Heat Transfer by High-Frequency Oscillations: A New Hydrodynamic Technique for Achieving Large Effective Thermal Conductivities

Nomenclature A c = cross-sectional area = Qifl-rf) c p = specific heat d h = hydraulic diameter = 4A C /P dp/dx = axial pressure gradient dt b /dx = axial gradient of bulk temperature (r 1 +r 2 ) + 2(r 2 -r 1 ) q = rate of heat input per unit length r = radial coordinate /*! = inner radius of duct r 2 = outer radius of duct r h = hydraulic radius = A c /P R = dimensionless radial coordinate = r/r 2 R l = radius ratio = r l /r 2 R h = dimensionless hydraulic radius = r h /r 2 Re = Reynolds number = pu b d h /p, t = fluid temperature t b = fluid bulk temperature ^-^ t w = wall temperature for the (Hi) case and average wall temperature for the (H2) case (-dp/dx)] U b = dimensionless mean velocity 8 = angular coordinate ti = dynamic viscosity p = density 0 = half opening angle of duct Introduction The continuing interest in compact heat exchangers has created the need for friction factor and Nusselt number data for different passage shapes. It has long been recognized that circular tube results are generally not applicable to noncircular passages even when the hydraulic diameter is used as the characteristic dimension. Hence, design data should be generated for each passage individually, and a good source of such information is Shah and London [1]. One duct geometry for which complete design information does not appear to be available in the open literature is that of annular sector ducts. Such configuration is encountered in multipassage internally finned tubes [2] and many other compact heat exchanger applications. The fluid flow problem for this configuraiton has been solved by Sparrow et al. [3], and more recently by Niida [4], However, to the best of the author's knowledge, the heat transfer results are not available yet. The purpose of this note is to summarize the analysis and results of fluid flow and heat transfer in annular sector ducts