On Steady Flow of a Reactive Viscous Fluid in a Porous Cylindrical Pipe
Abstract:
Studies of mass transfer in a porous medium are of interest to researchers as a result of its various uses in different fields of engineering practices. This work examined the steady flow of a reactive variable viscous fluid in a porous cylindrical pipe. Dimensionless variables were used to dimensionalize the governing equations. A regular perturbation technique was employed to obtain an approximate solution of the resulting dimensionless non-linear equations. Numerical simulation was done to get the threshold values for the flow parameters under consideration. The effects of viscous heating and permeability parameters on the steady flow were studied and reported.
Cite this paper: Farayola, P. (2017) On Steady Flow of a Reactive Viscous Fluid in a Porous Cylindrical Pipe. Open Journal of Fluid Dynamics, 7, 359-370. doi: 10.4236/ojfd.2017.73024.
References

[1]   Bird, R.B., Stewart, W.E and Lightfoot, E.N. (2002) Transport Phenomena. John Wiley & Sons, New York.

[2]   Bebernes, J. and Eberly, D. (1989) Mathematical Problems from Combustion Theory. Springer-Verlag, New York, 6-8.
https://doi.org/10.1007/978-1-4612-4546-9

[3]   Bowes, P.C. (1984) Self-heating: Evaluating and Controlling the Hazard. Elsevier Sciences, Amsterdam.

[4]   Balakrishman, E., Swift, A. and Wake, G.C. (1996) Critical Values for Some Non-Class Geometries in Thermal Ignition Theory. Mathematical and Computer Modelling, 24, 1-10.

[5]   Makinde, O.D. (2004) Exothermic Explosions in a Slab: A Case Study of Series Summation Technique. International Communications in Heat and Mass Transfer, 31, 1227-1231.

[6]   Makinde, O.D. (2005) Strong Exothermic Explosions in a Cylindrical Pipe: A Case Study of Series Summation Technique. Mechanics Research Communications, 32, 191-195.

[7]   Adegbie, K.S. and Alao, F.T. (2007) Flow of Temperature-Dependent Viscous Fluid between Parallel Heated Walls: Exact Analytical Solutions in the Presence of Viscous Dissipation. Journal of Mathematics and Statistics, 3, 12-14.
https://doi.org/10.3844/jmssp.2007.12.14

[8]   Makinde, O.D. (2009) Thermal Criticality for a Reactive Gravity Driven Thin Film Flow of a Third-Grade Fluid with Adiabatic Free Surface down an Inclined Plane. Applied Mathematics and Mechanics, 30, 373-380.
https://doi.org/10.1007/s10483-009-0311-6

[9]   Basak, T., Kaluri, R.S. and Balakrishnan, A.R. (2012) Entropy Generation during Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions. Numerical Heat Transfer, Part A, 62, 336-364.
https://doi.org/10.1080/10407782.2012.691059

[10]   Ajadi, S.O. (2010) Analytical Solutions of Unsteady Oscillatory Particulate Visco-Elastic Fluid between Two Parallel Walls. International Journal of Nonlinear Science, 9, 131-138.

[11]   Attia, H.A. (2005) The Effect of Suction and Injection on the Steady Flow between Two Parallel Plates with Variable Properties. Tamkang Journal of Science and Engineering, 8, 17-22.

[12]   Loganathan, P. and Sivapoornapriya, C. (2014) Viscous Dissipation Effects on Unsteady Natural Convective Flow Past an Infinite Vertical Plate with Uniform Heat and Mass Flux. Wseas Transactions on Heat and Mass Transfer. 9, 63-73.

[13]   Makinde, O.D. (2007) On Steady Fow of a Reactive Variable Viscosity Fluid in a Cylindrical Pipe with an Isothermal Wall. International Journal of Numerical Methods for Heat and Fluid Flow, 17, 187-194.
https://doi.org/10.1108/09615530710723957

[14]   Pal, D. and Mondal, H. (2014) Effects of Temperature Dependent Viscosity and Variable Thermal Conductivity on MHD Non-Darcy Mixed Convective Diffusion of Species over a Stretching Sheet. Journal of the Egyptian Mathematical Society, 22, 123-133.

[15]   Attia, H.A. (2009) Effect of Porosity on Unsteady Poiseuille Flow of a Viscoelastic Fluid with Temperature Dependent Viscosity. Tamkang Journal of Science and Engineering, 12, 215-221.

[16]   Brinkman, H.C. (1947) On the Permeability of Media Consisting of Closely Packed Porous Particles. Applied Scientific Research, A1, 81-86.

[17]   Chand, G. and Jat, R.N. (2014) Viscous Dissipation and Radiation Effects on MHD Flow and Heat Transfer over an Unsteady Stretching Surface in a Porous Medium. Thermal Energy and Power Engineering, 3, 266-272.

[18]   Mohamed, R.A. (2009) Double-Diffusive Convection-Radiation Interaction on Unsteady MHD Flow over a Vertical Moving Porous Plate with Heat Generation and Soret Effect. Applied Mathematical Sciences, 3, 629-651.

[19]   Uddin, M.S. (2013) Chemically Reactive Solute Transfer over a Plate in Porous Medium in Presence of Suction. Journal of Physical Sciences, 17, 97-109.

[20]   Makinde, O.D. and Eegunjobi, A.S. (2013) Effects of Convective Heating on Entropy Generation Rate in a Channel with Permeable Walls. Entropy, 15, 220-233.
https://doi.org/10.3390/e15010220

[21]   Gbadeyan, J.A. and Hassan, A.R. (2012) Multiplicity of Solutions for a Reactive Variable Viscous Couette Flow under Arrhenius Kinetics. Mathematical Theory and Modeling, 2, 39-49.

[22]   Olayiwola, R.O. (2012) Fixed-Bed Solid Fuel Arrhernius Combustion: Modelling and Simulation. Journal of the Nigerian Association of Mathematical Physics, 21, 111-120.

[23]   Celestina, A.O. and Ayeni, R.O. (2010) On the Theory of Filtration at a Decreasing Rate. Journal of the Nigerian Association of Mathematical Physics, 16, 305-316.

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