COMBINED EFFECTS OF VARIABLE VISCOSITY, VISCOUS DISSIPATION AND THERMAL RADIATION ON UNSTEADY NATURAL CONVECTION COUETTE FLOW THROUGH A VERTICAL POROUS CHANNEL

Authors

Keywords:

Natural convection, Thermal radiation, Variable viscosity, Viscous dissipation, Adomian decomposition method

Abstract

The present article investigates combined effects of variable viscosity, viscous dissipation and thermal radiation on unsteady natural convection Couette flow through vertical porous channel. Non-linear Rosseland heat diffusion is deployed for the solution of the flow equations which as a consequence; together with the effects of variable viscosity, viscous dissipation and thermal radiation have resulted to high non-linear equations for the flow formation. Appropriate similarity variables are used to convert the partial differential equations associated with the fluid formation into dimensionless ordinary differential equations (ODEs) and the emerging ODEs are solved using Adomian decomposition method (ADM) and computer aided algebra package. Influences of the physical parameters involved in the problem are presented, discussed and conclusions are drawn. During the investigation; it was found that the fluid velocity and temperature were found to increase with increase in Eckert number, viscosity variation and thermal radiation.

Dimensions

Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Boston, MA: Kluwer.

Ajibade, A. O., Jha B.K. and Andrew, O. (2011). Entropy Generation under the Effect of Suction/Injection. Journal of Applied Mathematical Modeling. 35: 4630-4646.

Alam M.M., Alim, M.A and Chaudhury (2006). Effect of viscous dissipation and pressure work in natural convection flow along vertical flat plate with heat conduction due to plate thickness. Journal of naval architecture and marine engineering 3(2006). pp. 69-76.

Carey,V.P. and Mollendorf, J. C. (1978). Natural convection in liquid with temperature dependent viscosity. In proceedings of the 6th International C onference in Heat Transfer. Toronto. 2:211-217.

Cherruault, Y. (1990). Convergence of Adomian’s method. Proceedings, 7th International Conference on Mathematical and Computer Modeling. 14: 83-86.

Gray, J., Kassory, D.R., Tadjeran, H. and Zebib, A. (1982). Effect of significant viscosity variation on convective heat transport in water-saturated porous media, J. Fluid Mech., 117: 233-249.

Hossain, M.A. Khanafer, K., and Vafai, K. (2001). The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate. Int. J. Therm. Sci., 40:115-124.

Ibanez, G., Cuevas, S. and Lopez de Haro, M. (2003).Minimization of entropy generation by asymmetric convective cooling. International Journal of Heat and Mass Transfer. 46:1321-1328.

Isreal-Cookey, C., Ogulu, A and Omubo-pepple , V.B. (2003) Influence of viscous dissipation on unsteady MHD free convection flow past an infinite heated vertical plate in a porous medium with time dependent suction. Int. journal of heat mass transfer. Vol.46. pp.2305-2311.

Jha, B.K., Yabo, I.B. and Lin, J. {2017). Transient Natural Convection in an annulus with Thermal Radiation. Journal of Applied Mathematics, 8: 1351- 1366.

Kay, A. (2017).Comments on ‘Combined effect of variable viscosity and thermal conductivity on free convection flow in a vertical channel using DTM’ by J.C. Imavathi and M. Shekar. Meccanica, 52 (6): 1493-1494.

Lai, E.C. and Kulacki, E.A. (1990). The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium. International Journal of Heat and Mass Transfer. 33(5):1028-1031.

Makinde, O.D. (2008). Entropy generation analysis for variable viscosity channel flow with non-uniform wall temperature. Journal of Applied Energy, 85:384-393.

Makinde, O.D., Olajuwon, B. I. and Gbolagade A.W. (2007). Adomian Decomposition Approach to a Boundary Layer Flow with Thermal Radiation past a Moving Vertical Porous Plate. International Journal of Applied Mathematics and Mechanics. 3(3):62-70.

Makinde, O.D., and Ogulu, A. (2011). The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field. Journal of Chemical Engineering Communications. 195:1575- 1584.

Magyari, E. and Pantokratoras, A. (2011). Note on the effect of thermal radiation in the linearized Rosssel and approximation on the heat transfer characteristics of various boundary layer flows. International Communications in Heat and Mass Transfer. 38: 554- 556.

Mehta, K.N. and Sood, S. (1992). Transient free convection flow with temperature-dependent viscosity in a fluid saturated porous medium, Int. J. Eng. Sci., 30:1083-1087.

Neild, D.A. and Bejan, A. (2013). Convection In porous media. 4th edition. Springer, New York.

Ingham, D.B. and Pop, I. (1998) Transport phenomena in porous media. Pargamon. Oxford.

Robert, W. and Murray, R. S. (2010). Schaum’s Oulines Series for Advanced Calculus. Third Edition.

Sahin,A.Z. (1999).Effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux. Journal of Heat and Mass Transfer. 35: 499-509.

Salem, A.M. (2007). Variable viscosity and thermal conductivity effects on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet. Physics Letters A, 369(4): 315-322.

Salem, A.M. (2013). The Effects of Variable viscosity, Viscous Dissipation and Chemical Reaction on Heat and Mass Transfer Flow of MHD Micropolar Fluid alond a Permeable Stretching Sheet in a Non-Darcian Porous Medium.Hindawi Publishing Company. Mathematical Problem in Engineering. Volume 2013.

Seddeek, M.A. and Salama, E.A. (2007). The effects of temperature-dependent viscosity and thermal conductivity on unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction, Computational Materials Science, 40(2):186-192.

Soundalgekar.V.M (1972) viscous dissipation effect on unsteady natural convective flow past an infinite vertical porous plate with constant suction. Int. journal of heat mass transfer.15:1253-1261.

Sparrow, E. M. and Cess. R. D. (1978). Radiation Heat Transfer, augmented edition. Hemisphere, Washington, D. C.

Yasutomi, S., Bair, S. and Winer, W.O. (1984). An application of a free volume model to lubricant rheology I. Dependence on viscosity on temperature and pressure, J. Tribol. Trans. ASME., 106:291-303.

Yabo, I.B., Jha, B.K. and Lin, J. (2016). Combined Effects of Thermal Diffusion and Diffusion-Thermo Effects on Transient MHD Natural Convection and Mass Transfer Flow in a Vertical Channel with Thermal Radiation. Journal of Applied Mathematics. 6: 2354-2373.

Yusuf, A.B. and Ajibade, O.A. (2018a). Unsteady Natural Convection Flow through a vertical Porous Channel filled with Porous Materials under the effect of Thermal Radiation. FUDMA Journal of Sciences, 2(2):101-115.

Yusuf, A.B. and Ajibade, O.A. (2018b). Combined Effects of Variable Viscosity and Thermal Radiation on Natural Convection Flow through a vertical Porous Channel, FUDMA Journal of Sciences, 2(2):273-287.

Yusuf, A.B. and Ajibade, O.A. (2019). Variable Fluid Viscosity and Thermal Radiation Effects on Natural Convection Couette Flow through a vertical Porous Channel. Journal of Advances in Mathematics and Computer Science, 13(1):1-17.

Published

02-07-2020

How to Cite

COMBINED EFFECTS OF VARIABLE VISCOSITY, VISCOUS DISSIPATION AND THERMAL RADIATION ON UNSTEADY NATURAL CONVECTION COUETTE FLOW THROUGH A VERTICAL POROUS CHANNEL. (2020). FUDMA JOURNAL OF SCIENCES, 4(2), 135-150. https://doi.org/10.33003/fjs-2020-0402-208

Issue

Vol. 4 No. 2 (2020): FUDMA Journal of Sciences - Vol. 4 No. 2

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

COMBINED EFFECTS OF VARIABLE VISCOSITY, VISCOUS DISSIPATION AND THERMAL RADIATION ON UNSTEADY NATURAL CONVECTION COUETTE FLOW THROUGH A VERTICAL POROUS CHANNEL. (2020). FUDMA JOURNAL OF SCIENCES, 4(2), 135-150. https://doi.org/10.33003/fjs-2020-0402-208

Most read articles by the same author(s)