Theoretical analysis of radiation effects in laminar flow over a von-Kármán body of revolution

Abstract

An analysis presents the impact of thermal radiation on the laminar boundary layer established due to the motion of a von-Kármán surface. The reason for choosing such a shape is its appearance in many aeronautical vehicles, especially the F-16 fighter jet nose cone. However, the transverse curvature effects are also observable in many other shapes of bodies of revolution. But considering such a practical body of revolution provides a chance to quantify the transport phenomena happening on sophisticated aerospace vehicles. As a result, a correct understanding of the momentum and the thermal process in actual situations can be achieved. Power-law form of wall temperature is assumed to cover a variety of non-isothermal wall conditions. The typical body contour of a von-Kármán surface does not allow the scaling symmetry in the longitudinal direction; thus making the flow of non-similar in nature. An efficient numerical scheme (Keller–Box) with the second order accuracy is used for the solution purposes. The results are found to be satisfactory regarding the previous published work for moving cylinder cases. This ensures the validity of the tabulated data for the von-Kármán surface case. Through numerous tables and graphs, the impacts of thermal radiation parameter, wall temperature exponent, and transverse curvature parameter have been highlighted and thoroughly analyzed. Once the radiation parameter is increased, it is noticed that the rate of heat transfer increases and the thermal thickness of the boundary layer grows, whereas the reverse behavior is seen when the wall temperature exponent is increased. Furthermore, it has been found that increasing the surface transverse curvature increases the thermal thickness of the boundary layer and the rate of heat transfer. To the considered body shape, the reported data are expected to serve as a good source for the development of approximate methods concerning complex flow geometries involving transverse curvature effects.