Analytical expression of dynamic cooling load of non-uniform environment considering the thermal mass of convective boundaries

Abstract

Conventionally, the cooling load of an indoor environment is calculated using a lumped model. For non-uniform environment, previous research has revealed how steady-state cooling load is influenced but currently, no theory on the dynamic cooling load of a non-uniform environment has been conducted because of the thermal mass of convective boundaries. To establish the analytical expression of dynamic cooling load of non-uniform environment, the inner surface temperature of convective boundaries is used as an intermediate variable in this study. The relationship between the convective heat gain and the inner surface temperature of convective boundaries, indoor heat sources has been built. After solving the transient heat transfer of building thermal mass by differential method, the inner surface temperature of convective boundaries, as well as the dynamic local cooling load can be obtained. The dynamic cooling loads of different airflow patterns and target zones are compared through case studies at last. The results show that: 1) when the flow field is fixed, there exists linear relationship between convective heat gain and setpoint of the local zone, temperature of other convective boundaries, and indoor heat sources, and three indices such as equivalent heat transfer coefficient , contribution of other convective boundary and contribution of heat source are proposed correspondingly to reflect the effect of each factor; 2) the proposed indices are constant for a specific airflow pattern when the flow field and location of the target zone are fixed, and the equivalent heat transfer coefficient of the external wall is 4.2 and 2.9 W/(m 2 ·K) as an example for the cases of mixing ventilation and displacement ventilation , respectively; 3) the thermal mass of the building envelope has a significant effect on the dynamic convective heat, and the fluctuation of the cooling load could be overestimated through steady-state calculation, as shown in the displacement ventilation case, the peak value of the dynamic cooling load is 76.8% of that obtained through steady-state calculation. • Convective heat of boundary is calculated by the temperature of target zone. • Temperature of other boundary and indoor heat source contribute to the convective heat of a boundary. • Theoretical expression for dynamic cooling load in a non-uniform environment is derived. • Thermal mass has a significant effect on the local cooling load of non-uniform environment. • Peak heat gain of advanced airflow pattern is 76.8% of the mixing ventilation.