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This article presents a numerical method of solution to laminar axisymmetric hydro magnetic flow of incompressible, electrically conducting and viscous fluid moving over the circular cylinder embedded in a thermally stratified medium. Fluid over the cylinder moves due to the stretching of cylindrical surface. Different physical conditions at the boundary are also considered. With the help of suitable similarity transformation the boundary layer equations are transformed into ordinary differential equations. The resulting nonlinear ordinary differential equations were solved by Runge-Kutta technique with shooting method. Obtained numerical results for different pertinent parameters are graphically shown for velocity distribution and temperature distribution. Due to the industrial applications point of view, it is evaluated that local Nusselt number at the surfaces increases due to the influence of thermal stratification. The skin-friction and heat transfer coefficients have presented in the form of table. Comparison of heat transfer coefficient is also illustrated. (C) 2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license.