Further Analyses of Laminar Flow Heat Transfer in Circular Sector Ducts

Abstract

Heat transfer in circular sector ducts is often encountered in multipassage tubes. Certain flow characteristics of circular sector ducts for apex angles up to {pi} have been determined as documented by Shah and London (1978). Recently, Lei and Trupp (1989) have more completely analyzed the flow characteristics of fully developed laminar flow for apex angles up to 2{pi}, including the location of the maximum velocity. Heat transfer results of fully developed laminar flow in circular sector ducts are also available for certain boundary conditions. Trupp and Lau (1984) numerically determined the average Nusselt number (Nu{sub T}) for isothermal walls. Eckert et al. (1958) initially derived an analytical expression for the temperature profile for the case of H1. Sparrow and Haji-angles up to {pi}. However, the above work required numerical integration (or equivalent) to obtain a value for Nu{sub H1}. Regarding the H1{sub ad} boundary condition, Date (1974) numerically obtained a limiting value of Nu{sub H1}{sub ad} for the semicircular duct from the prediction of circular tubes containing a twisted tape (straight and nonconducting tape). Hong and Bergles (1976) also reported an asymptotic value of Nu{sub H1}{sub ad} for the semicircular duct from their entrance region solution. Otherwise it appears thatmore » there are no published analytical results of Nu{sub H1}{sub ad} for circular sector ducts. The purpose of this technical note is to communicate these results. In addition, a novel series expression for Nu{sub H1} is presented together with results for apex angles up to 2{pi}.« less