Modeling of heat and high viscous fluid distributions with variable viscosity in a permeable channel

J Hona

Abstract


The flow field under study is characterized by velocity components, temperature and pressure in non-dimensional formulation. The flow is driven by suction through the horizontal channel with permeable walls fixed at different temperatures. In order to ascertain a better understanding of the dynamic behavior of the flow, the Navier-Stokes equations and the energy equation are solved concurrently applying a similarity transformation technique. The hydrodynamic structures obtained from the numerical integration include flow reversal or backward flow, collision zones due to the coexistence of wall suction and flow reversal inside the channel, the inflection through temperature distribution, the growth of thermal gradients near the walls, and the sensitivity of normal pressure gradients to the difference of temperatures at boundaries. These hydrodynamic structures are investigated considering the influences of the Péclet number P and the sensitivity of viscosity to thermal variations α which are the main control parameters of the problem.

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References


Taylor, C. L., Banks, W. H. H., Zaturska, M. B. and Drazin, P. G., Three-dimensional Flow in a Porous Channel, Quarterly Journal of Mechanics and Applied Mathematics, 1991, 44(1), 105–133. CrossRef

Zaturska, M. B. and Banks, W. H. H., Suction-driven Flow in a Finite Wedge, Acta Mechanica, 1991, 86, 95–101. CrossRef

Berman, A. S., Laminar Flow in Channels with Porous Walls, Journal of Applied Physics, 1953, 24(9), 1232–1235. CrossRef

Sellars, J. R., Laminar Flow in Channels with Porous Walls at High Suction Reynolds Number, Journal of Applied Physics, 1955, 26(4), 489–490.

Proudman, I. and Johnson, K., Boundary-layer Growth at a Rear Stagnation Point, Journal of Fluid Mechanics, 1962, 12(2), 161–168. CrossRef

Terrill, R. M., Laminar Flow in Uniformly Porous Channel, Aeronautical Quarterly, 1964, 15(3), 299–310.

Terrill, R. M. and Shrestha, G. M., Laminar Flow through Parallel and Uniformly Porous Walls of Different Permeability, Journal of Applied Mathematics and Physics, 1965, 16(4), 470–482.

Durlofsky, L. and Brady, J. F., The Spatial Stability of a Class of Similarity Solutions, Physics of Fluids, 1984, 27(5), 1068–1076. CrossRef

MacGillivray, A. D. and Lu, C., Asymptotic Solution of a Laminar Flow in a Porous Channel with Large Suction: A Nonlinear Turning Point Problem, Methods and Applications of Analysis, 1994, 1(2), 229–248.

Zhou, C. and Majdalani, J., Improved Mean-flow Solution for Slab Rocket Motors with Regressing Walls, Journal of Propulsion and Power, 2002, 18(3), 703–711. CrossRef

Robinson, W. A., The Existence of Multiple Solutions for the Laminar Flow in a Uniformly Porous Channel with Suction at Both Walls, Journal of Engineering Mathematics, 1976, 10(1), 23–40. CrossRef

Ferro, S. and Gnavi, G., Spatial Stability of Similarity Solutions for Viscous Flows in Channels with Porous Walls, Physics of Fluids, 2000, 12(4), 797–802. CrossRef

Li, B., Zheng, L., Zhang, X. and Ma, L., The Multiple Solutions of Laminar Flow in a Uniformly Porous Channel with Suction/Injection, Advanced Studies in Theoretical Physics, 2008, 2(10), 473–478.

Majdalani, J. and Zhou, C., Moderate-to-large Injection and Suction Driven Channel Flows with Expanding and Contracting Walls, ZAMM, 2003, 83(3), 181–196. CrossRef

Zaturska, M. B., Drazin, P. G. and Banks, W. H. H., On the Flow of a Viscous Fluid Driven along a Channel by Suction at Porous Walls, Fluid Dynamics Research, 1988, 4(3), 151–178. CrossRef

Gol’dshtik, M. A. and Ersh, N. M., Stability of Pipe Flow with Blowing, Fluid Dynamics, 1989, 24(1), 51–59. CrossRef

Terrill, R. M. and Thomas, P. W., On Laminar Flow through a Uniformly Porous Pipe, Applied Scientific Research, 1969, 21(1), 37–67. CrossRef

Brady, J. F., Flow Development in a Porous Channel or Tube, Physics of Fluids, 1984, 27(5), 1061–1067. CrossRef

Banks, W. H. H. and Zaturska, M. B., On Flow through a Porous Annular Pipe, Physics of Fluids A, 1992, 4(6), 1131–1141. CrossRef

Majdalani, J. and Flandro, G. A., The Oscillatory Pipe Flow with Arbitrary Wall Injection, Proceedings of the Royal Society of London A, 2002, 458, 1621–1651. CrossRef

Hona, J., Ngo Nyobe, E. and Pemha, E., Dynamic Behavior of a Steady Flow in an Annular Tube with Porous Walls at Different Temperatures, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2009, 19(9), 2939–2951.

Hona, J., Pemha, E. and Ngo Nyobe, E., Viscous Flow and Heat Transfer through Two Coaxial Porous Cylinders, International Journal of Multiphysics, 2015, 9(1), 45–60. Link

Ockendon, H. and Ockendon, J. R., Variable-viscosity Flows in Heated and Cooled Channels, Journal of Fluid Mechanics, 1977, 83, 177–190. CrossRef

Schäfer, P. and Herwig, H., Stability of Plane Poiseuille Flow with Temperature Dependent Viscosity, International Journal of Heat and Mass Transfer, 1993, 36(9), 2441–2448. CrossRef

Lin, C.-R. and Chen, C.-K., Effect of Temperature Dependent Viscosity on the Flow and Heat Transfer over an Accelerating Surface, Journal of Physics D, 1994, 27(1), 29–36. CrossRef

Wylie, J. J. and Lister, J. R., The Effects of Temperature Dependent Viscosity on Flow in a Cooled Channel with Application to Basaltic Fissure Eruptions, Journal of Fluid Mechanics, 1995, 305, 239–261. CrossRef

Pemha, E., Hona, J. and Ngo Nyobe, E., Numerical Control of a Two-dimensional Channel Flow with Porous Expanding Walls at Different Temperatures, International Journal of Flow Control, 2014, 6(4), 119–134. Link

Brown, H. R., Rayleigh-Taylor Instability in a Finite Thickness Layer of a Viscous Fluid, Physics of Fluids A, 1989, 1(5), 895–896. CrossRef

Davis, A. M. J. and Frenkel, A. L., Cylindrical Liquid Bridges Squeezed between Parallel Plates: Exact Stokes Flow Solutions and Hydrodynamic Forces, Physics of Fluids A, 1992, 4(6), 1105–1109. CrossRef

Brady, J. F. and Acrivos, A., Steady Flow in a Channel or Tube with an Accelerating Surface Velocity. An Exact Solution to the Navier-Stokes Equations with Reverse Flow, Journal of Fluid Mechanics, 1981, 112, 127–150. CrossRef

Stewartson, K., The Theory of Boundary Layers in Compressible Fluids, Oxford University Press, Oxford, 1964.




DOI: http://dx.doi.org/10.1260/1750-9548.9.4.341

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