SIMULTANEOUSLY DEVELOPING LAMINAR-FLOW AND HEAT-TRANSFER IN THE ENTRANCE REGION OF A CIRCULAR TUBE WITH CONSTANT WALL TEMPERATURE

The developing flow and heat transfer in the entry region of a heated circular tube is analyzed for the case of constant wall temperature. A n integral or boundary-layer solution is presented which has a number of advantages over earlier Karman-Pohlhausen integral analyses. Thus, in the present analysis, the velocity and temperature distributions, t he local and mean drag coefficients, and the local and mean Nusselt nu mbers approach their fully-developed values asymptotically. The new an alysis is based on the hydrodynamic inlet-filled region concept origin ally proposed by Ishizawa (1966) and later adopted by Mohanty and Asth ana (1978) to flow through a circular tube. This concept is extended t o the combined entry-length problem by introducing a thermal transitio n region, herein called the thermally-filled region, between the therm al inlet boundary-layer region and the thermally fully-developed regio n. A thermal shape factor is also introduced which ensures smooth tran sition of all pertinent thermal quantities from the entrance region to the fully-developed region. Results for the Variation of the local an d mean Nusselt numbers with axial distance along the tube for Pr = 0.1 , 0.5, 0.7, 1, 5, and 10 are presented. These results agree well with the numerical solutions of Hornbeck (1965), Manohar (1969), and Hwang and Sheu (1974) and also with the correlations of Churchill and Ozoe ( 1973).