Laminar mixed convection in the entrance region for horizontal semicircular ducts with the flat wall on top is investigated theoretically. The governing momentum and energy equations are solved numerically using a marching technique with the finite control volume approach following the SIMPLER algorithm. Results are obtained for the thermal boundary conditions of uniform heat input axially with uniform wall temperature circumferentially at any cross section ($H1$ boundary condition) with $Pr=0.7$ and a wide range of Grashof numbers. These results include the velocity and temperature distributions at different axial locations, axial distribution of local Nusselt number, and local average wall friction factor. It is found that Nusselt number values are close to the forced convection values near the entrance region and then decrease to a minimum as the distance from the entrance increases and then rise due to the effect of free convection before reaching constant value (fully developed). As the Grashof number increases the Nusselt number and the average wall friction factor increase in both developing and fully developed regions and the location of the onset of the secondary flow moves upstream.

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