Mixed-convection boundary-layer flow over a heated semi-infinite vertical flat plate with uniform surface heat flux, placed in a uniform isothermal upward freestream, has been investigated. Near the leading edge, the effect of natural convection can be treated as a small perturbation term. The effects of natural convection are accumulative and increase downstream. In the second region, downstream of the leading-edge region, natural convection eventually becomes as important as forced convection. The boundary-layer equations have been solved by an adaptive finite-difference marching technique. The numerical solution indicates that the series solution of the leading-edge region is included in that of the second region. This property is shared by many developing flows. However, the series solutions of local similarity or local nonsimilarity are only valid for very small distances from the leading edge. Numerical results for the local skin-friction factor, wall temperature, and local Nusselt number are presented for $Pr=1$ for a wide range of $Grx*∕Rex5∕2$, where $Grx*$ is a local modified Grashof number and $Rex$ is a local Reynolds number. The results indicate that $cfxRex1∕2$ and $NuxRex–1∕2$ increase monotonically with distance from the leading edge, where $cfx$ is the local skin-friction factor and $Nux$ is the local Nusselt number, and approach the free-convection limit at large values of $Grx*∕Rex5∕2$, although the velocity distribution differs from the velocity distribution in a free-convection boundary layer.

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