Original article Transient Dean flow in a channel with suction/injection: A semi-analytical approach Basant K Jha and Yahaya J Danjuma Abstract The mathematical model responsible for fully developed laminar transient flow formation between the gaps of two stationary concentric porous tubes due to the imposition of azimuthal pressure gradient (Dean flow) is solved semi- analytically. The tubes walls are porous so that a radial flow can be superimposed. The solution of the momentum and continuity equations are obtained semi-analytically by using the combination of Laplace transform technique and a Laplace inversion method called Riemann sum approximation method. The solutions for skin friction at R ¼ 1 (outer surface of the inner porous tube) and R ¼  (inner surface of the outer porous tube) are presented. The impact of suction/injection parameter and the ratio of the radii of the tubes are examined for the velocity profile and skin friction. Results show that the velocity profile decreases with increase in suction/injection parameter for various values of time, ðT Þ and at large value of time, (T), the velocity and the skin friction attain a steady state. Keywords Transient, Dean flow, suction/injection, annulus, Riemann sum approximation Date received: 26 February 2018; accepted: 2 January 2019 Introduction Unsteady flow in curved pipes 1,2 is important in rela- tion to blood flow in human arterial systems, heat and mass transfer in engineering systems as well as Dean flow because of its many applications in electrical, mechanical, and nuclear engineering including bio- medical engineering, where the fluid flows appears in most of the apparatuses (cardiopulmonary bypass pumps, extracorporeal circulation or heart–lung machine) transporting fluids. Understanding the flow behavior in a horizontal/vertically oriented annu- lar gap with both walls stationary, rotating or one of the walls rotating is an important problem within the broader scope of fluid flows within annular regions. This fluid–solid hydrodynamic contacting pattern, which is often referred to as an annular flow, occurs in many practical technology-driven application as mentioned above. In relation to the foregoing, Dean 3 is believed to be the first to study the motion of fluid in a curved channel due to a pressure gradient acting round the channel and the problem is termed ‘Dean flow’. This is defined as the motion of fluid due to a pressure gradient acting round the channel. Recently, a series of studies have been conducted in the field on Dean Flow. In order to cite a few works in this path, we shall carefully study the works of Richardson and Tyler, 4 Sexl, 5 Tsangaris, 6 Uchida, 7 and Womersley 8 analytically studied the viscous flow of an incompressible fluid due to an oscillating pressure gradient along a straight circular annular pipe with rigid walls in which the maximum velocity reduces rapidly by increasing the ratio of the smaller radius to the greater radius. Some researches were also carried out on the effect of Womersley number, ratio of the radii of the cylinders, transverse Reynolds number of fully developed incompressible fluid flow in a straight duct with constant cross section, and solid impermeable walls where oscillating pressure gradient is imposed for the following cases: a circular, 4,5,7,8 rectangular, 9–12 and elliptical. 13–15 Again, Tsangaris and Vlachakis 16 in their article also considered the effect of oscillating pressure gradients of viscous, incompressible fluid flow in a porous channel and found out that the effect of Womersley number, ratio of the radii of the annulus Proc IMechE Part E: J Process Mechanical Engineering 0(0) 1–9 ! IMechE 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0954408919825718 journals.sagepub.com/home/pie Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria Corresponding author: Yahaya J. Danjuma, Faculty of Science, Ahmadu Bello University, Zaria 810222, Nigeria. Email:yjdanjuma@gmail.com