The steady, laminar, natural convection flow of a third grade fluid in a vertical circular pipe is investigated when a constant temperature is maintained at the walls of the pipe. The flow is governed by a pair of coupled equations in velocity and temperature fields involving the parameters K, which is the product of the Eckert and Prandtl number, and [...] which is a measure of the third grade fluid parameter. Solutions are obtained (i) by numerical integration of the differential equations governing the flow, and (ii) by seeking a perturbation solution in terms of the parameter K. The results are compared and appropriate conclusions drawn regarding the applicability of the perturbation solution. It is shown that the effect of the third grade fluid parameter is to counteract the influence of the parameter K on the flow.
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This paper investigates the boundary-layer characteristics of a wind turbine blade of small chord length. The three-dimensional form of momentum integral equations is derived and used to predict the boundary-layer growth and limiting streamline angles on the blade surface for both attached and separating flow. The chordwise skin friction coefficient is used to identify boundary layer separation and shear layer reattachment locations. The nature of flow near the axis of rotation is discussed and the physical mechanism associated with 3-D and rotational effects is identified. A semi-empirical correction law for the lift coefficient based on 2-D airfoil data is established. Comparing calculated and measured lift curves of a stall controlled wind turbine, it is shown that the proposed correction law may improve significantly the accuracy of the predictions.
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