Group Similarity Transformation of a Time Dependent Chemical Convective Process

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, group transformation method, perturbation method. Nomenclature Latin characters a1, a2= unity elements c = species concentration C = non-dimensional species concentration c0 = concentration next to the plate c∞ = ambiant concentration D = chemical molecular diffusivity. F’ = horizontal velocity after transformation g = gravitational acceleration G = group k = chemical rate constant n = chemical reaction order Q, T = real valued coefficients S = subgroup Sc = Schmidt number ν/ D u = velocity in x direction v = velocity in y direction Greek characters β= volumetric coefficient of expansion with concentration ν = μ/ρ = kinematic viscosity of fluid ρ = fluid density ψ = stream function η =similarity variable ---------------------------------------------Magda Kassem, Prof. of Mathematics, is with Mathematics and Physics Department, Faculty of Engineering, Zagazig University, Egypt. Ahmed Rashed is with Mathematics and Physics Department, Faculty of Engineering, Zagazig University, Egypt.