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Received: 23 June 2018 Accepted: 4 September 2018 The transient flow formation due to sudden application of constant circumferential pressure gradient in an annulus partially filled with porous material has been considered. An exact solution of the governing equations has been obtained in Laplace domain using Laplace transform technique. Using suitable transformations, the equations are converted into standard Bessel equations whose solutions are available in the literature. The solutions to the Bessel equations are then inverted to the time domain using Riemann-sum approximation approach. The implicit finite difference scheme has also been employed in solving the governing equations in other to establish the accuracy of the Riemann-sum approximation approach for both transient and steady state solutions. The obtained solutions are then analysed for various dimensionless parameters entering the unified problem. There is a clear indication that large value of Da enhances the permeability of the porous region. Also, thin clear fluid region boosts τ1 but has no significant influence on τλ. While thin porous region enhances skin friction at both surfaces.

Transient pressure driven flow in an annulus partially filled with porous material: Azimuthal pressure gradient