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In this paper, we study the steady mixed convection boundary layer flow over a horizontal circular cylinder in a viscous fluid with the bottom surface of the cylinder heated by convection from a hot fluid. The resulting system of nonlinear partial differential equations is solved numerically using an efficient implicit finite-difference scheme known as the Keller box method along with Newton's linearization techniques. The special case at the lower stagnation point of the cylinder is considered. The solutions for the flow and heat transfer characteristics are obtained and presented for various values of the governing parameters, namely, the mixed convection parameter, the Prandtl number, and the conjugate parameter. The effects of these parameters on the flow and heat transfer characteristic are thoroughly examined in this study. [ABSTRACT FROM AUTHOR]