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Flow past a suddenly heated vertical plate. (English) Zbl 0597.76087

Boundary layer analysis is performed in this paper for the free convection flow of a viscous incompressible fluid along a vertical semi- infinite flat plate. By assuming that the wall temperature varies as a power of the distance from the leading edge of the plate, i.e. \(T_ w\sim A\) \(x^{\lambda}\) where A is a positive constant and \(\lambda\) a constant, a class of similarity solutions of the governing equations is presented.
The resulting ordinary differential equations which contain the parameter \(\lambda\) are discussed in a detail manner by complementing the previous known special cases with new analytical and numerical solutions. On the other hand, the approach to the steady-state solution is considered by investigating the temporal development of the flow when the temperature of the plate is suddenly increased from that of the surroundings. Numerical solutions are given which match the large- and small-time solutions. The local rates of heat transfer are tabulated for the Prandtl number equal to one and for a wide range of \(\lambda\). Such tabulations serve as a reference against which other approximate solutions can be compared in the future. Various figures complete the paper.
The paper is very well written, concise and readable; it is a pleasure to read and study it. There is a great deal of ”food for thought” in this elegant paper. Surely, the high quality and importance of this work appeal to anyone engaged in the field of convective heat transfer. The reviewer strongly recommends it as a required study.

MSC:

76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
76M99 Basic methods in fluid mechanics
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