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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 α and m the exponent of the free stream flow. It is shown that for α>0 the solution approaches the free convection limit, and for α<0, there is a range of α, α s <α<0, over which dual solutions exist. The nature of the bifurcation at α=α s and how the lower branch of solutions behaves as α0 - are also considered. It is established that the solution becomes singular as m1/5 and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely when α is of O(1) and when α 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 α and m to be deduced.

MSC:
76R05Forced convection (fluid mechanics)
76R10Free convection (fluid mechanics)
35Q99PDE of mathematical physics and other areas
76M99Basic methods in fluid mechanics
References:
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