Numerical Investigation of Unsteady Free Convection on a Vertical Cylinder with Variable Heat and Mass Flux in the Presence of Chemically Reactive Species

Affiliation(s)

Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.

Department of Mathematics, Faculty of Woman, Ain Shams University, Cairo, Egypt.

Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.

Department of Mathematics, Faculty of Woman, Ain Shams University, Cairo, Egypt.

ABSTRACT

A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for the situation in which the surface temperature and are subjected to the power-law surface heat and mass flux as and . The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.

Cite this paper

A. Kawala and S. Odda, "Numerical Investigation of Unsteady Free Convection on a Vertical Cylinder with Variable Heat and Mass Flux in the Presence of Chemically Reactive Species,"*Advances in Pure Mathematics*, Vol. 3 No. 1, 2013, pp. 183-189. doi: 10.4236/apm.2013.31A026.

A. Kawala and S. Odda, "Numerical Investigation of Unsteady Free Convection on a Vertical Cylinder with Variable Heat and Mass Flux in the Presence of Chemically Reactive Species,"

References

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[2] A. Bejan, “Convection Heat Transfer,” 2nd Edition, Wiley, New York, 1993.

[3] K. Vafai and C. L. Tien, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” International Journal of Heat and Mass Transfer, Vol. 24, No. 2, 1981, pp. 195-203. doi:10.1016/0017-9310(81)90027-2

[4] S. W. Churchill and H. H. S. Chu, “Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate,” International Journal of Heat and Mass Transfer, Vol. 18, No. 11, 1975, pp. 1323-1329. doi:10.1016/0017-9310(75)90243-4

[5] L. B. Evans, T. C. Reid and E. M. Drake, “Transient Natural Convection in Vertical Cylinder,” AIChE Journal, Vol. 14, No. 2, 1968, pp. 251-256. doi:10.1002/aic.690140210

[6] K. Velusamy and V. K. Garg, “Transient Natural Convection over a Heat Generating Vertical Cylinder,” International Journal of Heat and Mass Transfer, Vol. 35, No. 5, 1992, pp. 1293-1306. doi:10.1016/0017-9310(92)90185-U

[7] U. N. Das, R. Deka and V. M. Soundalgekar, “Effects of Mass Transfer on Flow Past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction,” Forschung im Ingenieurwesen, Vol. 60, No. 10, 1994, pp. 284-287. doi:10.1007/BF02601318

[8] G. Rama Murty and B. Shanker, “Skin Friction and Heat Transfer Analysis of MHD Flow for a Small Prandtl Number Fluid past Semi Infinite Plate,” Journal of I. E(I), Vol. 76, 1995, pp. 90-93.

[9] N. G. Kafuossias and N. D. Nanousis, “Magnetohydrodynamic Laminar Boundary Layer Flow over a Wedge with Suction or Injection,” Canadian Journal of Physics, Vol. 75, No. 10, 1997, pp. 733-745. doi:10.1139/p97-024

[10] A. Y. Ghaly and M. A. Seddeek, “Chebyshev Finite Difference Method for the Effects of Chemical Reaction, Heat and Mass Transfer on Laminar Flow along a Semi Infinite Horizontal Plate with Temperature Dependent Viscosity,” Chaos, Solitons and Fractals, Vol. 19, No. 1, 2004, pp. 61-70. doi:10.1016/S0960-0779(03)00069-9

[11] M. A. Seddeek, A. A. Darwish and M. S. Abdelmeguid, “Effects of Chemical Reaction and Variable Viscosity on Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow through Porous Media with Radiation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 2, 2007, pp. 195-213. doi:10.1016/j.cnsns.2006.02.008

[12] B. Carnahan, H. A. Luther and J. O. Wilkes, “Applied Numerical Methods,” John Wiley & Sons, New York, 1969.

[1] D. A. Nield and A. Bejan, “Convection in Porous Media,” 2nd Edition, Springer, New York, 1998.

[2] A. Bejan, “Convection Heat Transfer,” 2nd Edition, Wiley, New York, 1993.

[3] K. Vafai and C. L. Tien, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” International Journal of Heat and Mass Transfer, Vol. 24, No. 2, 1981, pp. 195-203. doi:10.1016/0017-9310(81)90027-2

[4] S. W. Churchill and H. H. S. Chu, “Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate,” International Journal of Heat and Mass Transfer, Vol. 18, No. 11, 1975, pp. 1323-1329. doi:10.1016/0017-9310(75)90243-4

[5] L. B. Evans, T. C. Reid and E. M. Drake, “Transient Natural Convection in Vertical Cylinder,” AIChE Journal, Vol. 14, No. 2, 1968, pp. 251-256. doi:10.1002/aic.690140210

[6] K. Velusamy and V. K. Garg, “Transient Natural Convection over a Heat Generating Vertical Cylinder,” International Journal of Heat and Mass Transfer, Vol. 35, No. 5, 1992, pp. 1293-1306. doi:10.1016/0017-9310(92)90185-U

[7] U. N. Das, R. Deka and V. M. Soundalgekar, “Effects of Mass Transfer on Flow Past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction,” Forschung im Ingenieurwesen, Vol. 60, No. 10, 1994, pp. 284-287. doi:10.1007/BF02601318

[8] G. Rama Murty and B. Shanker, “Skin Friction and Heat Transfer Analysis of MHD Flow for a Small Prandtl Number Fluid past Semi Infinite Plate,” Journal of I. E(I), Vol. 76, 1995, pp. 90-93.

[9] N. G. Kafuossias and N. D. Nanousis, “Magnetohydrodynamic Laminar Boundary Layer Flow over a Wedge with Suction or Injection,” Canadian Journal of Physics, Vol. 75, No. 10, 1997, pp. 733-745. doi:10.1139/p97-024

[10] A. Y. Ghaly and M. A. Seddeek, “Chebyshev Finite Difference Method for the Effects of Chemical Reaction, Heat and Mass Transfer on Laminar Flow along a Semi Infinite Horizontal Plate with Temperature Dependent Viscosity,” Chaos, Solitons and Fractals, Vol. 19, No. 1, 2004, pp. 61-70. doi:10.1016/S0960-0779(03)00069-9

[11] M. A. Seddeek, A. A. Darwish and M. S. Abdelmeguid, “Effects of Chemical Reaction and Variable Viscosity on Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow through Porous Media with Radiation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 2, 2007, pp. 195-213. doi:10.1016/j.cnsns.2006.02.008

[12] B. Carnahan, H. A. Luther and J. O. Wilkes, “Applied Numerical Methods,” John Wiley & Sons, New York, 1969.