Group Similarity Transformation of a Time Dependent Chemical Convective Process

Authors: M. M. Kassem, A. S. Rashed

Abstract:

The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.

Keywords: Time dependent, chemical convection, grouptransformation method, perturbation method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328052

References:

[1] M. B. Abd-el-Malek, M.M. Kassem and M. L. Mekky. "Similarity solutions for unsteady free-convection from a continuous moving vertical surface." J. Comp. Applied Mathematics, 165, pp. 11-24, Jan. 2004.
[2] F. W. Ames, Nonlinear partial differential equations in Engineering, Acad. Press 1972, pp.89-96.
[3] T. S. Chen and F.A. Strobel. "Buoyancy effects in boundary layer adjacent to a continuous moving horizontal flat plate." J. Heat Transfer, vol.102, pp. 170-172, April 1980.
[4] P. Ganesan and H.P. Rani. On diffusion of chemically reactive species in convective flow along a vertical cylinder. Chemical Engineering and Processing vol .39, pp. 93-105, Jan. 2000.
[5] B. Gebhart and L. Pera."The nature of vertical natural convection flow resulting from the combined buoyancy effects of thermal and mass diffusion." J. Heat Mass Transfer, vol.14, pp. 25-50. Jan. 1972.
[6] F. S. Ibrahim, A.M. Elaiw and A.A. Bakr. "Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction." Comm. In Nonlinear Sc. Num. Simulation vol.13, pp. 1056-1066, Nov. 2008.
[7] M. Kassem, "Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux." J. Comp. Applied Mathematics, vol .187, pp. 72-86, Jan. 2006.
[8] M. Kassem, "Group Analysis of a non-Newtonian flow past a vertical plate subjected to a heat constant flux." Int. J. of Applied Mechanics and Engineering, on line April 2008.
[9] V. G. Levich, Physico-Chemical Hydrodynamics, Prentice-Hall, Englewood, 1962. chap. 3.
[10] O. D. Makinde. "Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate", Int. Comm. Heat Mass transfer, vol . 32- 10, pp. 1411-1419, July 2005.
[11] A.J.A. Morgan. The reduction by one of the number of independent variables in some systems of partial differential equations, Quart. J. Math. vol. 3, pp. 250-259. Oct. 1952.
[12] A.S Rashed and M. M. Kassem. "Group analysis for natural convection from a vertical plate", J. Comp. Applied Mathematics, online 19 November 2007.