On the fluid flow and heat transfer between a cone and a disk both stationary or rotating

The present paper investigates the role that the radial component of heat conduction plays in a cone-plate viscometer. The cone and the disk may be taken as stationary or in action; both co-rotating or counter-rotating. Hydrodynamic and thermal fields are resolved by means of computationally simulating the resulting systems of equations. Upon working out the well-documented velocity field in the gap region from the similarity governing equations, the rates of heat transfer at both surfaces are calculated from an amended energy equation by further adding radial diffusive terms, which were missing in the previous data published in the literature. It is shown that addition of such physical streamwise heat conduction terms into the energy equation much influences the well-known results of heat transfer rates, particularly when the conical gap section is not small. The missing heat transfer rates pertaining to the cone wall are also presented here. In particular, it is demonstrated that the best cooling of cone-disk apparatus can be achieved for a rotating disk with a stationary cone, provided that the wall temperatures are kept as uniformly constant. The critical power index of passage from cooling to heating is determined to be 1.54492.