Heat transfer in laminar flow between parallel plates at small Péclét numbers

Summary

The problem of heat transfer for laminar flow between two infinite parallel plates, y=±l, x≤0, kept at a constant temperature T ₀, and y=±l, x≥0, kept at a different constant temperature T _s is formulated to take into account the effect of heat diffusion on the incident fluid. This has been achieved by obtaining solutions of the energy equation for the regions x≤0 and x≥0 and by imposing continuity conditions on the temperature and its derivative at the junction x=0. It is found that at small Péclét numbers the incident temperature is affected by the diffusion of heat from the right (x>0) to the left (x<0). This effect is negligible for large Péclét numbers (Pe ∼ O(1000)). Further the temperature of the incident fluid at x=0 cannot be taken as constant (=T ₀) if the heat generated by viscous dissipation is taken into consideration. Detailed solutions are given for Pe=1. Mean-mixed temperatures and local Nusselt numbers for x>0 and x<0 are tabulated and shown graphically.