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Sustainability 2018, 10, 191 9 of 32 temperature, load requirements, and other time-dependent conditions result in a variable collector outlet temperature. Many studies on the heating and cooling of packed beds have been published. The first analytical study was by Schumann [34], and the basic assumptions leading to this model are a one-dimensional plug flow, no axial conduction or dispersion, constant properties, no mass transfer, no heat loss to the environment, and no temperature gradients within the solid particles. The differential equations for the fluid and bed temperatures (tf, tb) are as follows: ρfcp,fε∂tf =−mfcp,f∂tf+kv(tb−tf) (5) ∂τ A∂x ρbcp,b(1−ε)∂tb =kv(tf−tb) (6) ∂τ where ρf is the fluid density; cp,f is the specific heat of fluid; ε is the bed void fraction; mf is the fluid mass; A is the bed cross-sectional area; kv is the volumetric (per unit bed volume) heat transfer coefficient between the bed and the fluid; τ is the time. For an air-based system, the first term on the left-hand side of Equation (5) can be neglected and the equations can be written as follows [35]: and the dimensionless time is ∂tf = NTU(tb − tf) (7) ∂(x/L) ∂tb = NTU(tf − tb) (8) ∂Θ NTU = kvAL (9) mf cp,f Θ = τmfcp,f (10) ρbcp,b(1 − ε)AL where A is the bed cross-sectional area; L is the bed length; NTU is the effectiveness. Analytical solutions to these equations exist for a step change in inlet conditions and for cyclic operation. For the long-term study of solar energy systems, these analytical solutions are not useful, and numerical techniques such as the finite-difference method must be employed. Nems et al. [36] present the results of a study into a packed-bed filled with ceramic bricks. The designed storage installation is supposed to become part of a heating system installed in a single-family house and eventually to be integrated with a concentrated solar collector adapted to climate conditions in Poland. The system’s working medium is air. The investigated temperature ranges and air volume flow rates in the ceramic bed were dictated by the planned integration with a solar air heater. The analysis of the obtained characteristics allowed for the conclusion that the process of heat storage in ceramic brick has high efficiency, which, during the experiment, was in the range of 72–93% for an airflow rate of 0.0050 m3/s and 74–96% for an airflow rate of 0.0068 m3/s. The choice of ceramic bricks as the filling material was dictated by several reasons. Structural stability can be provided more easily to a large bed filled with bricks than to a bed filled with, e.g., crushed stone or pebbles. Brick is also an easily available material and has good thermal properties. Additionally, brick is resistant to high temperatures and tolerates a high number of charge/discharge cycles. Brick does not emit any harmful gases in high temperatures, which is important, as the storage unit is to be located inside a residential house. As demonstrated in [36], a system in which heat is stored in a sensible heat storage material, such as ceramic brick, should be provided with a means to control airflow rate in order to maximize the effectiveness of heat storage process, if the heat comes from a source of variable intensity, such as a concentrated solar air collector.PDF Image | Comprehensive Review of Thermal Energy Storage
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