Unsteady Darcy-Brinkman Axial Flow in a Porous Concentric Annulus: A Semi-Analytical Riemann-Sum Approach
DOI:
https://doi.org/10.33003/fjs-2026-1010-5506Keywords:
transient axial flow, porous annulus, Darcy-Brinkman model, Laplace transform, Riemann-sum inversion, Skin FrictionAbstract
An unsteady pressure-driven axial flow in a saturated porous concentric annulus is investigated through a semi-analytical Laplace-transform and Riemann-sum framework. The incompressible Newtonian flow is formulated with Brinkman-Darcy resistance, no-slip walls, and a suddenly imposed constant axial pressure gradient. The initial-boundary-value problem reduces, after non-dimensionalization and Laplace transformation, to a modified Bessel equation; closed-form expressions are obtained for the transformed transient velocity, the steady velocity, and the inner- and outer-wall skin frictions. The transient fields are recovered by a rapidly convergent Riemann-sum inversion and are validated against the steady-state solution. The results show that the Darcy number strongly amplifies axial motion and wall shear by weakening porous drag, whereas the radius ratio controls the distribution and sign of the shear response. The velocity grows monotonically from rest toward a single-hump annular profile, while the wall shear is positive at the inner cylinder and negative at the outer cylinder under the adopted radial-derivative convention. Excellent agreement between the Riemann-sum solution and the steady limit confirms the accuracy of the semi-analytical formulation. The model provides a compact benchmark for transient porous annular transport and wall-shear prediction in coaxial engineering systems.
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