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The system of non-linear algebraic equations arising from the application of the central difference approximation to the fully developed Brinkman-Forchheimer flow equation is solved using the computer assisted continuation method based on the classical, explicit RungeKutta method of four slopes. The continuation method is found to be very effective in capturing boundary and inertia effects in the considered flow through porous media. Further, it succeeds in giving the required solution for large values of Forchheimer number when shooting method fails to do so. Heat transport in forced convective flow through the annulus is quantified in terms of the Nusselt number. It is found that the effect of increasing the radius of the inner cylinder is to increase the Nusselt number. The results of fully-developed, non-linear flow and heat transfer through a rectangular channel and a cylindrical porous tube are obtained as limiting cases of the present study.

Numerical Study of the Effect of Concentric, Thermally-insulated Insert on Brinkman-Forchheimer Flow and Heat Transfer through a Cylindrical Tube