621-630,2010.
-
Barletta, A., Celli, M., and Nield, D.A., Unstable Buoyant Flow in an Inclined Porous Layer with an Internal Heat Source, Int. J. Therm. Sci., vol. 79, pp. 176-182,2014.
-
Bhatti, M.M. and Abdelsalam, S.I., Bio-Inspired Peristaltic Propulsion of Hybrid Nanofluid Flow with Tantalum, Ta and Gold, Au Nanoparticles under Magnetic Effects, 2021. DOI: 10.1080/17455030.2021.1998728.
-
Chen, F., Convective Instability in Superposed Fluid and Anisotropic Porous Layers, Phys. Fluids A, vol. 3, p. 556,1991.
-
Deepika, N. and Narayana, P.A.L., Effects of Vertical Throughflow and Variable Gravity on Hadley-Prats Flow in a Porous Medium, Transp. Porous Media, vol. 109,pp. 455-468,2015b.
-
Deepika, N. and Narayana, P.A.L., Effects of Viscous Dissipation and Concentration Based Internal Heat Source on Convective Instability in a Porous Medium with Throughflow, Int. J. Math. Comput. Phys. Elect. Comput. Eng., vol. 9, no. 7, pp. 410-414, 2015c.
-
Deepika, N. and Narayana, P.A.L., Linear Stability of Double Diffusive Convection of Hadley-Prats Flow with Viscous Dissipation in a Porous Media, Procedia Eng., vol. 127, pp. 193-200,2015a.
-
Eldesoky, I.M., Abdelsalam, S.I., Askary, W.A., and Ahmed, M.M., Concurrent Development of Thermal Energy with Magnetic Field on a Particle-Fluid Suspension through a Porous Conduit, BioNanoSci., vol. 9, pp. 186-202,2019.
-
Eldesoky, I.M., Abdelsalam, S.I., Wageeh, A.E.A., and Ahmed, M.M., The Integrated Thermal Effect in Conjunction with Slip Conditions on Peristaltically Induced Particle-Fluid Transport in a Catheterized Pipe, J. Porous Media, vol. 23, pp. 695-713, 2020.
-
Elmaboud, Y.A., Mekheimer, Kh.S., and Abdelsalam, S.I., A Study of Nonlinear Variable Viscosity in Finite-Length Tube with Peristalsis, Appl. Bionics Biomech., vol. 11, pp. 197-206,2014.
-
Gebhart, B., Effects of Viscous Dissipation inNatural Convection, J. Fluid Mech., vol. 14, pp. 225-232,1962.
-
Hill, A.A., Double-Diffusive Convection in a Porous Medium with a Concentration Based Internal Heat Source, Proc. R. Soc. A., vol. 461, pp. 561-574,2005.
-
Horton, C.W. and Rogers, F.T., Convection Currents in a Porous Medium, J. Appl. Phys, vol. 16, pp. 367-370,1945.
-
Lapwood, E.R., Convection of a Fluid in a Porous Medium, Proc. Cambridge Philos. Soc., vol. 44, pp. 508-521,1948.
-
Mahmoud, S.R., Afifi, N.A.S., and Al-Isede, H.M., Effect of Porous Medium and Magnetic Field on Peristaltic Transport of a Jeffrey Fluid, Int. J. Math. Anal, vol. 5, no. 21, pp. 1025-1034,2011.
-
Matta, A., Narayana, P.A.L., and Hill, A.A., Nonlinear Thermal Instability in a Horizontal Porous Layer with an Internal Heat Source and Mass Flow, Acta Mech., vol. 227, pp. 1743-1751,2016a.
-
Matta, A., Narayana, P.A.L., and Hill, A.A., Double-Diffusive Hadley-Prats Flow in a Porous Medium Subject to Gravitational Variation, Int. J. Therm. Sci., vol. 102, pp. 300-307,2016b.
-
Matta, A., Mono-Diffusive Hadley-Prats Flow in a Horizontal Porous Layer Subject to Variable Gravity and Internal Heat Generation, Heat Transf.-Asian Res, pp. 1-14,2019.
-
Mekheimer, Kh.S., Abo-Elkhair,R.E., Abdelsalam, S.I., Khalid,K.A., andMoawad, A.M.A., Biomedical Simulations ofNanoparticles Drug Delivery to Blood Hemodynamics in Diseased Organs: Synovitis Problem, Int. Commun. Heat Mass Transf., vol. 130, p. 105756,2022.
-
Nield,D.A. andBejan, A., Convection in Porous Media, 4th ed., Berlin, Germany: Springer, 2013.
-
Nield, D.A., Barletta, A., and Celli, M., The Effect of Viscous Dissipation on the Onset of Convection in an Inclined Porous Layer, J. Fluid Mech., vol. 679, pp. 544-558,2011.
-
Nield, D.A., Convection in a Porous Medium with Inclined Temperature Gradient: Additional Results, Int. J. Heat Mass Transf., pp. 3021-3025,1994.
-
Parthiban, C. and Patil, P.R., Effect of Non-Uniform Boundary Temperatures on Thermal Instability in a Porous Medium with Internal Heat Source, Int. Commun. Heat Mass Transf., vol. 22, pp. 683-692,1995.
-
Rafeek, M.K.V., Reddy, G.J., Ragoju, R., Gundlapally, S.K.R., and Sheremet, M.A., Impact of Throughflowand Coriolis Force on the Onset of Double-Diffusive Convection with Internal Heat Source, Coatings, vol. 12, no. 8, p. 1096,2022.
-
Straughan, B., Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation, Transp. Porous Media, vol. 134, pp. 303-314,2020.
-
Taslim, M.E. andNarusawa, U., Thermal Stability of Horizontally Superposed Porous and Fluid Layers, J. Heat Transf., vol. 111, no. 2, pp. 357-362,1989.
-
Thirlby, R., Convection in an Internally Heated Layer, J. Fluid Mech, vol. 44, pp. 673-693,2013.
-
Thirupathi, T., Mishra, S.R., Abbas, M.A., Bhatti, M.M., and Abdelsalam, S.I., Three-Dimensional Nanofluid Stirring with Non-Uniform Heat Source or Sink through an Elongated Sheet, Appl. Math. Comput., vol. 421, p. 126927,2022.
-
Turcotte, D.L., Hsui, A.T., Torrance, K.E., and Schubert, G., Influence of Viscous Dissipation on Benard Convection, J. Fluid Mech, vol. 64, pp. 369-374,1974.
-
Tveitereid, M. and Palm, E., Convection Due to Internal Heat Sources, J. Fluid Mech., vol. 76, pp. 481-499,1976.
-
Umavathi, J.C. and Beg, O.A., Modelling the Onset of Thermosolutal Convective Instability in a Non-Newtonian Nanofluid-Saturated Porous Medium Layer, Chin. J. Phys., vol. 68, pp. 147-167,2020.
-
Umavathi, J.C. and Beg, O.A., Simulation of the Onset of Convection in Porous Medium Layer Saturated by a Couple Stress Nanofluid, Microfluid. Nanofluidics, vol. 25, no. 6, p. 53, 2021.
-
Umavathi, J.C., Sheremet, M.A., Ojjela, O., and Reddy, G.J., The Onset of Double-Diffusive Convection in a Nanofluid Saturated Porous Layer: Cross-Diffusion Effects, Eur. J. Mech. B/Fluids, vol. 65, pp. 70-87,2017.
-
Weber, J.E., Convection in a Porous Medium with Horizontal and Vertical Temperature Gradients, Int. J. Heat Mass Transf, vol. 17, pp. 241-248,1974.