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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. [ABSTRACT FROM AUTHOR]

This paper examines the three-temperature problem of convection at the indoor side of a complex fenestration system (CFS) based on recent theoretical developments, namely the extended Newton formulation and the dQdT technique. CFD solutions were obtained for natural convection at the indoor side of various CFS configurations. The dQdT technique was then implemented numerically to obtain the paired heat transfer coefficients of each configuration. The results were used to assess the approximate relations used in the ASHRAE Window ATachment (ASHWAT) tool. The comparison shows that while there is remarkable agreement between the ASHWAT estimates and dQdT results for roller blinds, discrepancies exist between results for venetian blinds. Furthermore, although use of a delta resistor network to model convection at the indoor side is valid and relatively accurate for roller blinds, the application of this model to CFSs with venetian blinds requires additional levels of approximation. Nevertheless, the heat transfer rates calculated based on the approximate resistor-network model are in close agreement with the CFD results. [ABSTRACT FROM AUTHOR]