Unsteady flows in a semi-infinite expanding pipe with injection through wall

A theoretical analysis of the unsteady incompressible laminar flow in a semi-infinite porous circular pipe with injection or suction through the pipe wall whose radius varies with time is presented. The present analysis simulates the flow field by the burning of inner surface of cylindrical grain in a solid rocket motor, in which the burning surface regresses with time. An exact similar solution of fully non-linear form of the Navier-Stokes equation is calculated numerically. The flow field can be subjected to expanding coefficient of pipe wall α(=aa/ν) and injection parameter R=aV/ν. The properties of flow such as velocity components are represented as functions of expanding coefficient and injection parameter. Concludingly, the effect of burning surface regression on the flow field in combustion chamber of a solid rocket motor is so little that it may be negligible.