Computational dynamics of unsteady flow of a variable viscosity reactive fluid in a porous pipe

The coupled nonlinear equations in cylindrical Cartesian coordinates governing pressure-driven unsteady flow of a reactive variable viscosity fluid and heat transfer in a circular pipe whose walls are porous, are derived and solved numerically using a semi-implicit finite difference scheme under axisymmetric conditions. The boundary conditions along the centerline of the pipe are rebuilt via an assumption on the continuity of derivatives at each stage of the computation and results are validated against the results obtained using well documented boundary conditions for flow with no suction/injection. The chemical kinetics is assumed to follow Arrhenius rate law while the fluid viscosity is an exponentially decreasing function of temperature. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.