# Mixed convection boundary layer similarity solutions: prescribed wall heat flux

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DOI: 10.1007/BF00945309

- Cite this article as:
- Merkin, J.H. & Mahmood, T. Z. angew. Math. Phys. (1989) 40: 51. doi:10.1007/BF00945309

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## Abstract

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*α*→0^{−} are also considered. It is established that the solution becomes singular as*m*→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*α* is of 0(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.