Viscous flow and heat transfer through two coaxial porous cylinders
DOI:
https://doi.org/10.1260/1750-9548.9.1.45Abstract
In this paper, a flow of a high viscous fluid with temperature-dependent viscosity through a porous industrial conduct is investigated by means of similarity transformation technique. The problem is modeled using mass, momentum and energy conservations. The variation of viscosity as function of temperature couples the vorticity equation to the energy equation. The numerical procedure for solving the differential equations of the problem is detailed. For low values of the main control parameters, the analytical solution of the problem is yielded. It appears from the numerical results of the problem that the variations of temperature are stopped in a large area around the middle of the flow domain. The maxima of thermal gradients are situated at the walls due to suction. The dominance of flow reversal agrees with the behavior of the normal pressure gradient inside the annular conduct.
References
Watanabe, T., Numerical Simulation of Oscillating Flow Field Including a Droplet, The International Journal of Multiphysics, 2013, 7(1), 19-30.
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. https://doi.org/10.1016/s0017-9310(05)80127-9
Raithby, G., Laminar Heat Transfer in the Thermal Entrance Region of Circular Tubes and Two-dimensional Rectangular Ducts with Wall Suction and Injection, International Journal of Heat and Mass Transfer, 1971, 14(2), 223-243. https://doi.org/10.1016/0017-9310(71)90091-3
Herwig, H. and Schäfer, P., Influence of Variable Properties on the Stability of Two-dimensional Boundary Layers, Journal of Fluid Mechanics, 1992, 243, 1-14. https://doi.org/10.1017/s002211209200260x
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.
Wylie, J. J. and Lister, J. R., The Effect of Temperature Dependent Viscosity on flow in a Cooled Channel with Application to Basaltic Fissure Eruptions, Journal of Fluid Mechanics, 1995, 305, 239-261. https://doi.org/10.1017/s0022112095004617
Ockendon, H. and Ockendon, J. R., Variable Viscosity Flows in Heated and Cooled Channels, Journal of Fluid Mechanics, 1977, 83, 177-190. https://doi.org/10.1017/s002211207700113x
Ferro, S. and Gnavi, G., Effect of Temperature-dependent Viscosity in Channels with Porous Walls, Physics of Fluids, 2002, 14(2), 839-849. https://doi.org/10.1063/1.1433969
Berman, A. S., Laminar Flow in Channels with Porous Walls, Journal of Applied Physics, 1953, 24(9), 1232-1235. https://doi.org/10.1063/1.1721476
Terrill, R. M., Laminar Flow in Uniformly Porous Channel, Aeronautical Quarterly, 1964, 15(3), 299-310. https://doi.org/10.1017/s0001925900010908
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. https://doi.org/10.1007/bf01593923
Dinarvand, S., Doosthoseini, A., Doosthoseini, E. and Rashidi, M. M., Comparison of HAM and HPM Methods for Berman's Model of Two-dimensional Viscous Flow in Porous Channel with Wall Suction or Injection, Advances in Theoretical and Applied Mechanics, 2008, 1(7), 337-347.
Sellars, J. R., Laminar Flow in Channels with Porous Walls at High Suction Reynolds Number, Journal of Applied Physics, 1955, 26(4), 489-490. https://doi.org/10.1063/1.1722024
Proudman, I., An Example of Steady Laminar Flow at Large Reynolds Number, Journal of Fluid Mechanics, 1960, 9, 593-602. https://doi.org/10.1017/s002211206000133x
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. https://doi.org/10.1007/bf01535424
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. https://doi.org/10.1016/0169-5983(88)90021-4
Cox, S. M., Two-dimensional Flow of a Viscous Fluid in a Channel with Porous Walls, Journal of Fluid Mechanics, 1991, 27, 1-33. https://doi.org/10.1017/s0022112091000010
Banks, W. H. H. and Zaturska, M. B., On Flow through a Porous Annular Pipe, Physics of Fluids A, 1992, 4(6), 1131-1141. https://doi.org/10.1063/1.858231
Majdalani, J. and Flandro, G. A., The Oscillatory Pipe Flow with Arbitrary Wall Injection, Proceedings of the Royal Society of London A, 2002, 458(2023), 1621-1651. https://doi.org/10.1098/rspa.2001.0930
Majdalani, J. and Zhou, C., Moderate-to-large Injection and Suction Driven Channel Flows with Expanding and Contracting Walls, 2003, 83(3), 181-196. https://doi.org/10.1002/zamm.200310018
Dauenhauer, C. E. and Majdalani, J., Exact Self-similarity Solution of the Navier-Stokes Equations for a Porous Channel with Orthogonally Moving Walls, Physics of Fluids, 2003, 15(6), 1485-1495. https://doi.org/10.1063/1.1567719
Li, B., Zheng, L., Zhang, X. and Ma, L., The Multiple Solutions of Laminar Flow in a Uniformly Porous Channel with Suction/Injection, Advance Studies in Theoretical Physics, 2008, 2(10), 473-478.
Lu, C., On the Asymptotic Solution of Laminar Channel Flow with Large Suction, SIAM Journal on Mathematical Analysis', 1997, 28(5), 1113-1134. https://doi.org/10.1137/s0036141096297704
Stewartson, K., The Theory of Boundary Layers in Compressible Fluids, Oxford University Press, Oxford, 1964.
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, 2009, 19(9), 2939-2951. https://doi.org/10.1142/s0218127409024566
Brown, H. R., Rayleigh-Taylor Instability in a Finite Thickness Layer of a Viscous Fluid, Physics of Fluids A, 1989, 1(5), 895-896. https://doi.org/10.1063/1.857389
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. https://doi.org/10.1063/1.858229
Brady, J. F., Flow Development in a Porous Channel or Tube, Physics of Fluids, 1984, 27(5), 1061-1067.
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. https://doi.org/10.1017/s0022112081000323
Published
How to Cite
Issue
Section
Copyright (c) 2015 J Hona, E Pemha, E Nyobe
This work is licensed under a Creative Commons Attribution 4.0 International License.