A natural-convection boundary layer along a vertical complex wavy surface with uniform heat flux has been investigated. The complex surface studied combines two sinusoidal functions, a fundamental wave and its first harmonic. Using a method of transformed coordinates, the boundary-layer equations are mapped into a regular and stationary computational domain. The transformed equations can then be solved straightforwardly by any number of numerical methods designed for regular and stationary geometries. In this paper, an implicit finite-difference method is used. The results were readily obtained on a personal computer. The numerical results demonstrate that the additional harmonic substantially alters the flow field and temperature distribution near the surface. The induced velocity normal to the $y$ axis can substantially thicken the boundary layer, implying that its growth is not due solely to the momentum and thermal diffusion normal to the $y$ axis along a wavy surface.

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