GEM - International Journal on Geomathematics (2020) 11:28 https://doi.org/10.1007/s13137-020-00164-w ORIGINAL PAPER Combined effects of suction/injection and exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow: a semi-analytical approach Basant K. Jha 1 · Dauda Gambo 1 Received: 21 January 2020 / Accepted: 22 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract A two-dimensional mathematical model is developed and solved semi-analytically in order to theoretically examine the impact of suction/injection and an exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow through a coaxial cylinder. The walls of the cylinders are porous so as to enable the superim- position of the radial flow. The solution of the governing momentum and continuity equations are derived using a two-step process, the Laplace transformation in conjunc- tion with the Riemann Sum-Approximation (RSA). For accuracy check, the steady state solution is computed and numerical values obtained using the Riemann-Sum Approximation (RSA) is compared with the already established results. It is found out that for an increasing time, a growing pressure gradient enhances the flow for- mation for both suction and injection, although the effect on the azimuthal velocity profile is subtle when suction is applied on porous walls. Moreover, the skin frictions on the walls can be minimized by imposing a decaying pressure gradient for suc- tion/injection, however the behaviour is seen clearly when fluid particles are injected through the porous cavity. Keywords Suction/injection · Dean flow · Unsteady · Riemann-sum approximation (RSA) · Time-dependent pressure gradient Mathematics Subject Classification 76D05 · 76A02 · 76S05 B Dauda Gambo daudagambo85@gmail.com Basant K. Jha basant777@yahoo.co.uk 1 Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria 0123456789().: V,-vol 123