LAUSR

Abstract Laminar free convection in a vertical channel with isothermal walls is a classical heat transfer problem. In general, the channel walls may be at different temperatures, leading to a difference in the rate of heat transfer at the walls. Although numerical and experimental results are often presented in terms of average wall Nusselt numbers, separate correlations for heat transfer at each wall are rarely available. The few existing relations are complex in form due to the extra parameters introduced to facilitate the correlation of results. Moreover, the existing correlations do not reflect the physics of the problem in full. In this work, the three-temperature problem of laminar-free convection of air in a tall vertical channel with isothermal walls is studied in a new theoretical framework, namely the extended Newton formulation. This formulation eliminates the need for an effective temperature difference, hence simplifying the presentation and correlation of the results. The dQdT technique was utilized along with computational fluid dynamics to calculate the average paired Nusselt numbers that characterize the extended Newton formulation of the problem. The dQdT results were then used to derive heat transfer correlations which are both simpler in form and more accurate than the existing correlations. The proposed correlations are applicable to cases of both channel walls hotter or both colder than the ambient air.