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Mixed convection boundary layer similarity solutions: Prescribed wall heat flux. (English) Zbl 0667.76126
The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameter $$\alpha$$ and m the exponent of the free stream flow. It is shown that for $$\alpha >0$$ the solution approaches the free convection limit, and for $$\alpha <0$$, there is a range of $$\alpha$$, $$\alpha_ s<\alpha <0$$, over which dual solutions exist. The nature of the bifurcation at $$\alpha =\alpha_ s$$ and how the lower branch of solutions behaves as $$\alpha \to 0^-$$ are also considered. It is established that the solution becomes singular as $$m\to 1/5$$ and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely when $$\alpha$$ is of O(1) and when $$\alpha$$ is small. Finally it is shown that for m large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parameters $$\alpha$$ and m to be deduced.

##### MSC:
 76R05 Forced convection 76R10 Free convection 35Q99 Partial differential equations of mathematical physics and other areas of application 76M99 Basic methods in fluid mechanics
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##### References:
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