The unsteady problem of impulsive stagnation-point ow on a vertical circular cylinder along with mixed convection heat transfer was solved numerically for the rst time. The mentioned problem suered from shortcomings of similarity solution techniques when encountering various physical conditions such as time-dependent states. Initially, the uid was considered to be at rest, with a uniform temperature T1. At t = 0, this uid starts owing toward a vertical cylinder at the strength rate of k, and the cylinder surface's temperature rises to Tw, simultaneously. The Navier-Stokes and energy equations in a cylindrical coordinate system were discretized and solved in a 2D domain using a SIMPLE-based algorithm. The solution was obtained in three cases: rstly, when cylinder's wall temperature, Tw, is constant; secondly, when Tw varies linearly along cylinder's axis; thirdly, when it has parabolic variations. Considering a sample case of incompressible ow with Re = 1 and Pr = 0:7, the results of Nusselt number, wall shear-stress, and dimensionless velocity and temperature were obtained under dierent states of cylinder's wall temperatures for some selected values of Grashof numbers. An entropy generation analysis for the case of constant wall temperature is performed, which is the rst of its kind as conducted in this paper. © 2018 Sharif University of Technology. All rights reserved. 1. Introduction The problem of stagnation-point ow and heat transfer on a plate or cylinder has always been a highly intriguing issue to study due to its various industrial applications. For example, in metal, plastic, or food products manufacturing by extrusion process, the output product is usually cooled by blowing a peripheral uid ow. Since the cooling process aects the resis- *. Corresponding author. Tel.: 098 5138805018 E-mail address: rahimiab@um.ac.ir (A.B. Rahimi) doi: 10.24200/sci.2017.4347 tance and

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