# Niall McMahon

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# André Lévêque - His Doctoral Thesis, Page 285

2006

Where Lévêque describes convective heat transfer close to a surface.

On p285, Lévêque writes that neglecting , and substituting the simplified velocity profile ( ) into Eqn. 85, results in Eqn. 95: With the boundary conditions described, it is a fact that Eqn. 95 has a solution of the form: Or, simply: where is some, as yet undefined, function. The only constraint on is that it satisfies the solution to Eqn. 95 and it is a function of and .

Putting this solution for into Eqn. 85 (on p277), you end up with: Rewriting: Lévêque observed that if we set , and we define , then . By defining and in this way, this equation reduces to: This is something we can solve. The important point to note is this: is some function of that satisfies Eqn. 95 - it translates from to . depends on raised to any power , so we are free to define . Lévêque chose some that makes the equation easy to solve. Once in defined, then and a that satisfies Eqn. 95 are automatically defined.

This is how and why Lévêque chose .

The rest of p286 and p287 is pretty straightforward, leading to a solution for and .