In this thesis, chemically reacting flows are studied mainly for detonation problems under 1D, cylindrical and spherical symmetry conditions. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equations and finite-rate chemistry is described. The Euler equations with finite-rate chemistry are discretized by Finite-Volume method and solved implicitly by using a time-spliting method. Inviscid fluxes are computed using Roe Flux Difference Splitting Model. The numerical solution is implemented in parallel using domain decomposition and PVM library routines for inter-process communication. The solution algorithm is validated first against the numerical and experimental data for a shock tube problem with and without chemical reactions and for a cylindrical and spherical propagation of a shock wave. 1D, cylindrically and spherically symmetric detonations of H2:O2:Ar mixture are studied next.

MSc (Mathematics) / Department of Mathematics and Applied Mathematics / The unsteady hydromagnetic chemically reacting mixed convection MHD ow over a permeable stretching sheet embedded in a porous medium with thermal radiation and heat source/sink is investigated numerically. The original partial di erential equations are converted into ordinary di erential equations by using similarity transformation. The governing non-linear partial di erential equations of Momentum, Energy, and Concentration are considered in this study. The e ects of various physical parameters on the velocity, temperature, and species concentration have been discussed. The parameters include the Prandtl number (Pr), Magnetic parameter (M), the Schmidt number (Sc), Unsteady parameter (A), buoyancy forces ratio parameter (N), Chemical reaction (K), Radiation parameter (Nr), Eckert number (Ec), local heat source/sink parameter (Q) and buoyancy parameter due to temperature ( ). The coe cient of Skin friction and Heat transfer are investigated. The coupled non-linear partial di erential equations governing the ow eld have been solved numerically using the Spectral Relaxation Method (SRM). The results that are obtained in this study are then presented in tabular forms and on graphs and the observations are discussed. / NRF