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van Gorder, Robert A.; Vajravelu, K.

Unsteady boundary layers: convective heat transfer over a vertical flat plate. (English) Zbl 1181.76122

ANZIAM J. 50, No. 4, 541-549 (2009).
Summary: We extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

MSC:

76R10 Free convection
76D10 Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

unsteady boundary layers; coupled nonlinear ordinary differential equations; similarity solution; analytical solution; numerical solution
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References:

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