Abstract Laminar stagnation flow, axi-symmetrically yet obliquely impinging on a rotating circular cylinder, as well as its heat transfer is formulated as an exact solution of the Navier-Stokes equations. Rotational velocity of the cylinder is time - dependent while the surface transpiration is uniform and steady. The impinging stream is composed of a rotational axial flow superposed onto irrotational radial stagnation flow normal to the cylinder with strength Γ. The relative importance of these two flows is measured by a parameter γ. The governing parameters are the stagnation - flow Reynolds number Re = Γa2 /2υ and the dimensionless transpiration S = U0 / Γa, where a is cylinder radius, ν is kinematic viscosity of the fluid and U0 is the transpiration rate. An exact solution is obtained by reducing the Navier-Stokes equations to a system of differential equations governed by Reynolds number and the dimensionless wall transpiration rate. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number and Prandtl number.

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