Heat transfer in laminar flow on a vertical wall

2 Heat transfer in laminar flow on a vertical wall 

We will now deal with free flow on a vertical, flat wall whose temperature d0 is constant and larger than the temperature in the semi-infinite space. The coordinate origin lies, in accordance with Fig. 3.43, on the lower edge, the coordinate x runs along the wall, with y normal to it. Steady flow will be presumed. All material properties are constant. The density will only be assumed as temperature dependent in the buoyancy term, responsible for the free flow, in the momentum equation, in all other terms it is assumed to be constant. These assumptions from Oberbeck (1879) and Boussinesq (1903), [3.45], [3.46] are also known as the Boussinesq approximation although it would be more correct to speak of the Oberbeck-Boussinesq approximation. It takes into account that the locally variable density is a prerequisite for free flow. The momentum equation (3.294) in 

3 Convective heat and mass transfer. Single phase flow 

As we have presumed small density changes, we have 

This leaves the following system of equations to solve  

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