SIMULTANEOUS DEVELOPMENT OF VELOCITY AND TEMPERATURE PROFILES IN THE ENTRANCE REGION OF A PARALLEL PLATE CHANNEL: LAMINAR FLOW WITH UNIFORM WALL HEAT FLUX

Available boundary layer type solutions to the combined hydrodynamic and thermal entrance region problem are known to exhibit a discontinuity in the gradients of the velocity and temperature distributions in the entrance region. A new solution is presented which alleviates this shortcoming. The new solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Das (1982) to hydrodynamically developing flow in a channel. This concept is extended to the combined entry length problem by dividing the thermal entrance length into two lengthwise regions, a thermal inlet region and a thermally filled region. In the former, the effect of heat transfer between fluid and wall is confined within the thermal boundary layer developing along the wall. At the end of the thermal inlet region, the thermal boundary layers meet at the duct axis but the temperature profile is not yet developed. In the thermally filled region, the heat effects propagate throughout the entire cross section and the temperature profile undergoes adjustment in a fully thermal region to finally attain the fully developed form. A thermal shape factor is also introduced in the thermally filled region which ensures that all thermal quantities attain their fully developed values asymptotically. The new model is used to obtain solutions to the combined entry length problem for laminar flow through a parallel plate channel under the constant wall heat flux boundary condition. The analysis gives considerably better results for the local Nusselt number and thermal entrance length than previously available.