The laminar mixed (free and forced) convection heat transfer from an isothermal horizontal cylinder of elliptic cross-section immersed in a uniform stream of a Newtonian or a Bingham plastic fluid is numerically investigated in the aiding-buoyancy configuration. The fluid flow and heat transfer characteristics are investigated over the range of conditions as: Richardson number, 0.1 <= Ri <= 10, Reynolds number, 1,<= Re <= 40, Prandtl number, 0.7 <= Pr <= 100, Bingham number, 0 <= Bn <= 100, and the shape of the cylinder represented by its axis ratio (axis along the flow to axis normal to the flow), 0.1 <= E <= 10 for the constant wall temperature condition imposed on the surface of the elliptical cylinder. The combined influence of the buoyancy and shape of the cross-section of the cylinder is examined on the local and global flow and heat transfer characteristics such as distribution of the pressure coefficient and local Nusselt number along the surface of the horizontal cylinder as well as in terms of the force coefficients (individual and total drag) and the average Nusselt number. Depending upon the values of the influencing parameters, i.e., E, Ri, Pr, Re and Bn, a range of morphologies of the yield surfaces are encountered for this shape and/or orientation. Both the total drag and its pressure component bear a positive dependence on the Richardson number and Bingham number and an inverse dependence on the both Reynolds number and Prandtl number. Similarly, the average Nusselt number is determined by a complex interplay between the viscous, yield stress and buoyancy effects, albeit for fixed values of the Bingham number, it shows a positive dependence on the Reynolds number and Prandtl number. Finally, predictive correlations are presented for the average Nusselt number thereby enabling its a priori estimation in a new application. (C) 2015 Elsevier Ltd. All rights reserved.