A semi-analytic method for buoyancy-induced thermal stratification in hot water tanks during standby periods

Buoyancy-induced thermal stratification is a spontaneous phenomenon arising from standby periods of hot water tanks. Accurate estimation of temperature levels is crucial for energy-efficient operations of hot water tanks and associated water heating systems. However, temperature estimation by numerical schemes requires sophisticated algorithms and considerable computation resources. This study proposes a novel semi-analytic method to address buoyancy-induced thermal stratification conveniently without iterative calculations. An explicit water temperature function to tank height and time is analytically derived from the modified energy balance equation where the heat convection term is disregarded. The convection effect is compensated for by artificial enhancement of heat conduction, which is indicated by a synthetic parameter, amplification factor. A comprehensive numerical study is carried out to investigate static and transient characteristics of buoyant flows and temperature distribution in a hot water tank during standby periods. The findings imply a strong analogy between buoyancy-induced thermal stratification and a bottom-initiated heat conduction process, which reinforces the physical rationale for the semi-analytic method. The experimental verification of the semi-analytic method is conducted against published experiment data, the proposed method shows excellent estimation accuracy with the rooted mean square error of less than 0.42 °C. Furthermore, suitable case-specific amplification factors are determined with numerical simulations, and a ready-for-use correlation equation of the amplification factor is formulated for a wide range of tank volumes and aspect ratios. This novel semi-analytic method substantially reduces computation time compared with numerical solvers, and the simple form of the water temperature function can help in formulating more detailed hot water tank models in energy system studies.