Transport enhancement in the laminar rotating disk boundary layer

Abstract

Enhanced momentum and heat transport in a three-dimensional rotating disk boundary layer due to the consideration of a wavy disk surface is an already known fact in the literature. Such a transport enhancement is primarily associated with two fundamental attributes of the wavy disk: the increased surface area and the enhanced convection due to the surface undulations. However, there exists no further information about their individual role, mutual interaction, and individual share in enhancing the convective transport in the rotating disk boundary layer. This study aims to investigate these facts in detail by considering radially heterogeneous different wavy configurations on the disk surface. It is revealed that the said attributes contribute non-trivially to enhance the transport phenomena. Their impactful role is identified due to the strengths of circumferential and crossflow velocity components, the magnitude of flow swirl angle, and hence due to the coefficients of skin friction and their inter relationship. In this regard, a fundamental benchmark regarding the relative strength of the two coefficients of skin friction is identified from the flat disk case. Decisive observations regarding the impact of surface undulations and the increased surface area of the wavy disk on the enhanced convective transport are made with the aid of this benchmark. It is observed that the enhanced transport phenomena, especially the heat transfer, mainly depend upon the further dominance of the circumferential velocity component. In the situations of increased dominance of rotational flow Kw>Kf, the increased convection and surface area collectively contribute to enhance the thermal transport while in a reverse situation Kw<Kf the convection contributes adversely by even reducing the impact of the increased surface area. In the neutral situation where the dominance of rotational velocity is neither increased nor decreased (i.e., Kw≈Kf), any increase in the transport phenomena is wholly due to the increased surface area. Therefore, the presence of surface undulations or increase in surface area is not the only criterion for an optimum rise in the transport phenomena, rather the impact of surface undulations on the velocity profiles is important which is manipulated due to their positioning on the disk surface. It is observed that the presence of surface undulations in the central and intermediate regions on the disk surface causes to increase the gradients of the crossflow velocity while their presence in the near rim location causes to enhance the gradients of the circumferential velocity. Thus, the configurations that have higher undulations in the near rim region outperform the other configurations.