Determination of the Local Nusselt Number in the Thermal Entrance Region of Flow Between Two Parallel Plates

This study investigates heat transfer in the thermal entrance region for flow between two parallel plates maintained at different constant surface temperatures. The fluid enters the channel between the parallel plates at a constant temperature. The flow is assumed to be hydrodynamically fully developed but thermally developing, a condition commonly encountered in compact heat transfer engineering applications. An adiabatic surface positioned between the two plates is considered, and separate analyses are carried out for the regions above and below this surface. Initially, velocity profiles for each region are obtained through hydrodynamic analysis, respectively. Using these profiles, the governing energy equations are nondimensionalized and solved employing the method of separation of variables. This approach yields detailed expressions for the temperature distribution, local heat transfer coefficient, and local Nusselt number along the flow direction. Accordingly, following the comprehensive thermal analysis, the local heat transfer coefficients and local Nusselt numbers are determined for the regions above and below the adiabatic surface. This work provides a comprehensive understanding of the interplay between velocity and temperature fields in such systems, which is particularly significant for accurately predicting local and average heat transfer performance. The findings support the design and optimization of thermal systems where precise control of heat transfer rates is essential for operational efficiency and reliability.